TITLE: Which topics of mathematics should I study?
QUESTION [11 upvotes]: I'm a first year econometrics student with a great interest in mathematics. I very much enjoy my study, but still I am interested to learn about more topics in mathematics which are not part of my study. Some of the main topics which I am already familar with or which will soon be covered in my study are: calculus, linear algebra, optimization, statistics/probability/combinatorics.
Which topics in mathematics would you advise me to study still (that are not part of this list)? I have a general interest in mathematics, so any advice on interesting and or essential topics in mathematics that are worth studying is appreciated. 
If possible, could you also give me advice on books/references which I should study from?
Thanks in advance.
Edit: To be more specific, I am looking for topics on which the general consensus is that they are essential to know of for any mathematician or very interesting to study.

REPLY [7 votes]: This is a link to the Mathematics Programs offered at the University of Toronto (St. George):
http://www.artsandscience.utoronto.ca/ofr/archived/1213calendar/crs_mat.htm
If you scroll down you'll find the course requirements for "Mathematical Applications in Economics and Finance Specialist Program" which includes subjects like Real and Complex Analysis and PDE's which aren't on your list. However, if you'd like to follow the Mathematics Specialist program I could tell you which texts they use/have used for quite a few of them. A course number with a Y indicates a full year course (72 hrs of lecture) and a course number with H indicates a half year course (36 hrs of lecture):
First Year
MAT157Y1 - Analysis I
Text: Calculus by Spivak. 
Used in the past: Principles of Mathematical Analysis by Rudin.
If you have never been exposed to abstract mathematics Spivak is probably better to go with. UofT has been teaching from Spivak's for awhile now. 
MAT240H1 & Mat247H1: Linear Algebra I & II
Text: Linear Algebra by Friedberg et al.
Used in the past: Linear Algebra Done Right by Axler.
Second Year
MAT257Y1 - Analysis II
Text - Analysis on Manifolds by Munkres
Used in th past: Calculus on Manifolds by Spivak
Go with Munkres on this one. Spivak is barely a little over 100 pages in length! So you can imagine how terse it is.
MAT267H1 - Advanced Ordinary Differential Equations
Text - Differential Equations, Dynamical Systems, & Introduction to Chaos by Hirsch et al. & Elementary Differential Equations by Boyce and DiPrima
Third Year
MAT347Y1 - Groups, Rings, & Fields
Text: Abstract Algebra by Dummit and Foote
MAT354H1 - Complex Analysis I
Text: Complex Analysis by Stein & Shakarchi. 
Used in the past: Real and Complex Analysis by Rudin
MAT315H1 - Introduction to Number Theory
Text: An Introduction to the Theory of Numbers by Niven.
Used in the past: A Friendly Introduction to Number Theory by Silverman. 
MAT344H1 - Introduction to Combinatorics
Text: Applied Combinatorics by Tucker
MAT327H1 - Introduction to Topology
Text: Topology by Munkres. 
MAT357H1 - Real Analysis I
Text: Real Mathematical Analysis by Pugh. 
Used in the past: Real and Complex Analysis by Rudin.
MAT363H1 - Introduction to Differential Geometry
Text: Elementary Differential Geometry by Pressley. 
Fourth Year
A lot of these courses are cross listed so they're actually graduate courses. Check here for texts and references:
http://www.math.toronto.edu/cms/tentative-2012-2013-graduate-courses-descriptions/
Hope this helps!