title list | subreddit list | post_id list | score list | link_flair_text list | is_self list | over_18 list | upvote_ratio list | post_content stringlengths 0 20.9k ⌀ | C1 stringlengths 0 9.86k | C2 stringlengths 0 10k | C3 stringlengths 0 8.74k | C4 stringlengths 0 9.31k | C5 stringlengths 0 9.71k |
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[
"The Pizza Theorem - Vsauce2"
] | [
"math"
] | [
"8p3ul6"
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17
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""
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true
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false
] | [
0.79
] | null | Really not getting his proof without words. | I don't think I understand, isn't this solved by symmetry? | I thought so too, but there's also the case where there isn't a line going straight through the center and so it's asymmetric. | And I always thought that the pizza theorem was that the amount of pizza in a cylindrical shaped pizza of radius [; z ;] and height [; a ;] is [; \pi z z a ;] | Yeah, I have no ides why he labelled the "pre-cut" slices, it makes the entire thing far too confusing. Then he labels the final slices with the upper/lowercase letters, but doesn't pair them by the original 8 slices (like the tool he shows at the end, each ~octant only has either upper or lowercase letters, actually s... |
[
"Getting back into math"
] | [
"math"
] | [
"8p3i2m"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | I used to enjoy math a lot and liked going through hours of frustration to finally solve a problem. I've stopped doing math for a number of reasons and I want to get back into it. I haven't properly done a math problem for what seems like 2 years now. I've been passing my math classes by BS'ing tests instead of learnin... | Euclid, the elements. It's 2300 years old and beautiful in its simplicity and clarity. | Archimedes' work on conics You mean Apollonius? That one is a bit of a tough read; it will take quite a dedicated summer. | Perhaps he could supplement it with Bryne's slughtly mire modern coloured illustration of it. In similar vein he could look for other antique work (e.g Archimedes' work on conics). | Yes how could I make such a basic mistake. | Well then I suppose you could attempt some math olympiad questions taking your time on each one. |
[
"Questions about prime counting function."
] | [
"math"
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"8p3fyq"
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5
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""
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true
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false
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0.74
] | [deleted] | Did you look? " New bounds on the prime-counting function " is relevant, and oft-cited. The paper by Dusart is useful. Google "bounds on value of pi(x)" for more references. | You can find an analytic function that exactly equals pi(x) on all natural number inputs, and is therefore “better” than li(x) for most reasonable notions of being a good approximation even with your added restriction (though its theoretical and computational significance is not so great). | Ask any professional, in almost all cases "efficient" is synonymous with "polynomial time complexity". No need to be overly pedantic, it was easily understood by everyone what the OP meant. | There are definitely functions that are easier than others to compute. (In terms of computational complexity) So a good bound would be a function that is easier to compute | A precise way to formulate the question might be to ask for the differentiable (or smooth or continuous or...) function that approximates pi(x) best. This is a very classical question of great interest and the answer is known: the logarithmic integral function or li(x) approimates pi(x) best, is well behaved and moreov... |
[
"How do I create a sinusoidal function along a line?"
] | [
"math"
] | [
"8p2w3m"
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0
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""
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true
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false
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0.42
] | I was reading about the business cycle here: The sinusoidal function is along the line. Any resources on how to do graph/find this and how to type the sinusoidal function disregarding the line OR just what type of function it's called so I can learn more about it. Tried googling but to no avail. Would definitely apprec... | Have you tried f(x)=sin(x)+x or something of the sort? | It's not any specific type of function as far I know (you could look at functions of the form f(x)=Asin(Bx+C) +D but I'm not sure thats what you want). My thought process was that the business cycle looks like a sine function but 'follows a line' like you said, so as my input grows (time on business cycle graph) the si... | Just as a heads up, business cycles aren’t really sinusoidal, and that picture is a bit misleading. Business cycles are actually rather difficult to identify from the data. I’d suggest downloading GDP data and looking at it. There is a rather technical literature on business cycle extraction (known as trend-cycle decom... | There is only one Fourier Series for a function, think you mean a truncated Fourier Series. Also, as you increase the amount of terms in the Fourier Series, its gonna come closer to the function f(x)=x, the oscillations of the business cycle will diminish which is not what you want in this case. | There is only one Fourier Series for a function, think you mean a truncated Fourier Series. Also, as you increase the amount of terms in the Fourier Series, its gonna come closer to the function f(x)=x, the oscillations of the business cycle will diminish which is not what you want in this case. |
[
"What Are You Working On?"
] | [
"math"
] | [
"8p1uxt"
] | [
5
] | [
""
] | [
true
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false
] | [
0.7
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on over the week/weekend. This can be anything from math-related arts and crafts, what you've been learning in class, books/papers you're reading, to preparing for a conference. All types and levels of ... | I'm busy calculating fundamental groups of sheaf toposes and doing lots of things with site theory and the etale/fppf sites on scheme categories and formal scheme categories. | Having fun with a graph with 4 axes instead of two. The extra two being xi and yi, for imaginary values. Oh and the fun doesn't end: the space between x and xi acts as xC, for complex number coordinates, same for the space between y and yi, yC | Waiting for collage acceptance letters I already have one waiting on the others :) and catching up on old /r/math discussions and inside jokes | I have to write an internal assesment for My IB math SL class, which is supposed to be an investigation into an area of mathematics to demonstrate skills and application. I have enjoyed the math so far, especially calculus and trigonometry but I am completely lost as to what I can write about for this assessment. | This summer I'm taking a class called advanced mathematics for engineers. This week we've been doing Fourier series, and yesterday we did the double Fourier series (god help me!). |
[
"Optimisation problem I have encountered. Does this problem have a name and common solution?"
] | [
"math"
] | [
"8p0z6c"
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21
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""
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true
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false
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0.81
] | Hello, in my work I have encountered a problem where I need to decide to which service point should a customer come depending on their place of residence (simply find a closest one to where they are). However, each service point can handle only a specific fraction of customers (those fractions sum up to the total numbe... | This is called the Hitchcock transportation problem. Basically you need to compute a min-cost flow on a bipartite graph between customers and service centers. | I think this would simply be the classical assignment problem . To make this formulation work you should, instead of thinking about each service station as having a given capacity of n, I would create n “agents” for that service station and keep track of this backend. The formulation will then ensure that each customer... | Thanks, that's jus what I needed. | With capacities this is actually the generalized assignment problem, which is NP-Hard. With only one agent this is knapsack. There is a greedy solution that achieves a (1+c)-approximation given a c-approximation for knapsack. | Must be less, but since these numbers in all service points add up to the number of custumers it ends up that each number is specific. Actually, I think that solution in either case works for me. |
[
"Putnam Competition"
] | [
"math"
] | [
"8p0ssw"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.57
] | null | One (possible) area that an engineer could have a disadvantage in is writing mathematics clearly. Take some time to practice organizing your thoughts and writing clear, concise proofs. Also be sure to be comfortable with standard proof techniques (induction, contrapositive, etc). | It occasionally includes some basic group theory, but not enough to put someone who doesn't know it at a noticeable disadvantage. The bigger issue is if you haven't taken any proof based math courses. | Usually A1,A2,B1,B2 (at least) can be solved with basic (first-year or maybe even less) math. Seeing as completing four questions is by itself a very good result, and will be better than most math majors do anyway, there's no reason why an engineer shouldn't give it a go. | No reason why an engineering student couldn’t participate. I’m pretty sure many do at my school. And no disadvantage if they have the skills and prepare just as much as a math major. | I suspect that the biggest factor in performance on the Putnam is performance in high school math contests. It is quite common for people who did well in high school math contests to go on to major in some subject that is not math, but still participate in the Putnam. |
[
"Can I add immaginary numbers to a cartesian plane (the x and y one) by adding two separated xi and yi axes, rotated 45° from the originals?"
] | [
"math"
] | [
"8p0p1n"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.38
] | null | Nope. You can certainly have a space with two complex numbers, but it'd take 4 spacial dimensions to depict, not 2. | My point is those two procedures give you the same point. | The thing, you run into a few problems: what is the point which is normally called (1,1) in this system? On the one hand, it's still (1,1); on the other hand, its also (i*sqrt2,0) [assuming your imaginary "axes" are scaled the same way]. This is a real problem - if representation isn't unique, I don't think "coordinate... | Obviously they are different numbers but if you tried to draw them on a plane with axes like you described (the x-imaginary axis rotated 45 degrees anticlockwise to the x axis) you would find that they end up in the same point. | You are mistaken on the value of sqrt(2), put it into a calculator and you should see that it is 1.4142... which is precisely the distance between (0,0) and (1,1). |
[
"Everything About Mathematical Education"
] | [
"math"
] | [
"8p2ri0"
] | [
232
] | [
""
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true
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false
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0.94
] | Today's topic is . This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week. Experts in the topic are especially encouraged to contribute and participate in these threads. These threa... | A good piece of advice I received "Your job as an instructor is to convince the students that understand something". Remember that /r/matheducation exists! I recently summarized my thoughts/experiences over there in this post - which I also posted on my website as a blog-post . I'll copy it here (but see the original p... | I know this might be irrelevant but I still recommended a mathematician's lament to those who haven't read it already. | A blind spot in mathematics education is . Definitions, theorem, proofs, notations, vocabulary, figures of speech, or even whole topics, that are perpetuated in math class by tradition, and that should be seriously questioned in view of their value or detriment to understanding. Let's collect some here. My suggestions:... | Unpopular opinion: the curriculum is fine. The problem we've got is an embarrassingly low bar for "passing" a given course. In New York, a 27/86 scaled up to a passing score of 65 on the Algebra 1 exam this past January. Of course, if they pass that test no one is going to hold them back from the next course, but the s... | I'd argue that there are plenty of open problems. |
[
"Help with a logarithmic equation!"
] | [
"math"
] | [
"8ozr0i"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.4
] | null | Logging on | Raise both sides to the power of 3: 3 =3 Remember that a =b, by the definition of logarithms: 10x=243 x=24.3 Voila! | Thanks! It concerns me that I didn’t know you could raise it like that... is this called something? | No problem! I'm not sure it has a specific name... Raising to a power, or exponentiating maybe? | My apologies |
[
"Is it worth doing the problems from math competitions if you're not going to be a contestant?"
] | [
"math"
] | [
"8p0hjq"
] | [
120
] | [
""
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true
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false
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0.88
] | I'm interested in questions in these competitions and have a few more questions. Are there websites or subreddits discussing math competitions? What are the branches of mathematics usually covered? Are there websites providing both the problem sets and solutions? Which competitions have the most interesting problems? A... | There is an amazing site http://artofproblemsolving.com where you can find math problems from contests all over the world. Each problem has thread for discussion and solutions. | Contest problems have a known, 'neat' solution, whereas research problems generally don't, which is why some people think they can sort of stunt your intellectual taste or growth. I think I could see that happening at really extreme levels of competition involvement, but... I personally think they're a transition from ... | Worth doing in what sense? Toward what goal? | Richard Rusczyk, the founder of Art of Problem Solving, goes over solutions for some of the contests on their Youtube channel . Definitely worth a watch! | Compared to watching youtube, yes. Compared to doing exercises from books that were specifically designed to teach you a concept, no. |
[
"Teaching/advice - As a first year, which classes would you teach??"
] | [
"math"
] | [
"8oy1hy"
] | [
1
] | [
""
] | [
true
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false
] | [
0.67
] | I’ve also posted in but I thought I might get some decent input here as well. Hello, I just received my teaching certificate in 4-8 math, however I may be taking a high school position for my first year. I could either teach algebra 1&2 (I really enjoyed algebra as a student) as well as one section of AP calc (yikes! I... | You might want to ask /r/matheducation . | Keep in mind you will probably have more motivated/mature students in the AP class. | First. Think of what you will do in your future and choose a theme based on it. Second. Take the theme in which you are the most interested and the one where you get your best results (grades etc.) | Thanks for the link! | Get good at calculus. Teaching AP Calculus means fewer students of low intelligence and motivation. |
[
"TOP SECRET"
] | [
"math"
] | [
"8oy71f"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.5
] | null | Uh, you alright bud? | OP's account is 12 years old. What's up with them? | Actually one image is missing :-) | Ah I see, it’s 51 u | Fixed. |
[
"Why isn't there a (standard) name for non-integer rational numbers?"
] | [
"math"
] | [
"8ox0il"
] | [
3
] | [
""
] | [
true
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false
] | [
0.64
] | One thing that always bothered me in college level math books is that when categorizing the different types of numbers, non-integer rationals don't seem important enough to warrant their own name. The natural candidate for the name would be "fraction", but the problem with that word is that it's a rather informal name ... | I don't think I've ever seen the set of non-integer rationals be meaningful. The properties that non-integer rationals share they also share with integers. My guess is that its complement is pretty meaningless, meaning classifying something as a "non-integer rational" or a non-"non-integer rational" is a weird thing to... | "non-integral" is a good name. Parallel to "irrational" and "non-negative". | We could call negative numbers "unnatural integers". | and change irrational numbers to cthulu numbers | I want a name for 0<x<1. "Multiple by a fraction.. err a fraction that's less than one...err but bigger than zero" |
[
"Lie Group Cosmology by Garrett Lisi"
] | [
"math"
] | [
"8ovyl5"
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12
] | [
""
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true
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false
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0.77
] | null | Garrett Lisi is a complete hack and his knowledge of not only the general subject of Lie Groups but specifically of the very group he proposed as a GUT group is atrocious at best. Which is one of the reasons why his proposal can be discarded immediately: the math is wrong. | Distler wrote a paper showing that well -known representation theory implies that the representation Lisi's model would require does not exist. Distler also had some blog posts on it and some discussion pointing out problems in the nCafe under "e8 quillen superconnections" | Hey, if I got any math wrong in my talk, please let me know. | A very detailed, if a bit rude, deconstruction of Lisi's madness is Luboš Motl's post on Lisi's original E_8 paper from way back in 2007. | Listening to that was relaxing and nice, and meaningful too. |
[
"For those who have read Jurassic Park..."
] | [
"math"
] | [
"8ovzkm"
] | [
20
] | [
""
] | [
true
] | [
false
] | [
0.8
] | The mathematician Ian Malcolm is a central figure in this book, and he says a lot of things relating to math and specifically chaos theory. I’m wondering how much he got right and how much he got wrong with his claims and explanations. Here is a quote from him; “You hit a pool ball, and it starts to carom off the sides... | Chaotician, chaotician, actually. | I'll stay away from talking about whether his descriptions of chaos theory are accurate. I don't really think they are, but remember that Malcom throughout the book is trying to explain some difficult math to a bunch of people who know nothing about math and constantly ask for Malcom to water down his explanation. So I... | Even disregarding imperfections in the table, etc, it is surprisingly difficult to work out what will happen with a billiards shot on a strangely shaped table. This is actually an active area of research with many open questions. Of course, an ideal table which is a perfect rectangle we more or less understand but I'... | The first quote about chaos theory is actually a surprisingly fair ELI5 of chaotic systems. | Imperfections aside, what do you mean by strangely shaped? Sides are not a rectangle, or the surface of the table is a manifold rather than a flat surface. Either will drastically change the dynamics. To what area of research are you referring? Dynamical billiards is an area of research within Hamiltonian dynamical sys... |
[
"What is mapping an old range of numbers to a new range of numbers called? Is there a word for it? Is there an online converter that does this?"
] | [
"math"
] | [
"8ouqjb"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.31
] | null | This would be perfect for the Simple Questions thread. | I'll admit that at first I thought the OC was being a bit of a jerk, but now I realize they do have a point and were being perfectly reasonable. You may be able to field your question there with a much greater reception and chance of a useful response. Info in the sidebar. | "Rescaling", or if you want a fancy term, "affine transformation". I'm not aware of an online tool, but it's a very straightforward process. For example, suppose you want to map [10,20] onto [300,400]. You need to make your interval ten times as long, and then shift it upward to start at 300. The first step gives you [... | Thanks so much! Yeah, haha, sorry, didn't mean to sound jerky. | Is it? Because I can't find the answer anywhere. |
[
"What is the probability of rolling 9 on 2d6 with one re-roll?"
] | [
"math"
] | [
"8ourmz"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.14
] | null | As other comments have already described, there's a 4/36 chance of getting a 9 before the re-roll. Then you get to reroll one die. If both of your dice are 1s and 2s, you're out of luck; no reroll will save you. If you have at least one die which is a 3 or higher, then there's a 1/6 chance of getting the number you nee... | It looks like you're assuming you to re-roll one of the dice which is doubtfully what they're asking. | 2/3 *1/6 = 1/9 (must roll >2 so 2/3 chance on first dice, then 1/6 of getting the matching pairing on the second) | oh right i interpreted it as "roll 2 dice add the sum" but it's actually a bit more than that okay | We have 6 choices for the first d6 and 6 choices for the second... To calculate the total number of rolls, we multiply these together, to get 36 total possibilities. There are 4 ways to roll a 9. You can get 3-6, 6-3, 4-5, or 5-4. We have 4 out of 36 possible ways to roll a 9. This is equal to 1/9, or about an 11% chan... |
[
"Do you have to be good at programming for higher level mathematics?"
] | [
"math"
] | [
"8ougj5"
] | [
2
] | [
""
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true
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false
] | [
0.56
] | Title. I’m in high school right now but my current endgame goal is to get a PhD in Mathematics. How necessary or beneficial will it be to understand programming down the line? | Based on some of the code I've seen written by mathematicians, I'd say it's quite the opposite. Required to be at programming to do higher mathematics. (just kidding. Sorta.) | They always used acronyms for variables without even commenting what it meant Sounds just like math papers! :-) | Depends very highly on field. Some fields you might use it, some you might not. However, it's a great skill to have in case you change your mind in the future, and even if you don't it's often nice to be able to write a little script to do something you want to do, or verify something or another. Overall I'd recommend ... | If anything 90% is an underestimate since a fairly large fraction of mathematicians in academia also do research that depends in part on coding. | Necessary - probably not. Useful - maybe. That said, programming uses some similar skills to mathematics so it might be a good idea to learn the basics anyway. |
[
"A conjecture on when a continuous function can be continuously extended to its completion."
] | [
"math"
] | [
"8ouig8"
] | [
8
] | [
""
] | [
true
] | [
false
] | [
0.9
] | So, from a discussion I had on this sub, I ended up with a certain conjecture that I’m not quite sure how to prove or disprove. The statement is this: Let Y be a complete metric space, and X a metric space. Then a continuous function f: X -> Y has a unique continuous extension to its completion C if and only if at ever... | If local compactness seems too strong, see if just requiring the space be Polish helps. This feels to me like something that should be false in complete generality but true in more than just lcsc spaces. | Sorry, noticed that myself and deleted, thinking noone had seen but you were too fast :) And yes, I was thinking about Lipschitz...ianity | Sorry, noticed that myself and deleted, thinking noone had seen but you were too fast :) And yes, I was thinking about Lipschitz...ianity | Sorry, noticed that myself and deleted, thinking noone had seen but you were too fast :) And yes, I was thinking about Lipschitz...ianity | Sorry, noticed that myself and deleted, thinking noone had seen but you were too fast :) And yes, I was thinking about Lipschitz...ianity |
[
"Formula for the equation of a tangent?"
] | [
"math"
] | [
"8ouixk"
] | [
2
] | [
""
] | [
true
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false
] | [
1
] | null | y = f'(a)(x-a) + f(a) | Like yours but simpler | Oh yes Oopsie EDITED | Oh yes Oopsie EDITED | https://en.wikipedia.org/wiki/Linear_approximation |
[
"The values given from a square root shortcut (black) versus real square root (red). Shortcut from TecMath YouTube channel."
] | [
"math"
] | [
"8ova5l"
] | [
440
] | [
"Image Post"
] | [
true
] | [
false
] | [
0.9
] | null | For some real black magic, take a look at the Fast Inverse Square Root . | For those wondering how this works, the tl;dr is that the typically binary representation of floating point numbers is a piecewise-linear approximation of a scaled and shifted logarithm. The algorithm takes advantage of the fact that log(1/sqrt(x)) = -(1/2)log(x). The -(i >> 1) handles multiplication by -1/2, and the m... | All the video is doing is computing the tangent line approximation at each perfect square. In other words, the value f(x) = x is approximately equal to x ~ a + (x - a)/(2a ) if x is not too far away from a. If is a squared integer and x is an integer, then the above expression is a rational number. This is a standard a... | Quake devs are mad lads | You know you can "share" links directly from Desmos instead of taking a screenshot, right? Also, this post would be more useful with a bit more context/explanation about what you are trying to show. |
[
"The Reimann Hypothesis"
] | [
"math"
] | [
"8outns"
] | [
11
] | [
""
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true
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false
] | [
0.64
] | I've recently picked up the music of the primes by Marcus du Sautoy again and I'm midway through, I was wondering if anyone knew of many developments into the Reimann Hypothesis that have been made recently. | Riemann != "Reimann" | That's it, I'm opening up a brewery called the Rye-man hypothesis. | That mispelling does explain why a friend of mine had a student call it a "Rayman sum" during an oral exam. | My personal impression is that we're getting quite close to some kind of resolution to the Riemann Hypothesis. Really? I've gotten almost the exact opposite impression: all these new tools and machinery are telling us lots of things but none of them seem to quite be able to say anything about RH. It's sort of similar ... | Heck, i've heard all combinations of the following: Ree-man , Ray-man , Rye-man Leeb-nitz , Lye-ber-nitz Oy-ler, Oil-er , You-ler , e-you-ler, e-uller Lee-algebra Lye-Algebra Co-she, coach-e, couch-e |
[
"Proof by Contradiction"
] | [
"math"
] | [
"8otr1w"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.54
] | Hi, I just started taking linear algebra and we got into proofs by contradiction. I’m having a hard time understanding how a proof by contradiction actually works. To me if this format of a proof were valid why couldn’t I just prove that the moon was made of cheese by just disproving it was made of bread. I’m not sur... | Your two statements are not negations. With negations there are only two possibilities, either the moon is made of bread, or the moon is not made of bread. You can't have both of those be true and you can't have neither of those be true. So if you disprove that the moon is made of bread, you can prove that the moon is ... | Hit the "reply" link below a comment, instead of at the top of the thread. Then the reply will be threaded and the person you are replying to will get a notification. Otherwise it looks like you're talking to yourself, and no one will know to followup to your question. | The logic of a proof by contradiction is as follows. Let's say that we want to prove that some statement P is true. Well, either P is true or P is false. So, we start to think about what might happen if P were false. We start going down the rabbit hole- if P is false, what else follows? If eventually we can conclude so... | This is true, but people sometimes use the term "proof by contradiction" when LEM is not necessary. Let's say we want to prove P. Proof by contradiction goes like this: assuming ¬P, we can derive a contradiction. In other words, ¬P → ⊥. But in intuitionistic logic, ¬X is as X → ⊥, so proof by contradiction is the same ... | To me if this format of a proof were valid why couldn’t I just prove that the moon was made of cheese by just disproving it was made of bread. If you disprove that the moon is made of bread, you have only proven that it is not made of bread. “The moon is made of cheese” is not the opposite of “the moon is made of brea... |
[
"Why did you get into math?"
] | [
"math"
] | [
"8ostqb"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.57
] | Why did you choose pure/applied/computational math? Has your perception of the field changed for the better or worse since then? | I was bad at English | I didn't like math until I took calculus in my freshman year of college. Most high school for me was just bland and we weren't really taught what was happening "under the hood", it was a lot of plug and chug so, it left a bad taste in my mouth for a few years. After calc. I found my self wanting to learn more and I swi... | this is the only true answer here | just speak in binary nigga, problem solved | Can’t rite good |
[
"Recommended reading on group theory"
] | [
"math"
] | [
"8osh8y"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.82
] | [deleted] | What applications would group theory have to philosophy? | I guess we might disagree on what "active" means, but I don't think it's accurate to say that people aren't actively studying groups. I know people who are working on e.g. Artin groups, RAAGs, cyclicly-presented groups, Thompson's groups, various decision and search problems in groups, growth of groups, and triangle gr... | I have seen group theory applied to problems of epistemology and ontology. For example, if you want to reconcile the Sellarsian dichotomy between the scientific image (itty bitty particles) and the manifest image (chairs and tables), you might appeal to the notion of groups and homomorphisms as a model for ideas like ... | It probably comes up in logic. Like the sort of really abstract formal logic that people like Saul Kripke work on. | Artin, Michael. Algebra. 2nd ed. Artin, Emil. Geometric Algebra. Mac Lane, Saunders. Mathematics: Form and Function. Stillwell, John. Naive Lie Theory. |
[
"Is Brilliant worth the money?"
] | [
"math"
] | [
"8oswo4"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.54
] | Hey . I have heared nothing but good things about Brilliant but the only two options are 20€ a month or 7€ a month for 12 months. 12 months seems a bit too much of a comintment for me. But 20 a months is also too much. I would like to hear about your opinions on Brilliant. | Isn't this basically the same as paying for porn? Except the paid porn is superior to the free version. If you want to learn math there's plenty of free resources online, and I doubt brilliant is superior to them all. | There are libraries. And LibGen. | There's still PatrickJMT, KhanAcademy, 3blue1brown, Coursera, the great courses (paid, pricey, but much higher quality), MIT open courseware. The last 3 of these proudly list the professor and institution they're attached to. For Brilliant, I guess it's fine for the high school stuff and the lower level uni stuff, but ... | there are these things called books | I think gamified educational content is worth the money for people who are not naturally bookworms. |
[
"Alternate (eh) proof of 0.999... = 1"
] | [
"math"
] | [
"8osl89"
] | [
0
] | [
"Image Post"
] | [
true
] | [
false
] | [
0.38
] | null | but this is just a more confusing way of writing 1/9 = 0.1111.... and 9/9=1=0.99999999.... | IMO, this doesn’t qualify as an alternative proof. To rigorously close the proof, you’d need to show that 0.111... is equal to 0.1 in base 9. It’s not at all clear to me that this is different than showing 0.999... equals 1. | I see what you are trying to say, but it the same thing, just written different. Also, and quite honestly, who cares about ultrafinitists? They also claim that there aren't infinitely many natural numbers. Ultrafinitism doesn't actually make any sense, so why are you trying to pander to them? | But, they also don't believe that 0.111... = 1/9, so your proof wouldn't solve anything. | Yeah, but it actually is the same thing. |
[
"Langley's Adventitious Angles"
] | [
"math"
] | [
"8os3k3"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.75
] | Hello, my name is Anderson Moffitt, I was given a math problem in geometry by the name of Langley's Adventitious Angles. Here is the original problem; Angle B = Angle C = 80° CF at 30° to AC cuts AB in F. BE at 20° to AB cuts AC in E. Draw FE. Find Angle BEF. A solution was developed by James Mercer in 1923 stating tha... | (reposted from /r/wikipedia ) You claim that lengths BF and CE are equal because angle B = angle C. You can claim that length AC = AB from the law of sines (AB/sin 80 = AC/sin 80, therefore AB = AC), but not BF = CE, since points B, F, C and E do not form a triangle at all. You can, for instance, imagine moving poi... | How do you get that BF and CE are congruent from angles B and C being congruent? Isn't all that you can get is that AB and AC are congruent? The side CE is formed by the angle EBC and the side BF is formed by the angle FCB, so aren't these the angles that you would need to show are congruent before you could conclude... | The converse of the base angles theorem states that if two angles of a triangle are congruent, then sides opposite those angles are congruent. In this case, angle B and angle C are congruent, proving BF and CE to be congruent. | Is not angle B the angle formed by segments AB and BC and is not angle C the angle formed by segments AC and BC? I thought segment CE subtended the angle that was formed by the segments BE and BC, which has an angle measure of 20 less than 80, and I thought segment BF subtended the angle that was formed by the segment... | Here is the picture: https://goo.gl/images/rHsVnw |
[
"How to be more mathematically productive teenager."
] | [
"math"
] | [
"8optye"
] | [
36
] | [
""
] | [
true
] | [
false
] | [
0.84
] | So I'm 16 and love mathematics I want to become a mathematician. I'm familiar with real analysis, elementary number theory. I'm currently doing David Burton number theory and "A course in calculus and real analysis" by Sudhir ghorpade and balmohan Limaye My productivity(how much times spend to think about concepts and... | It's real easy, just start comparing yourself to the very best mathematicians in history, realize how far you fall short, and harness all that dread and stress so that you can work 14 hour days! I also reccomend moving a desk and lamp into a closet and working there. | Subject wise: something algebraic seems to be what you're missing to round out your experience of different areas of maths. These excellent notes would be a good place to start for a very gentle intorduction that will leave you in a place to jump into most introductory textbooks. Productivity wise: I don't know a singl... | Start solving Project Euler problems, they start fairly easy but as you get into harder ones you really have to think about the mathematics before jumping into the programming. | What grade are you in? I’m 17, and will be majoring in math and CS next year. By far the best math experience I could recommend is the Canada-USA Mathcamp. It is an incredible way to spend time with incredible people (personally as well as mathematically) who love math as much as you do, receive mentoring from incredib... | Agreed, breaks are important. There's nothing wrong with pausing for a while to let things process; it may feel like you're wasting time but really it's vital to deeply understand and visualize core concepts to make the rest come easier. I always give myself at least ten minutes (or more, depending on complexity) or so... |
[
"Does anyone else get excited by factorials!"
] | [
"math"
] | [
"8ophpd"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.33
] | [deleted] | there's a subreddit devoted to people excited for factorials. sorta. r/unexpectedfactorial | I enjoy combinatorics and there's a lot of factorials in that. | Double factorials are even more exciting!! | I just shout 'n' instead of saying 'n factorial' | are clean proofs more likely to have factorials? I guess any proof that needs it would be messy without it. |
[
"High school mathematics curriculum in Australia"
] | [
"math"
] | [
"8opgw8"
] | [
10
] | [
""
] | [
true
] | [
false
] | [
0.69
] | Following the Russia thread, I thought people might be interested in seeing the Australian mathematics curriculum. Australian education is broken into primary school and high school. I didn't include primary school because I can hardly remember and you can get a good idea from the start of high school. This is the curr... | I’d hardly say this is Australia’s high school curriculum, maybe for your school, but the majority of public schools in Australia have an extremely flawed mathematics curriculum, barely touching complex numbers or calculus | Similar to a square root/Cube root if it's irrational then it's a surd, In the UK GCSE maths students are taught this. | Perhaps my ignorance is showing, but what is a surd? | This is a public school in Queensland | No |
[
"Is Q isomorphic the Q^n?"
] | [
"math"
] | [
"8oqkz0"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.54
] | And if so/not then how to prove it? My intuition tells me it probably is because of how N is isomorphic to Q (and you can view Q as N ) and there's probably some sort of inductive argument, however I can't think of how to adapt the diagonal argument to suit this. Edit: the reason I'm interested in this is because I thi... | When you say "ismorphic", a certain algebraic structure is implied. As such they are not isomorphic as Q-vector spaces for instance. However, since you say that Q can be viewed as N . You certainly mean "do they have the same cardinal?", then the answer is yes. Elements of Q can be seen as 2n-tuple of integers. You can... | They are isomorphic in the category of sets... But yeah that's not how you usually use the word isomorphic. | They have different dimension. Q has dimension 1 as a Q vector space while Q has dimension n. | I doubt that this argument works: an open interval is a dense subset of a closed interval and it's homeomorphic to the unit circle minus a point which is a dense subset of the unit circle, but a closed interval is not homeomorphic to a circle. | The mathematical version of the stoner's "what if the entire universe is one atom in the toenail of a giant?" |
[
"Why is Multiplication (and division) more important than Addition (and subtraction)?"
] | [
"math"
] | [
"8oos1u"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.56
] | Edit: One possible conclusion that I've got from discussing with many is that multiply is a shorthand for lots of addition and exponents are shorthand for lots of multiply. So that's why modern convention gave them invisible brackets. This is because when you want to use different operations together, they need to be c... | We don't do them first because they're "more important" (whatever that even means...) we do them first because a lot of common mathematical formulas are easier to write if we do multiplication first. For example, think about a quadratic function like ax +bx+c. It's a lot easier to just write it like that than it would ... | It’s not a rule the * has to be performed before +, it’s just the way the world is. It absolutely is a rule we made up. There's nothing in the world that says we to do it that way. We could totally do all of math with + coming before *. It would just be annoying, and would need a lot more brackets, so we don't do it. 1... | Yup. It's basically just a matter of convenience, since things like polynomials show up a lot more in math than things that would be easier to write with a different order of operations. It's not a statement about how important different operations are. | Right. So we do it in that order, not because certain signs are more important, rather because that's how the equations were wrote. And it's just the conventional agreement that if no bracket is written, it means the equation was written with the brackets implied in this order. Thank you | Using PEMDAS 1 + 5 x 10 = 51 , but 10 x 1 + 5 = 15 . 51 =/= 15. We have demonstrated that this approach will not provide consistent results, right? No, it's just that 1 + 5 x 10 is shorthand for 1 + (5 x 10) and we can't switch this to (10 x 1) + 5 because those are two entirely different operations. Similarly, if we w... |
[
"Take any 3 digit natural decimal and repeat it n time(s) results in a composite number?"
] | [
"math"
] | [
"8onzu6"
] | [
3
] | [
""
] | [
true
] | [
false
] | [
0.8
] | Take any three digit natural decimal (001 through 999). If you repeat the triplet* *n time(s), the result appears to always be a composite number going up to n=39 (120 digits) (e.g. take 871, repeat 1 more time: 871871 = 7 * 11 * 13^2 * 67) This is base-1000 repunits. Examples: (each triplet shares similar rep-fa... | Such a number is a multiple of 1001, or 1001001, or 1001001001, or however many times you've repeated your string. | Any repeating triplet is (that triplet) times (the appropriate chain of 001's), thus composite. This is exactly the same thing as why repunits are always composite, except in base 1000 instead of base 10. | Any repeating triplet is (that triplet) times (the appropriate chain of 001's), thus composite. This is exactly the same thing as why repunits are always composite, except in base 1000 instead of base 10. | 001 repeated n times can be written (1000 - 1)/(1000 - 1). The numerator is a difference of cubes and can be factored as (10 - 1)(100 + 10 + 1). As long as both of these numbers are greater than 1000 - 1 = 999, this implies the number is not prime, so when n > 3. n = 3 and n = 2 can easily be shown to give a composite ... | Repunits are not always composite. 11 is prime, 1111111111111111111 is prime, 11111111111111111111111 is prime, etc. See A004022 |
[
"Has there been a whole lot of mathematician linguistics?"
] | [
"math"
] | [
"8omjfv"
] | [
9
] | [
""
] | [
true
] | [
false
] | [
0.91
] | You see a lot of crossover between mathematics and other fields involving technical knowledge or logic; traditionally things like physics, computer science, or philosophy. I don't think I've ever heard of anyone in math with a second interest in linguistics, though, not even the polymaths -- which is kind of surprising... | My bachelors was in linguistics and mathematics. Many who are in linguistics also study statistics and computer science for application in natural language processing and computational linguistics so the combination of math and linguistics is very much a thing. | I don't think I've ever heard of anyone in math with a second interest in linguistics This is not at all my experience. I know a number of people who are interested in math and linguistics. Pursuing even one of those professionally is rather difficult so few pursue both. | I don't know, but from my experience there is a ton of crossover between linguistics and computer science. Which is...kind of math related? For example linguist Noam Chomsky created the Chomsky Hierarchy of formal grammars, which are important in computability theory and programming language design. I've also just gene... | Joachim Lambek is a notable example. | I seem to know disproportionately many people doing/was doing math+linguistics too |
[
"Graphs with edge functions instead of edge costs?"
] | [
"math"
] | [
"8olne3"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.93
] | Hi, I found this on youtube, (short description below) and it made me wonder: Is there a branch of graph theory that studies graphs where passing over an edge doesn't just add some fixed edge cost to the total cost of a path, but performs different operations on the accumulated cost, such as doubling or dividing it, or... | This is equivalent to pricing an exotic derivative using a path-dependent tree. Generally speaking, unless you assume some more about the class of functions that are allowed, this is an NP-hard computational problem. For things like an American call option there already are efficient algorithms to price them. | The easy answer to the question is to expand the base graph into a graph (tree, even) of the state-space of the underlying problem -- i.e. each node is a path, and you have a branching factor of at most 3. This can represent any underlying set of functions, but at a horrendous blowup, which can make representing the wh... | This could be described by a representation of a quiver . A quiver is just a directed graph. The graph in the question can be considered as a directed graph with two edges going in different directions between each pair of adjacent vertices. A of a quiver is given by assigning a vector space to each vertex and a matrix... | That's a lot of word salad that doesn't even begin to address the question. | In general, most things involving multiple costs tends to be additive. If I pay $5 and then pay another $2, my total cost is $7. Even if later I earn back $3, a negative cost, it still adds to my total. Same if the cost is in terms of time/effort/resources. The typical example for costs in graph theory is the Trave... |
[
"Who is Grigori Perelman?"
] | [
"math"
] | [
"8olt4g"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.27
] | I want to seek information on him because I quote his lines "As long as I was not conspicuous, I had a choice. Either to make some ugly thing or, if I didn't do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit." This... | Googling his name should come up with plenty of resources. | A documentary about Perelman, with some testimony from people who knew him. https://www.youtube.com/watch?v=Ng1W2KUHI2s (there is an english subtitle). | Then use duckduckgo or Bing or some other search engine... | Check out Masha Gessen's book, Perfect Rigour. It's pretty good. | Thanks, nice even got a good rating on Goodreads. Surely I'll check out. |
[
"Question regarding unknown matrix X in a equation with multiple X. Is it possible to solve it?"
] | [
"math"
] | [
"8om8v0"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.85
] | Hello, let's say I have an unknown matrix and multiple known matrices etc. I have an equation similar to the following: • + • • + • • • = Is it possible to solve after ? Maybe I'm just absolutely stupid right now, but I just can't see the solution. | If you are writing code, then you don't need a closed-form solution. The size of the matrices is borderline irrelevant; reshape as /u/Asddsa76 suggests, solve the reshaped system, then convert back. But maybe you're having trouble figuring out how to cast your system as Ax==b in higher dimensions. Is that the issue? | It's a system of equations. Reshape the NxM matrices into N*M vectors and you see it. | Thanks for the input! Unfortunately the matrices can be of a size up to 10x10, so solving by hand and on a case to case basis is almost impossible. In the end I need to use this as an automated code in my program | Yes, that is the issue... I have a system with disturbances and want to compensate the disturbance on my exit with a proportional output feedback. For that I created the Laplace-Transformation for my state space model and tried solving for the proportional feedback matrix, but it appears in almost all therms. Thanks fo... | You should be able to reshape programmatically. |
[
"Incredible Liner Algebra Video Series by Grant Sanderson"
] | [
"math"
] | [
"8oldhc"
] | [
1202
] | [
""
] | [
true
] | [
false
] | [
0.94
] | null | 3b1b conveys math in the most beautiful and conceptually stimulating way, and the best part is his awareness of the limits of math video learning... so he truly cares to put as much effort as possible into teaching each concept! That voice also just puts me on a cloud floating away into the realm of math. | I suspect many of you have seen this before, but I just came across it, and it's so fantastic. If you're reviewing linear algebra, or currently studying it, I cannot recommend the series enough. It really helped me clarify a lot of big ideas that sometimes get lost in focusing too much on performing the computations. | https://reddit.com/r/math/search?q=essence+linear+algebra&sort=top&restrict_sr=on&t=all (also linked many other times under alternative titles; comes up like once a week in comment threads) | His videos on neural networks for machine learning is what really helped me wrap my mind around it while going through a course earlier this year. Then I started watching the rest of his videos and I think I may have a man-crush on him now. Simply beautiful explanations on abstract math concepts. | Sure, but not everyone has taken a good freshman linear algebra course. |
[
"Question Regarding Time Evolution of Wave Function"
] | [
"math"
] | [
"8ojvgb"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
1
] | In Brian Hall's Quantum Theory for Mathematicians, page 70-71 he does the following: Assume the wave function initially has definitive energy E, so E is an eigenvalue of the Hamtiltonian operator. He then states that since energy is proportional to temporal frequency, that the wave function must evolve in time as follo... | As far as I can tell one cannot say this without the Schrödinger equation. Are you sure he didn't sneak it in somewhere? He mentioned the Hamiltonian, after all. Maybe there's something along the lines of "the Hamiltonian is the generator of time translations" in there. | I think I have an idea: Use that energy is proportional to temporal frequency, decompose your wave function into a Fourier series with respect to time, then assume that this decomposition correspond to eigenvectors of the hamiltonian. In the book, he assumed it had a specific initial energy, so I think this implies all... | He's appealing to the de Broglie relation. | You can refer to http://webpages.ursinus.edu/lriley/courses/p212/lectures/node35.html | But where does the fact that energy is proportional to frequency come from? It's essentially the same as what we've been saying. |
[
"2 Postulates to make dividing by 0 possible?"
] | [
"math"
] | [
"8ojh07"
] | [
1
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
1
] | null | The problem isn't that when you divide n by 0 you get +inf or -inf, but the problem is that there's no way to adapt the concept of division to zero. Division can be defined as a variation of multiplication: a * b = c means that a = c * b . But, if b is zero, c is also zero. a = 0 * 0 is bound to break some other postul... | Actually, dividing by zero is an undefined operation the same way "ashfb ojwrkanfa iwhrian" is an undefined phrase in English: no one bothered giving it meaning because both of them (the division by zero and that strange-looking phrase) would break an already functional system adding nothing to it. Sure, you could nega... | Ask in the simple questions thread why division by 0 doesn't work. Also 0+0i, -0, and 0 are not distinct numbers. Ask in the simple questions thread why. This post is removed. | It's not compatible with the group axioms, and hence incompatible with the real and complex numbers under addition and multiplication. Try the simple questions thread if you want an explanation about why this stuff does not work. | Let's look at a group made of a set and operation (G,*) with an identity elements e,f (these are the "0"s if the operation is addition). By definition of the identity e*a=a and a*f=a for every a in G. Then e=e*f=f, and the two identity elements are equivalent. If there are two different kinds of 0s then 0 can't carry t... |
[
"Solutions Found By Solving Similar Problems"
] | [
"math"
] | [
"8ojgxk"
] | [
5
] | [
""
] | [
true
] | [
false
] | [
0.67
] | [deleted] | Mathematics | In computer science terminology, this process is usually called reduction. "Solving problem A is reduced to solving Problem B, of which we already know the solution". | It's just referred to as solving a problem "by analogy". Here is an article about it in a very general, not-necessarily mathematical context. In math itself, it's really depends on the context. Change of variables. Change of basis. Transformation. Functorality. No, real, unified name. Though, Polya does call it solving... | I've heard the term "relaxation of a problem" used in contexts such as optimization and PDE/SDEs to try to assume a less general function (usually setting certain things to constants) to get an idea of the qualitative behaviour. Also, if you literally have no idea what kind of behaviour to expect, this is a good way to... | Lol, minimizing is not easier than maximizing. 1) would be projection on a higher/lower dimensional space I think. 2) is just a convenient representation since it is easy to solve linear systems. A better example for 3 would be tackling linear or quadratic problems instead of non linear objectives. In DFO the notion of... |
[
"Why does cross product have to be a vector?"
] | [
"math"
] | [
"8oi9yi"
] | [
1
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
1
] | null | Why would that be desirable? If you want that quantity, you can always use |a×b|. The vector itself is often useful. | Most properly, a rotation is a bivector, not a vector. But in 2D, it takes a single real number, the angle say, to specify a rotation or a bivector, so sure, let it be a scalar (pseudoscalar, meaning it changes sign under reflection, unlike true scalars). In 3D it takes 3 components. You have to specify not only the an... | |axb| is always positive. The sign of |a||b|sin(ø) contains information about the sense of rotation from to . | Er, right. Brain fart aside, that information is already contained in the cross product. But the cross product contains more information than just which way the rotation goes, namely the direction perpendicular to both a and b. This is probably the most important and useful property of the cross product; if you got rid... | Having the cross product be a vector is often handy because you get a vector which is perpendicular to both of the vectors you put in. One instance where this is useful is when studying differential geometry , where we use this property of the cross product to find a set of three orthonormal vectors associated with any... |
[
"What Are You Working On?"
] | [
"math"
] | [
"8oihba"
] | [
13
] | [
""
] | [
true
] | [
false
] | [
1
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on over the week/weekend. This can be anything from math-related arts and crafts, what you've been learning in class, books/papers you're reading, to preparing for a conference. All types and levels of ... | Generating (hopefully all) irreducible representations of S_n as subrepresentations of a representation of the action of S_n on a particular simplicial complex. | Sheldon Axler Linear Algebra. Finishing an undergraduate degree in math but feel like my linear algebra is a bit weak so I want to refresh. Also reading Dumit and Foote Abstract Algebra. | Limits and derivatives | No, actually. But a vaguely similar approach in a different setting. | Making a script for a numberphile-esque video on a logic puzzle and its connections to number theory, including Fermat and Mersenne numbers. Hope to make it sometime soon, I'll post it to this sub if I do. |
[
"Math curriculum in Russia (specialized school)"
] | [
"math"
] | [
"8oiuco"
] | [
156
] | [
""
] | [
true
] | [
false
] | [
0.95
] | After seeing , I decided to write up a similar breakdown of the math curriculum as experienced by someone in a specialized math/physics school in Russia. Please note that this is in no way representative of the average school in Russia. However, Russia has a great mathematical tradition and a number of great specialize... | No you don't... | set theory and formal logic in freshman year of high school?? that sounds crazy. How rigorous was it? In the other thread, people were saying that US collegiate math looks more like high school math. Which it is. Here we find that in Russia, at the math schools at least, high school is more like university, with people... | As an American just getting their master's in secondary math education after a pure math undergrad, I be drooling a little wishing I could teach this. | The goal of that section on logic is to teach students to use the formal language of maths, formulate theorems without any words and write down proofs by using logical operations and symbols. It deals with basic statement and predicate logic with truth tables and such. Geometry, in my opinion, complements this beautifu... | This feels only slightly more advanced than the typical curriculum (non-specialized school) in China. Not sure how difficult the questions are, would you happen to have some example test questions? |
[
"What will be the value of 0 power -1?"
] | [
"math"
] | [
"8ogy1y"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.13
] | null | Division by zero is undefined. | Who said it had to be trivial? You wanna divide by zero, you gotta deal with the consequences. | Unless I read that wrong, I think the OP meant 0 = 1/0. | Unless I read that wrong, I think the OP meant 0 = 1/0. | Actually it’s 1/0 |
[
"Please tell me the answers of these questions:"
] | [
"math"
] | [
"8og0gl"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.25
] | null | P3. I think is just divide in two groups of 512 and 512 heaviest group has the ball, then half again to 256 and repeat then 128, then 64, then 32, then 16... well you get the rest | Thanks alot! | P5. 30 grapes =120 Grape=4 10 grapes +5 strawberries=80 40+5 strawberries =80 5 strawberries =40 Strawberries =8 10 strawberries + 10 apricots=180 80+10 apricots=180 10 apricots=100 Apricot=10 | Guys I just want the answers of P2,p6 and p9. | P6. Everything cancels out to 1/10of 1000, which is 100 (I think) 1/2x2/3 the twos cancel out x3/4 the threes cancel out x4/5 the fours cancel out and so on |
[
"Another set theory problem I solved. At least I think I did because the book gives me a different answer."
] | [
"math"
] | [
"8og6w6"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.27
] | null | Probably take the rest of your solutions to r/learnmath | Inverse cosine is a function, so it can only give you one of those values for each input. You're taking the inverse cosine of 0, -1, and 1, so you can only get at most three of the numbers in that set. Infinitely many numbers is more than 3 numbers. | Yup! (Typically, inverse cosine is defined to give you back an angle from 0 to π, but you could also use 2π to 5π/2, -π to 0, or a lot of other things. You have to make a consistent choice though, or else it's not a function.) | If you insist on using cosine you could do {x real : cos(x) integer} | So it's wrong then. I see. Since inverse cosine is a function, all elements in it's domain must have only one relation with the range. I now see where I mess up. Thanks! |
[
"My attempt at a simple set theory problem. I'm confused."
] | [
"math"
] | [
"8og04w"
] | [
23
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.74
] | null | You're both correct, 1/2 = 2 and the range of x is the integers, so you're fine. | The answer I came up with was {x∈ℤ : 1/2 } I think you mean {1/2 : x∈ℤ}, right? | Yes. The bit on the left are the elements of the set, and the bit on the right describes what those elements on the left are. The : can be read as "where", or something synonymous with that. | Thank you so much. A lack of sleep made me miss that. Oh well. At least I got it right! | Btw you should read the colon in sets as "such that". It doesn't really make sense to put it the way around that you've put it. |
[
"Should undergrads apply category-theoretic methods (not taught in class) in algebra classes?"
] | [
"math"
] | [
"8oflw7"
] | [
2
] | [
""
] | [
true
] | [
false
] | [
0.63
] | null | methods (not taught in class) Nope. It's important to learn the concrete stuff that abstract nonsense replaces before learning the abstract nonsense. | No. Category theory is great and all, however you should learn how to do something in due time. | Abstract nonsense means category theory. It's poking fun at category theory. But undergrad algebra is actually rather difficult to talk about in category theoretic language since category theory isn't great at talking about things like orders and elements. But what /u/tick_tock_clock is saying is true. Attempting to... | No. But I can't even figure out what this would look like? What results from undergrad algebra get nice proofs with category theory? I can only think of a couple and they're all just homework problem kind of questions. | Oh, I wasn't sure if you were aware and even if you're not aware someone reading this probably isn't familiar. It is kinda funny, concrete is relative. 1-categories are concrete when compared to infinity categories, varieties to schemes, etc. |
[
"I need help fast"
] | [
"math"
] | [
"8oeaq7"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
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0.33
] | null | Lol serious? | Quality shitpost | Well this isn’t really a math help reddit. This is a reddit to talk about broader topics in math and our love for it, not the quadratic formula. For algebra 1, this is all you should need to know off of the top of my head: Basic computations Solving linear and quadratic equations Quadratic formula Linear regression Equ... | Kind of | I'm being serious please help |
[
"Can somebody explain the concept of and the importance of hypercomplex numbers?"
] | [
"math"
] | [
"8oeg8v"
] | [
16
] | [
""
] | [
true
] | [
false
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0.92
] | For example with Quaternions, I can see that i=sqrt (-1) like you’d expect, but if i remains to be the imaginary constant, then what’s the point of having 2 other “imaginary constants” (j and k) if they also equal the square-root of -1? Can somebody eli5? | Quaternions 'are' quotients of vectors in 3-dimensional space, just like complex numbers are quotients of vectors in a plane. The point of them is that you can describe motion and spatial relationships in 3-dimensional space algebraically. This is useful for beings in a universe with 3 spatial dimensions. | Sometimes it's fun to start with the formal construction from which the complex numbers are derivable from the reals , keep going with it, and see what you get out of it. | A side effect of this is that it's not just i, j, and k that are square roots of -1, but in fact an entire sphere of points in the hypercomplex plane. i, j, and k remain 'special' only because they are the basis vectors. (And it could be argued that only two of i, j, and k are actually unique since any pair of them mul... | The 4 dimensional vector space used to analyze spacetime in physics is not equipped with a metric. It is equipped with the "Minkowski metric" (x,y,z,w) \mapsto sqrt(x + y + z - w This is not a metric in the usual sense because it is not positive definite. | Some aerospace engineers also swear by them to make clean rotation calculations (for satellites, for example). Noelhughes.net |
[
"Jobs after masters in mathematics."
] | [
"math"
] | [
"8ofu8l"
] | [
229
] | [
""
] | [
true
] | [
false
] | [
0.93
] | Hey guys, I will be going to complete my master's in mathematics in the next year. I have studied both applied and pure sections of mathematics during my course. Having a hons degree in mathematics I have no idea about programming skills. Now I wanted to apply for some jobs related to my field in future. Could anyone p... | Every time I see a thread like this I think of this and I die a little bit inside. That said there are some really cool jobs you can do with maths and as others have said python is probably the way to go. | The last panel should be "We need you to create an algorithm that identifies dick pics" | Maybe it's just something about the city I live in, but I'm going to have to disagree with what many people have said here about programming. I have an MS in math, and I've found that every job I've considered applying for is like, "Well it wants a BS in X, but I have a MS in Math... it's KIND OF applicable..." It's l... | Do we also have our own way of making lists, using underscores? | Do we also have our own way of making lists, using underscores? |
[
"Taking a practice test for an important test I’m taking tomorrow, and I have no idea wtf this means."
] | [
"math"
] | [
"8odib8"
] | [
0
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
0.25
] | null | r/learnmath | B | Subtracted 11 by 4. I believe “m” is only a variable, or, yes, any other letter in algebra. | Quotient rule of exponents. Google it and learn you shall. | It takes a bit to completely grasp it but the exponent rules are easy once they click. This is a decent review of them. http://www.mesacc.edu/~scotz47781/mat120/notes/exponents/review/review.html |
[
"Need help, fairly easy"
] | [
"math"
] | [
"8odjti"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.18
] | null | Tell Erika she needs to run faster if she wants the gold. | Try /r/cheatatmathhomework | Try /r/cheatatmathhomework | 100.0 yards = 91.44 metres Info PM Stats Remove_from_this_subreddit Support_me v.4.2 | You would use dimensional analysis |
[
"Famous scientists aware of Srinivasa Ramanujan"
] | [
"math"
] | [
"8odhga"
] | [
12
] | [
""
] | [
true
] | [
false
] | [
0.7
] | I was just thinking about this but did Einstein or maybe Hilbert or any other big names at that time, were they aware of Srinivasa Ramanujan at all? Did they collaborate maybe? Sorry for random question. | Ramanujan barely lived long enough to make it to England. His game was likely very local you Hardy and his associates until after he died. | Barely is a bit strong. He lived for 5 years in England. Other than that I agree, takes time to become famous in maths, and I guess the world was otherwise occupied in 1914-1919 as well. | 'The Man Who Knew Infinity' didn't mention any connection that I recall. | Huge role for Russell who then knew Godel who was best friends with Einstein though. | It's possible given Ramanujan's connection to Russell. Godel, the mathematician who walked with Einstein to work every morning, held Russell in very high esteam and had talked to him multiple times. But it is unlikely given how short a time ramanujan lived for. |
[
"Good research papers for undergraduates"
] | [
"math"
] | [
"8ocfn3"
] | [
100
] | [
""
] | [
true
] | [
false
] | [
0.94
] | I'd like to get into reading research papers but all I see are way over my head. Do you guys have any suggestions on good papers to read? Especially pertaining to calculus, I've taken up to calculus 3 in US, but I'm not familiar with other maths, so entry level would be awesome. | The MAA releases a journal called the American Mathematical Monthly here . It's a selection of papers targeted towards undergraduates so most of them don't require much background knowledge. Your school should allow you to access the papers as well. | reading papers your professors wrote and then going to office hours to talk about it. I doubt that there are many papers professors write that are accessible by undergrads. | A great paper from this journal is the Gale-Shapley stable marriage paper , which basically won the authors a Nobel Prize. It requires no mathematical knowledge, just the ability to follow a mathematical argument. | Reading papers absolutely should be something people do for fun. The above comment treats reading papers and research in general as something people only do to get ahead in the academic rat race. It doesn't have to be that way. It's fine to read stuff above your level, not only will you still get something out of the e... | Bit of an overstatement -- the paper is a work of beauty, but the algorithm had been discovered earlier by government bureaucrats of all people, whereas the Nobel prize was awarded half a century later . |
[
"Algebraic Fraction"
] | [
"math"
] | [
"8obws4"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.17
] | null | Homework problems, practice problems, and similar questions should be directed to /r/learnmath , /r/homeworkhelp or /r/cheatatmathhomework . Do not ask or answer this type of question in /r/math . | What exactly don’t you get? | My apologies. Next time I’ll be sure to post it there | You basically do the opposite of simplifying fractions so each fraction has a denominator of (x | Multiply the upper and bottom halves such that u get x as your denominator everywhere. Then you can write your long sum of terms into one, and the x in the numerator will cancel out and you can easily combine the left terms into ax+b. I got did it quickly on a piece of paper and got a=3, b=-18. You should check it your... |
[
"Function on the rationals."
] | [
"math"
] | [
"8ob78v"
] | [
6
] | [
"Image Post"
] | [
true
] | [
false
] | [
0.6
] | null | I think this graph tells you more about the graphing software you are using than about the function itself. For instance, the line from (0, 1000) to (1, 2000) is entirely an artifact of the points being sampled. Otherwise there would be points like (1/1000000, 1000000) way over the line. | Looks like /u/ItsAndwew is using all of the fractions / where { , } ∈ [1, 1000] and gcd( , ) = 1. I don’t think the diagonal line is supposed to be an especially important part of the picture. Personally I would recommend descending some number of levels in the Stern–Brocot tree instead. https://beta.observablehq.com/@... | The function is F(p/q)= p+q-1 I've only plotted between (0,1). Some cool things going on here. On the left and right you'll notice some points live inside a scaled inverse function. Working from the middle on out, there's some kind of parabolic thing going on, coupled with self similarity. Or this is just chaulked up t... | Also, this is assuming p and q are coprime. | Apropos Stern-Brocot Tree: can you find to solve the 'guessing game' for arbitrary rational numbers? By guessing game we mean: A thinks of a number, and B gets to make queries of candidate numbers to A who answers with 'smaller', 'equal' or 'larger'. The goal for B is to get an 'equal'. Now following the Stern-Brocot T... |
[
"What Mathematician do you think is irreplaceable?"
] | [
"math"
] | [
"8obkxw"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.42
] | By this question I mean by the work he has/had done, for example(by this I don't mean that Pythagoras is replaceable or was useless), Pythagoras is know for being the first person know to prove the Pythagoras theroem, but as the as time passed, many proofs began to appear, and I believe that, if he didn't prove it, any... | Euler? One classic concern is think of the statistical number of "math geniuses" who never were able to develop their potential due to their social position. Of course technically all you need is something to write with, but some formal education and textbooks go a long way. | Also you don't have time to do any thinking, if all your time is farming and not starving. That's the status for basically everyone before industrialization. | I don't believe most of is original to Euclid. He is just the textbook author. It's still hard to overstate its influence, but without him, very likely some other text(s) would have partially filled its place. | Seems you are not aware of Grothendieck's work in algebraic geometry. | While in no way denigrating his work, I really don't think the story is as one-sided as people often claim. |
[
"Favourite memory of classes or lectures during your mathematical education"
] | [
"math"
] | [
"8ob6dm"
] | [
14
] | [
""
] | [
true
] | [
false
] | [
0.9
] | Inspired somewhat by my old alma mater's old website (above) and a memory of my lecture on extending an entire module's result to a multidimentional version as an exercise (Riemann integrals, to be exact, I order to use the intermediate value theorem in the context of manifolds or something). Any anecdotes or stories t... | Nothing specific in mind but during my first few years of university, I was a math TA for a number of first-year classes (calc I & II, linear algebra, discrete math). It was an absolute joy helping students break down a concept and having them finally get their "Eureka!" moments when it all made sense. I convinced a lo... | Teaching Algebra 2 one year, and had a lot of students who weren't exactly fired up by the subject. One in particular, who was a theater student and I'd seen in a few plays, never really understood how it was that I could enjoy both drama and math. We had covered completing the square, and had memorized the quadratic f... | The professor who was supposed to teach multivariable calculus our second semester was on medical leave due to a concussion. An older lady, professor emerita, was brought back from retirement and taught the course instead. For our last lecture, she brought a huge cake which she had decorated with the Divergence Theorem... | My best professor was in Topology and it would have otherwise have been a very boring subject, but he made it very interesting. Memorizing metrics and what makes a Hausdorff space a Hausdorff space etc isn't super interesting, and it's all a little too abstract. He introduced a lot of cool stuff though. He used ston... | You must've had a knack for teaching! |
[
"Since math proofs AFAIK use logic, why can't a computer program confirm the ABC conjecture proof?"
] | [
"math"
] | [
"8obg3c"
] | [
12
] | [
""
] | [
true
] | [
false
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0.64
] | [deleted] | Mathematics is written in logic. Generally, people are happy to think that proofs be "formalized", i.e., could be written in formal logic, of the form that a computer could check. But they're much less happy to actually go through the effort of formalizing them. Which would be way more effort than just reading and unde... | Here is an example of a typical semi-formal proof of a well-known basic result in set theory, the Schröder-Bernstein Theorem. Here is a fully formal proof of the same statement, the sort that could be verified automatically by a computer. Note that many of the references are themselves other theorems with nontrivial fo... | Here is an example of a typical semi-formal proof of a well-known basic result in set theory, the Schröder-Bernstein Theorem. Here is a fully formal proof of the same statement, the sort that could be verified automatically by a computer. Note that many of the references are themselves other theorems with nontrivial fo... | Let me quote Peter Scholze from https://galoisrepresentations.wordpress.com/2017/12/17/the-abc-conjecture-has-still-not-been-proved/: "One small thing I would like to add is that most accounts indicate that no experts have been able to point to a place where the proof would fail. This is in fact not the case; since sho... | creating a neural net for converting current math proofs, which still at heart have to be based on sound logic Ayy lmao. No one, not even the most strident proponents of formal proof verification thinks that this is reasonable. That's a project that (if possible) that would take the better part a century with a good s... |
[
"Looking for a simple intuitive explanation of what a Cartesian product is"
] | [
"math"
] | [
"8oa0vt"
] | [
0
] | [
"Removed - ask in Simple Questions thread"
] | [
true
] | [
false
] | [
0.5
] | null | The Cartesian product on n sets is a SET of all ordered n-tuples such that: Each "coordinate" of the n-tuple is an element of one of the n original sets. The order of the coordinate (first, second, third...) will tell you which set it came from. All such n-tuples are in the SET. | You could take the Cartesian Product of B with itself to get BXB= {{H,H},{H,J}, {J,H}, {J,J}} You can do that. | Ok so essentially this is a way of saying that if you have a series of values and you want to take the "Cartesian product" of R, you're basically saying that all of the values are (R) Real values? And I suppose you're also saying that they're in order? | Yea I read the wikipedia article before posting but unfortunately it didn't help. When I think of product I think of combining things like multiplying number or placing (1, 2, 3) in a Cartesian coordinate system with x, y, z so resulting in (1x, 2y, 3z). This understanding doesn't help me wrap my head around why the au... | |
[
"Clarification about the difference between integration and antidifferentiation"
] | [
"math"
] | [
"8oaze7"
] | [
62
] | [
""
] | [
true
] | [
false
] | [
0.92
] | I just want to make sure I understand something before asking a more technical question. In a now-removed in , I asked a question about integration that received some rather forcefull pushback from and for being confused about the difference between integration and antidifferentiation. My understanding is that the fund... | My understanding is that integration and antidifferentiation are distinct concepts Right. which are related by the fundamental theorem of calculus, Right. if I use a Riemman sum and take a limit to derive the area under the curve of f(x) = x on the interval [0,a], I can use this result to usefully inform me about what ... | This likely isn't your fault, people use horrible names for these things. The problem is that what's called "indefinite integration" is really antidifferentiation and indefinite integration is actually far different from (definite) integration, which is about limits of Riemann sums. | One half of the FTC is literally about constructing antiderivatives using definite integrals with variable limits. So an antiderivative of e is F(x) = Int[e , {t,0,x}], which is a perfectly well-defined function using limits of Riemann sums and can be calculated at any point just as rigorously as any other transcendent... | Antiderivatives are the preimage of the derivative linear map. Integration is a linear map to the underlying field, or an explicit mapping to the space of functions if one of the bounds is a variable, assuming uniqueness of the integral. | One way to tell that they are different: They result in completely different things. Antidifferentiation results in a function, or family of functions, whereas integration results in a number. Integrals provide you with the area under a function. Now, you can use this to construct antiderivatives (let F(x) be the integ... |
[
"What is the type of this probability problem? How do you work it out?"
] | [
"math"
] | [
"8o8bxh"
] | [
1
] | [
""
] | [
true
] | [
false
] | [
0.53
] | Assume it can only be rainy or sunny. If it is rainy on a certain day, the probability that it'll be rainy next day is p and the probability that it'll be sunny next day is (1-p). If it is sunny on a certain day, the probability that it'll be rainy next day is q and the probability that it'll be sunny next day is (1-q)... | Even if a Markov matrix is invertible, its inverse will not in general be a Markov matrix. For example, [[1, 1/2], [0, 1/2]] has inverse [[1, -1], [0, 2]]. Conceptually, the reason why your approach fails is you're asking the wrong question. You're asking: what's the distribution in Day 1 which sun on Day 3? But there'... | "Most of the time" is not at all a meaningless statement. The subset of square matrices with determinant zero is measure zero. Inverting still isn't the right thing to do, of course. | "Most of the time" is not at all a meaningless statement. The subset of square matrices with determinant zero is measure zero. Inverting still isn't the right thing to do, of course. | In general, you solve this kind of problem using the time reversal of the Markov transition matrix. The entries of the transition matrix P are P(i,j) = probability of being in state j at time n+1, given that you are in state i at time n The entries of the time reversal of P are Q(i,j) = probability of being in state j ... | Do you understand discrete time markov chains? Well if p=q then that means that no matter the weather yesterday it will be rainy or sunny today. So the probability it was rainy on Sunday isn't uniquely determined by the probability that it was rainy on Tuesday. Moreover the probability that it is rainy on day n (n>1) s... |
[
"Looking to restart at a high school level."
] | [
"math"
] | [
"8o8kdu"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.4
] | Ok so I have been learning Machine Learning Engineering and my math comes down to about a freshman high school level. Yesterday I taught myself cost function and it took me about 2 ish hours to do the formula because i had no idea what sigma and theta was at that point. I want to learn math from the start of high schoo... | A resource like the Khan Academy sounds like a pretty good fit for you. At least it's a reasonable start. Be cautious - it'll take time. | I wonder if we mean different things when we talk about Newton's method. The Newton's method I know only uses first derivatives as well. (Although the common method to describe the rate of convergence uses two derivatives, that's quite different). | For a bit of additional context, gradient descent is essentially an application of an idea first learned in basic calculus (called Newton's Method) to a situation usually represented and manipulated with ideas learned in basic linear algebra (matrices, vectors, linear operators). It's possible to learn and perform some... | WOW, this looks really good. Thanks for the suggestion. | Gradient descent is very different from Newton’s method for finding minima. Gradient descent uses only first order derivatives while Newton’s method uses first and second derivatives. Both require a good command of multivariable calculus though. And it is quite irresponsible to go at it without the mathematical knowled... |
[
"Failed precalc. Should i retake college algebra?"
] | [
"math"
] | [
"8o755a"
] | [
0
] | [
"Removed - see Career & Education Questions thread on front page"
] | [
true
] | [
false
] | [
0.33
] | null | professors screw up Algebra Math professors with years of doing extensive algebra calculations themselves, teaching algebra to others, grading algebra papers and spotting obvious and subtle mistakes become quite fluent in algebra, and don't make algebra mistakes any more than a native English speaker would accidentally... | I think he meant even professors screw up teaching algebra. Knowing about rings and higher level algebra does not translate into I can teach people with no math experience what a function is. In fact, sometimes the opposite is true when the professor knows so much that he just ends up confusing the students. | Depends on just how much retouching you feel you need. Maybe you can simply brush up using a book and some exercise sets, and if that's not enough you can always retake it. You're right that you will need to do something if precalc algebra is giving you trouble. For what it's worth at this point, it would've been bette... | Go through the text again, and do it in the campus library or math center. There should be a tutor center there as well. Algebra is a lot of rote skills. Even professors screw up Algebra. | Professors with years of teaching experience can also be good teachers, but I agree that lots of them don't care much about teaching and go through the motions or do a half-ass job. Knowing about rings and higher level algebra does not translate into I can teach people with no math experience what a function is. True..... |
[
"Why does 0^0 not equal to 1?"
] | [
"math"
] | [
"8o5rjj"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.5
] | null | https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero | Zero to the power of zero, denoted by 00, is a mathematical expression with no necessarily obvious value. Possibilities include 0, 1, or leaving the expression undefined altogether, and there is no consensus as to which approach is best. Several justifications exist for each of the possibilities, and they are outlined ... | Seems like a pretty fuzzy concept. Many people do actually believe that it equals 1. Take a look at this link: https://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml It runs you through a couple of theories - one using the binomial theorem, and another the limit of x as x approaches 0. | What happens when you add 0+0? You get zero. Multiplication is just addition many times over. Zero to the power of zero or any number makes it zero. | My two cents: consider the expression a / a . a / a can be rewritten as a = a = 1. But if you were to let a = 0 in that original context, you would be dividing by 0 = 0, which is undefined. |
[
"Number Theory crash course in a jupyter notebook"
] | [
"math"
] | [
"8o55zi"
] | [
21
] | [
""
] | [
true
] | [
false
] | [
0.92
] | null | "A prime number is a number p>1 whose only divisors are 1 and itself." I suspect it's not going to be algebraic number theory | "Well, it turns out that every number has a unique factorization into primes!" I'd expect a number theory crash course to prove that. | It does indeed! See here :) | Yep! No algebraic number theory. But I'd love to learn more in the future. Do you have any recommendations on how to get my feet wet? | That depends a lot on how's your background in abstract algebra and commutative algebra (and a bit of Galois theory too) |
[
"FINAL EXAM"
] | [
"math"
] | [
"8o591w"
] | [
0
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.44
] | null | Ok | Uh, good luck | Nobody learns anything instantly, it takes time to understand things, especially more abstract stuff like math. No video is going to fix that, next time actually assign some time for studying and don't leave it to the last minute. | Spend the rest of the weekend watching Khan Academy videos and solve the exercises. Start with Algebra 1 , I know your class is Algebra 2 but if math is hard for you you're probably missing the basics. If you have time continue with Algebra 2 . The exercises are important so don't skip them and try to not look at the a... | Talk to your teacher, ask to meet with them to review topics. Go over your previous work in the class. |
[
"Doing Math in Moscow next semester, do you have any advice?"
] | [
"math"
] | [
"8o6300"
] | [
16
] | [
""
] | [
true
] | [
false
] | [
0.9
] | Hi everyone, I will be in Math in Moscow next semester and have browsed several posts here relevant to MiM, but also wonder that people who have done it, do you have any advice, such as which courses to take, how to manage time, and living in Russia in general? Thank you, guys! | Russians are VERY nice to foreigners, though they may not seem so. Their way of interacting with strangers may seem rude at first, especially as an American, but you'll get used to it. But it is also easy to strike up very interesting conversations, especially with taxi drivers and people who work in less crowded store... | If you can, avoid setting up a set-in-stone list of courses for yourself at the beginning. The program is meant to be flexible, and is very accommodating to people who want to push beyond their backgrounds. Other than that, do some travelling and see some museums. | I did MiM a few years ago and I’m always happy to share any advice I might have. I did my undergrad at a cushy liberal arts college where I wasn’t challenged. This program was the push I needed to get into graduate level math. | I do intend to take Russian I course, and learn some basic Russian words and phrases.. | i’m Russian and learning at HSE university (Moscow, math faculty, 1th course). So i can tell you, that it’s very nice (probably the best) Russian math faculty. if you want, i can say something about it. Living is easy here: low prices, soft climate; but Russian are very different (such as architecture in Moscow), but t... |
[
"Can someone summarize the contents of American Pre-Calc, Calculus I...IV etc?"
] | [
"math"
] | [
"8o83hb"
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413
] | [
""
] | [
true
] | [
false
] | [
0.95
] | Hello, I am not an American. On here though I often see references to numbered courses with non-descriptive names like "Calculus II" or "Algebra II", also there is something called "Precalc". Everyone seems to know what they're talking about and thus I assume these things are fairly uniform across the state. But I can'... | In the United States, at the primary and secondary school level curriculums are usually set by the state or school district. So in principle there could be 50 different standards or more for these course names and what years they are taken,in secondary school. And at the university level, curriculum is totally up to ea... | This is it. Exactly what I took in the US in the right order and material. | Taken senior year = 12th grade = 1 years old. Not required for all students. You were advanced. | We need a post like this for UK education levels too. Often see people mention things like "A-levels", that I have no idea what they mean. | In the US, Precalc was teaching the basics of sin waves, trig, and a bit of polar co-ordinates. There was also approximations of tangent lines via 2 close points, and approximations of area under curves via several rectangles. Calc 1 was basic integration and differentiation, with simple tricks like u substitution, and... |
[
"Linear Algebra proofs are so mundane."
] | [
"math"
] | [
"8o5ahu"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.46
] | I'm an undergraduate and this year I took four math classes. ODE, PDE, LINEAR ALGEBRA AND STATISTICS. Linear Algebra seems so boring. I mean a lot of stuffs there specially proofs seem to so obvious and not so exciting. In Khan Academy's words, "mundane". Like (AB)C= A(BC), and like you need three vectors to go around... | Many of the basic facts in linear algebra (and any branch of mathematics for that matter) are going to have less interesting proofs, but that's largely because the definitions are chosen so that the desired properties will be obvious. The more interesting theorems, like the spectral theorems, have more interesting proo... | It may be a bit boring and obvious, I can see that. I would view it however as a proof of a larger point, that if some problem can be cast as a problem of linear algebra, you have a very convenient and powerful algebra, or machinery, to take from. Fourier analysis is of course in one sense quite different, however, in ... | Many basic facts in linear algebra are subtle. For example vector spaces having a single number invariant called dimension is pretty subtle. I find it more subtle than the proof of spectral theorem for orthogonal operators on finite dimensional vector spaces which depends on the simple observation that a subspace stabl... | In Khan Academy's words, "mundane". Like (AB)C= A(BC) Funny you should mention this example... So if you want to prove matrix multiplication is associative, there's a "direct" proof consisting of evaluating each th coordinate of the product in two different ways. Such a proof is perfectly valid, but it provides no insi... | It may be a bit boring and obvious, I can see that. I would view it however as a proof of a larger point, that if some problem can be cast as a problem of linear algebra, you have a very convenient and powerful algebra, or machinery, to take from. So a lesson learned here that the most simplest of objects can have the ... |
[
"Help with Angles! Wanna build but need cut angles!"
] | [
"math"
] | [
"8o44bm"
] | [
0
] | [
"Image Post"
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true
] | [
false
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0.29
] | null | If anyone is wondering how to solve this, draw a straight line from the top corner down to the bottom. You now have two right triangles. You can use pythag theorem to find the length of the straight line from the top down (but you don't actually need it). Then use any inverse trig function to find the angles. Convert f... | and you don't even need that if you already know the answer! | Don't forget, when the angle indicator on a miter saw is set to zero, it results in 90 degree cut. In other words, the angle indicator doesn't tell you what angle you're cutting on the board, it tells you how many degrees away from 90 (square) your cut is. So depending on how you do your math, you may need to subtrac... | Why not build it 24-24-24 or 21-21-21 so that the cut angles are nice and easy? | Yep |
[
"Is there more integers between 1 and infinity when compared to 0 and infinity?"
] | [
"math"
] | [
"8o3mqm"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.36
] | [deleted] | u/Brightlinger is right that it depends on what you mean by "more". The typical way of comparing the sizes of two sets is to check for a "bijection". In other words, see if you can match each thing in the first set with a partner in the second. For example, there are just as many numbers in {1,2,3} as in {4,5,6} becaus... | That depends on what you mean by "more". There are the same number of them, but the latter has one extra. There is no contradiction there, since |N|+1=|N|. | The phrase "cardinal number" is not especially unconventional. I mean precisely that they have the same cardinality, and saw little reason to confuse OP with jargon. | Oh wow! Thanks a tonne mate. | Nope. There’s a 1-1 correspondence between the first and second set: assign 1 in the first set to 0 in the second set, then 2 in the first set to 1 in the second set, and so forth ad infinitum. |
[
"I painted my nightstand-- thought you guys might enjoy it."
] | [
"math"
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"8o3jlc"
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51
] | [
"Removed - see sidebar"
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true
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false
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0.86
] | null | those shoes | Alright, math equation: If the large square has an area of 1 square unit, what is the limit* of the sum of the areas of every black portion? (not sure if that's the correct term... whatever value can contain it completely, like how adding 1+0.5+0.25... will never reach 2) | So this would be a fairly difficult problem to do. To start you’d have to figure out the area of the first black portion, then you could express the rest as a geometric sequence/series (getting smaller by ‘r’ each time, where r equals the rate of change). The easy part, (once you have figured out the area of the first ... | I think if I set it to paper I could find the area of the black with geometry, but I'm wondering how to do an equation in which it provides the sum of every term in a geometric sequence | I came here to ask this too. |
[
"Is it a property that all functions without elementary antiderivatives cannot be evaluated as a definite integral on a non-infinite region?"
] | [
"math"
] | [
"8o24g1"
] | [
2
] | [
""
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true
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false
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0.67
] | Sorry if the title makes no sense. What I am trying to ask is if definite integrals (that aren’t improper) of functions like ln(cosx) and e can have answers that aren’t decimal approximations? Is there any way to get “exact” answers in terms of a finite number of algebraic operations? Are there answers that will not re... | A simple rescaling does the job. For example, the integral of sec (x) exp(-tan (x)) over the finite interval (-pi/2, pi/2) is sqrt(pi). | I think the class of numbers that is expressible via finite number of algebraic, log, and exp operations is not usually considered, at least not that I’ve seen. However numbers that are a finite number of purely algebraic operations are called algebraic numbers, which are well-studied, so it might be a good place to s... | Well there's the trivial answer, the integral from a to a of any function is zero. But more generally, integrals over algebraic domains of algebraic functions are called periods . They're mostly transcendental. I suppose you're asking whether they are ever rational? Is there a finite value a such that ∫ e or an ellipti... | it was such a stunningly evocative and poetic (and mathematically accurate) analogy. Yes, it left an indelible impression on me. | it was such a stunningly evocative and poetic (and mathematically accurate) analogy. Yes, it left an indelible impression on me. |
[
"Course in Lebesgue Measures as first course in Real Analysis?"
] | [
"math"
] | [
"8o1j51"
] | [
4
] | [
""
] | [
true
] | [
false
] | [
0.7
] | Hello All, I have the option to take a course in Lebesgue Measures this summer. I will be taking two courses and have chosen one, and as for the other there are good options, but this course honestly interests me more than my other options (intro to number theory, a course on conjecture in proof). However, I have not t... | Typically a course on measure theory would assume a strong background in: topology of R infima and suprema, liminfs/limsups, a rigorous construction of the Riemann integral, continuity and differentiability (if the class will cover multi-variable functions, how comfortable are you with understanding derivatives as the ... | Ok well it doesn't sound impossible but will be a challenge | Have you taken anything higher than calc? I know you haven't taken real analysis, but what about other proof-based classes? In principle measure theory could be learned before classical real analysis. In practice however measure theory is taught to beginning grad students who have had several years to develop proof tec... | Classes are 2 hours a day, 4 days a week. Let me be a nattering nabob of negativism (look up American politician Spiro Agnew) and say you're going to go under and drown taking a serious course in measure theory two hours a day, four days a week, with your background. Take the number theory class. Everyone needs to know... | Behavior under limiting operations is the of the Lebesgue integral. Many of the important theorems, and even the construction of the Lebesgue integral, will involve sequences of functions. If you're not comfortable dealing with sequences of functions and limits in general--pointwise convergence, uniform convergence, li... |
[
"Examples where the first n dimensions are exceptions to the general pattern?"
] | [
"math"
] | [
"8o2irv"
] | [
7
] | [
""
] | [
true
] | [
false
] | [
0.82
] | So, I know of plenty of things where ℝ behaves differently from higher-dimensional spaces. I know some examples where ℝ and ℝ² behave differently from higher-dimensional spaces (e.g. the unit sphere is simply connected except in those two), and some where ℝ through ℝ³ are different from higher ones (e.g. composition of... | The volume of an n-ball (the generalization of a sphere to higher dimensions) approaches 0 as n gets larger. I think this is relevant cause the volume increases until n = 5, after which it decreases. | Where by “volume” you mean “volume in proportion to an -cube” (a choice based on cultural baggage). Relative to an -simplex, the “volume” of the -sphere approaches ∞. | I think this is relevant cause the volume increases until n = 5, after which it decreases. This is meaningless because they have different units. You get different turning points for different radii. | Exotic spheres only exist in dimensions 4 and above. If you throw out dimension 4 (which is weird in general), they only exist in dimensions 7 and above. | We don't know about dimension 4 though! That's the smooth Poincaré conjecture. |
[
"Help with mathematics? No direct solutions"
] | [
"math"
] | [
"8nzon2"
] | [
0
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
0.5
] | null | You want /r/learnmath . Start by figuring out what and ( ) represent. Then find some specific values of and come up with the associated values of ( ). Now find a general rule that matches your examples. | First, calculate how many guests show up when the price is 0. Then, the demand function is D(p)=D(0)-0.1p, where p is price and D(p) is demand depending on price. Is there any cost? If not, the revenue function is demand multiplied by price, so R(p)=D(0)p-0.1p This should have an extreme point. | thanks | The profit is what you want to maximize, so you expect the profit to be equal to some quadratic expression (so that it must have a maximum or minimum). You know that profit = price of ticket × number of guests. You need to find a way to express the number of guests in terms of the ticket price. Then you just expand the... | My "homework" told that if you make the price higher by 0,10€, 1 guest less shows up, if you e.g. make the price from 8€ (standard) to 7,50€, its 0,50€ (5 x 0,10€) so 5 guests more show up. I came to the function , being the Guests and the number of times the ticket gets reduced by 0,10€. (in the first "(" i put x bec... |
[
"New Here, I hope personal project questions are ok."
] | [
"math"
] | [
"8nyad4"
] | [
0
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""
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false
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0.38
] | So I am trying to write validation code for a project of mine. Just to cut to the chase: Let's say you have a List of Symbols (S) and in the List of Symbols some Symbols are Duplicated (D) Each Symbol needs to be paired with another Symbol but each Pair must be unique ( !@ == @!) After Determining the max combination w... | It is impossible only when more than half of the symbols look the same. You can prove this by induction (repeatedly pair together the two most common symbols and the invariant is maintained). | I agree, this does not seem possible. | You can pair them up, I can't be bothered to actually do it but if you keep pairing up the two most common symbols you are guarenteed to succeed. | By the pigeonhole principle, if more than half of your symbols are duplicates (let's consider the symbols {?,%,&,$,$,$,$,$}) then two identical symbols must be paired together. You can think about this as pairing each dollar sign with every symbol that isn't a dollar sign, but then you have two dollar signs left over t... | Thanks for the reply, what if you have something like this (I'll use letter in this case ) {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,a,a,a,b,b,b,c,c,c,m,m,m,m,m,h,h,h,h,h,h,h,i,i,i,i} In this case there are over half duplicates in total but not of one type? Could this pigeon hole principle still be applied... |
[
"What areas in Geometry/Topology?"
] | [
"math"
] | [
"8nycck"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.42
] | Or rather Geometric Topology that has no connections to Physics? I have read some papers, there seems to be a lot going on with quantum topological field theory... | I'd suggest not to pursue string theory directly, but fields of math adjacent to it. | Since when was TQFT and string theory listed under physics? To answer your question, you might want to look up moduli spaces or say topological recursion/Mirzakhani's recursion. If you want absolutely no connection to physics, I invite you to name any mathematical subject that has this property. | Sorry, my comment was a little tongue in cheek. I guess my point was, "who even distinguishes between mathematics and physics at these levels?" Everyone I know who knows string theory calls themselves a mathematical physicist in the mathematics department. | Since when was TQFT and string theory listed under physics? I'm a little confused by this opinion. Certainly string theory is a subject in physics -- it doesn't have a mathematical formalism, for example. And TQFT is definitely a mathematical subject, but there is also a physics side of TQFT, where physicists ask QFT-l... | Depends on what you consider physics. I can't immediately think of anything that isn't at least vaguely connected to String Theory / TQFT. |
[
"Why is Rudin starting the proof of Schwarz Inequality this way? I’m so confused. Thm 1.31 for reference."
] | [
"math"
] | [
"8nwe96"
] | [
1
] | [
"Image Post"
] | [
true
] | [
false
] | [
0.57
] | null | Because it gets the result. Rudin is not really known for providing proofs. | A better question is why this is being done at all. The CS ineq. can be proven using only the properties of the inner product, avoiding the need to write any sums at all. (Here the inner product is the dot product between n-dim complex VSs). | Look at the proof of that sqrt(xy) <= (x+y)/2: Set A=sqrt(x) and B=sqrt(y), then Therefore 2AB <= A +B , which proves the result. "Fucking why" do you start with (A-B) ? Because it's positive and ends up working. | Rudin works backwards. He starts with what he wants to prove, which is C ≤ AB. Then manipulates it until he gets something obvious like B > 0. Then he erases all his tracks and reverses the proof. If you can't duplicate the proof in this manner, then try it with n=2. | Presumably, he wants to show that the last expression there is greater than or equal to zero. Then divide by B, which is positive by assumption, add the square of norm C to both sides, and you're done. Edit: Also, if this is your first brush with analysis, I suggest Abbott as an easier alternative if you find Rudin too... |
[
"Rational and Irrational"
] | [
"math"
] | [
"8nw6lk"
] | [
1
] | [
"Removed - try /r/learnmath"
] | [
true
] | [
false
] | [
1
] | null | If it can be expressed as a fraction then rational if not irrational | pi=pi/1, so pi is rational. /s | Correction both bits if the fraction have to be whole numbers | Yup. And also you need an equivalence relation so fractions that can be simplified to each other represent the same number. | thank you! |
[
"pretty sure my math test doesn't know how pyramids work"
] | [
"math"
] | [
"8nvoyt"
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1
] | [
"Removed - see sidebar"
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true
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false
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0.99
] | null | The perspective is off (the edge closest to you should appear longer than the edge furthest away from you, because perspective). But it says it is not drawn to scale. You have an extra measurement that you don't need - if the pyramid is regular, the length of the side is uniquely determined by the distance of an edge f... | What exactly is supposed to be wrong here? | I believe that OP expected a pyramid to only have a square or rectangular bottom | A pyramid with the dimensions given is impossible | https://en.m.wikipedia.org/wiki/Pyramid_(geometry) They do know what a pyramid is. |
[
"Modern \"Set Theory\" - is it a religious belief system? | Set Theory Math Foundations | NJ Wildberger"
] | [
"math"
] | [
"8nvxuw"
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0
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""
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true
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false
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0.35
] | null | Oh NJ. I am possibly the most sympathetic of all regulars here to ultrafinitism but the absurd comparisons to religious dogma are counterproductive hyperbole. Most mathematicians don't whether or not there is any reality to what they're doing. Unless someone finds a contradiction in ZFC (really it would have to be in ... | If there's contradiction it's either in AoI or PA (or both), right? I think for ultrafinitism, you'd need to wreck PA itself not just AoI. But of course none of the ultrafinitists actually have a formalization of whatever it is they're talking about so it's hard to determine. Personally, I'd say that rejecting AoI but... | No. Well maybe, I have no idea what what the definition of a religious belief system if there even is one. Set theory (actually ZF since that's what he means here) is not the only viable choice for foundations (see type theories, various constructive set theories and other ones that I am not familiar with). There are ... | What in the world would PA being inconsistent even look like? I have no idea. I can't even envision ZFC being inconsistent. but is really an issue with the axiom of the power set of with the axiom of replacement? I know there are set theories without power set they're all pretty bizarre and it seems to me that what yo... | Powerset is arguably the most philosophically suspect axiom under some interpretations. Why should we assume that it’s possible to exhaust all the sets of natural numbers, put them together into a set, and then make more sets which will never allow us to make new sets of natural numbers? Generally allowing for more com... |
[
"People rarely discuss HOW mathematical research is done. This article tells the story of the strong perfect graph conjecture, including missteps, intuitions, scooping, breakthroughs, abandoned definitions, and loose ends. If you want to know what it's like to do research in mathematics, check it out"
] | [
"math"
] | [
"8nvvsg"
] | [
1092
] | [
"PDF"
] | [
true
] | [
false
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0.97
] | null | I thought math research was given to you by the gods while you're dreaming | Silly. It's actually given to us when we are pooping. Great researchers are just people who shit a lot. | Thanks for submitting this! This perspective on research is also encapsulated by this Abstruse Goose comic . | You can save posts without commenting. | You can save posts without commenting. |
[
"If you pick 2 positive integers at random, the odds of them having no common divisor are 6/π² ≈ 61%"
] | [
"math"
] | [
"8o10f0"
] | [
1827
] | [
"Image Post"
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true
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false
] | [
0.95
] | null | What does "picking 2 positive integers at random" mean? EDIT: I guess it means picking 2 positive integers from {1, ..., N} and letting N go to infinity, in the sense of natural density . | I've always loved this, it's such a cute little proof. In general if you pick k positive integers at random the probability they are all comprime to each other is 1/ζ(k). | That's not picking uniformly at random though. And limits are perfectly well-understood. Maybe not by you, but we're not letting that stop us. | Am I out of touch? No, it's the entire mathematical community at large that is wrong. Do you have any specific gripes with limits that we can try to address? | In this case, picking two natural numbers uniformly in {1,...,N} and then taking the limit of the probability as N goes to infinity. |
[
"Book suggestions for a philosophy student?"
] | [
"math"
] | [
"8nv5eg"
] | [
15
] | [
""
] | [
true
] | [
false
] | [
0.86
] | Hi, I am not a philosophy student on paper (I am actually a law student) but I am actually studying philosophy and I am very interested in maths too. However, my understanding of maths is regrettably limited and even though I had maths classes in primary school and high school, I know virtually nothing of it thanks to... | I do not want to be good at calculating numbers but to know, say, why when we add 2 to 2, the result is 4 and not 5. One way of deriving this axiomatically is by the set-theoretic construction of the natural numbers . I first encountered this in a course taught by a certain Velleman and George , so their textbook migh... | I think most of your questions can be answered by doing some reading on the philosophy of mathematics . You might also be interested in intuitionistic type theory or Peano arithmetic as an example of a formal system in which you might encode that 2 + 2 = 4. | I was interested in this as an undergrad. Majored in math. Minored in philosophy. I highly recommend the works of Saul Kripke . Wittgenstein on Rules and Private Language is the best place to start. Naming and Necessity is great too, but the Wittgenstein book is a masterpiece. Methods of Logic by Willard Van Orman Quin... | Not strictly rigourus nor strictly about maths but you would probably enjoy Hofstadter's Goëdel Escher Bach | I second the Bertrand Russell book. It's not where I want to stop studying, but I've definitely enjoyed reading it |
[
"How does one go about creating or solving an equation?"
] | [
"math"
] | [
"8nuju7"
] | [
0
] | [
""
] | [
true
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false
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0.36
] | [deleted] | Unsolved problems get solved by being late to class and mistaking it for a homework problem. | :-) - Remind me what unsolved problem is the focus of this story? And is the story verified, or is it just an urban myth? | I don't know the problem, but the guy's name was George Dantzig and it's true. | Thank you; here's Snopes on this . | I would guess that, like me, most people here have no idea what you're referring to. |
[
"Hard math problem"
] | [
"math"
] | [
"8nunde"
] | [
0
] | [
""
] | [
true
] | [
false
] | [
0.4
] | null | why not? | why not? | You shouldn't use the = sign like that. This belongs in r/learnmath not here. | Having not heard a math joke would seem to indicate that I do have a life. But no, I have not heard this "joke". | Having not heard a math joke would seem to indicate that I do have a life. But no, I have not heard this "joke". |
[
"What does this mean???"
] | [
"math"
] | [
"8ntjls"
] | [
2
] | [
"Removed - see sidebar"
] | [
true
] | [
false
] | [
0.6
] | null | Apparently you're not the one. | Simply expand both as Maclaurin series and it should become obvious. | The bit in brackets is a trigonometric identity. For any x, sin (x) + cos (x) = 1. | You're the only one for me. | Yeah, that seems about right. |
[
"Need help formulating a probability formula."
] | [
"math"
] | [
"8nt9xj"
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1
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""
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true
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false
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0.57
] | [deleted] | At least 1 event = 1 - (0.8) | 0.99999999999999999999999999999999999575531709672066922100827678637729 Thats what I got with an online mathematical software (Wolfram Alpha) | (0.8) is very close to 0, so the probability would be a number very close to 1. In other words, it's extremely likely (practically certain, even) that there will be at least 1 captured event in a year. | (0.8) is very close to 0, so the probability would be a number very close to 1. In other words, it's extremely likely (practically certain, even) that there will be at least 1 captured event in a year. | Decimal times decimal equals a smaller decimal. Do that a lot and you get a very small number |
[
"What Are You Working On?"
] | [
"math"
] | [
"8nt482"
] | [
6
] | [
""
] | [
true
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false
] | [
0.73
] | This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on over the week/weekend. This can be anything from math-related arts and crafts, what you've been learning in class, books/papers you're reading, to preparing for a conference. All types and levels of ... | dysfunctional analysis I see you've read my analysis homework. | The Unit Circle. I'm a semi-old fart meandering through math with plans to study through calculus at least. It's a much funner journey without exams! | Well, better functional analysis than dysfunctional analysis! | Have you read Chow's "You Could Have Invented Spectral Sequences" ? It's a solid article that may provide some useful perspective. | Divergence , stokes and greens theorem |
[
"I've made a perfect square with sides equal to 1 feet. Is the hypotenuse equal to square root of 2 in the real world? Is there a distinction between the physical world and the mathematical world?"
] | [
"math"
] | [
"8nsvmp"
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""
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false
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0.21
] | [deleted] | This type of thinking typically stems from the idea that the world exists on a grid of "pixels", and everything is made up of very tiny pixels. Some fixed (integer) number of pixels make up 1 foot. that were how the world worked, then you would be right that there can't be a length of sqrt(2) in nature. But all physica... | Quantum Mechanics? Yeah. That's one way to look at it. Once you get into quantum mechanics the idea of the "location" of a particle is essentially meaningless. Also again, even if you could measure lengths exactly, the idea of a length being rational or irrational is still meaningless, because it depends on the units y... | Quantum Mechanics? Yeah. That's one way to look at it. Once you get into quantum mechanics the idea of the "location" of a particle is essentially meaningless. Also again, even if you could measure lengths exactly, the idea of a length being rational or irrational is still meaningless, because it depends on the units y... | Special relativity rules out the pixel idea without resort to QM. | Not perfectly defined, I believe under current definitions a foot is defined in terms of a meter, which is in turn ultimately defined in terms of resonance frequencies in certain isotopes but these depend subtly on the environment in which the atom is placed. We can idealize to an atom existing in a perfect infinite va... |
[
"The logic of conditional statements with false hypothesis"
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"math"
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"8ntwkn"
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14
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false
] | [
0.86
] | Probably not the perfect subreddit for this question, but I couldn't find an active logic subreddit. Let's look at the following example: If 0 = 1 then 1 = 2. This statement is true by definition. But my intuition still can't really comprehend how this works. Basically my intuition is telling me that if a condition is ... | Imagine I run a bar. The inspector comes by to see if I'm following the law. He reminds me that the law states: "If someone is under 21, they must be drinking water." There's only one person inside, and they are: In which cases am I following the law? In which cases am I breaking the law? What does this tell you about ... | Look at it this way: We certainly want P⇒P, for any proposition P. If we let P be a falsehood, say 0=1, we get if 0=1, then 0=1. Still seems reasonable, I'd say. So, if (and this if is important) Q⇒R is to be a determined solely by the truth-values of Q and R, then "false ⇒ false" is inescapable. | In particular (for those that don't get it): do you need to check if the 30 year old is drinking water or alcohol, to determine if they are following the law? | The trivial ring is only ever considered so mathematicians can feel superior when someone forgets to consider it and they get to point it out | It's a somewhat odd consequence of how we want logical implication to work. In a standard P -> Q situation, all we really want is this: p is true, q is true q is false, p is false (contrapositive) as long as these two conditions are satisfied, then we're happy and we conclude that the implication is valid (true). if p ... |
[
"What skills from Calc 1 and 2 do I need a very good grasp and understanding of in order to be successful in Calc 3?"
] | [
"math"
] | [
"8nt03z"
] | [
0
] | [
""
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true
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false
] | [
0.5
] | [deleted] | You might actually try gaining some breadth at this point, as traditional Calc III rests on broader foundations, if you will. Without too much concern for mastery, perhaps try to learn some linear algebra. You could look at Treil's (and then also Axler's , if it turns out you really like linear transformations). There ... | Yup, linear algebra (at least in R2 and R3) is super helpful in understanding what's happening in Calc 3, but since Calc 1 and 2 are almost exclusively on functions mapping R -> R, you don't get much experience or familiarity with vectors. | As rodya says, pretty much everything. Differentiation, integration, vectors, graph sketching, functions, limits... | Sorry about not being clear, I'll edit it now! Thanks for the heads up!! Edit: done! | Sorry about not being clear, I'll edit it now! Thanks for the heads up!! Edit: done! |
[
"Why is the function (1)/(1+x^2) divergent?"
] | [
"math"
] | [
"8nsi2c"
] | [
6
] | [
""
] | [
true
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false
] | [
0.63
] | Apparently the sum like this: 1-x +x -x +x -x ... Is divergent when x=1, but that doesn't make sense to me because the formula for the sum of this is (1)/(1+x ) and if you plug in 1 it's just 1/2. I need like, an ELI5 because I'm really bad at math. | A function whose series converges to it is called analytic. For example the series 1 – x /2 + x /4! – ... converges to cos x with infinite radius of convergence, and therefore cos(x) is analytic everywhere on the real line. On the other hand, the series for 1/(1+x ) centered at zero is 1 – x + x – ... , which has radiu... | Indeed. This function ↦ 1/(1 + ) is analytic everywhere in the complex plane except at the poles ± . Which is to say at any point except those poles it is locally given by a convergent power series. This statement ... But 1/(1 + ) is not analytic outside the interval –1 < < 1. ... is false. | plug in 1: 1-1+1-1+1-1+... look at the partial sums: 1 = 1 1-1 = 0 1-1+1 = 1 1-1+1-1 = 0 and so on. the sum bounces back and forth between 0 and 1 forever and so the infinite sum does not have a defined UNIQUE value i.e. it does not converge (side note: 0 and 1 are called cluster points of the sequence and every conver... | I think the terminology is that ∞ is an , but not a pole, of cos(x). I think the term "pole" is reserved for values a such that 1/f(a) = 0, Or such that lim (x – a) f(x) exists for some k. So x has a pole at infinity, but not cos(x). | A nitpick, but are you sure about your definition of analytic here? |
[
"Does anyone know if 'Principles of Mathematical Analysis' by Rudin is a good book for an intro to analysis?"
] | [
"math"
] | [
"8nrz69"
] | [
0
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""
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true
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false
] | [
0.43
] | Next year i will be taking my first module in analysis on the real line and I was looking into getting a head-start on things this summer. Can anyone recommend the above mentioned book or possibly an alternative? Thanks | Check out Spivak's Calculus first. It's good preparation for Rudin. (And don't do what I did in college and get Papa Rudin by accident and then become discouraged.) | In the preface, Rudin points out with pride that the book doesn't contain a single diagram. That's a sign of how much the book values intuition. Rudin's proofs are generally short and clever; this tends to obfuscate what's going on and you can miss out on some useful techniques. On the other hand, if you've already see... | The third edition doesn't mention having no diagrams. But the book definitely could use a lot more of them. | It depends very much on your background. I thought this book (minus the last chapter or two) was great when I first read it. If you do not have much mathematical maturity you may need a more "hand-holding" type of text. Essentially, if you have zero issues reading theorems and proofs then it should be fine (challenging... | I liked the book a lot, would not consider the exposition horrible. |
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