What classes should I take as an undergrad?

[isaiahtx]

Hello! I will be attending UCSD in the fall as a freshman where I plan on majoring in pure mathematics with a minor in CS. I am looking to get some course recommendations. I want to take what will prepare me best for grad school and the classes that would benefit me most as a prospective quant.

Right now, I know I will be taking these math classes before I graduate:
31AH: Honors Linear Algebra
31BH: Honors Multivariable Calculus
31CH: Honors Vector Calculus
20D: Introduction to Differential Equations
100A: Abstract Algebra I
100B: Abstract Algebra II
100C: Abstract Algebra III
140A: Foundations of Real Analysis I
140B: Foundations of Real Analysis II
140C: Foundations of Real Analysis III

I still have 9 more upper division math classes that I need to take. These classes specifically stuck out to me as potentially useful (all classes that do not require anything beyond 31A-B-CH or 20D are listed as having no prerequisites):
102: Applied Linear Algebra - Prerequisites: None
104A: Number Theory I - Prerequisites: 100B
104B: Number Theory II - Prerequisites: 104A
104C: Number Theory III - Prerequisites: 104B
105: Basic Number Theory - Prerequisites: None
110: Intro to Partial Differential Equations - Prerequisites: None
114: Intro to Computational Stochastics - Prerequisites: 180A
130: Differential Equations and Dynamical Systems - Prerequisites: None
146: Analysis of Ordinary Differential Equations - Prerequisites: 140B
148: Analysis of Partial Differential Equations - Prerequisites: 140B
154: Discrete Mathematics and Graph Theory - Prerequisites: None
158: Extremal Combinatorics and Graph Theory (credit not offered for 154 if 158 is taken) - Prerequisites: None
170A: Introduction to Numerical Analysis: Linear Algebra - Prerequisites: None
170B: Introduction to Numerical Analysis: Approximation and NonLinear Equations - Prerequisites: 170A
170C: Introduction to Numerical Analysis: Ordinary Differential Equations - Prerequisites: 170B
174: Numerical Methods for Physical Modeling - Prerequisites: None
175: Numerical methods for Partial Differential Equations - Prerequisites: 174
180B: Intro to Stochastic Processes 1 - Prerequisites: 180A
180C: Intro to Stochastic Processes 2 - Prerequisites: 180B
182: Hidden Data in Random Matrices - Prerequisites: 180A
183: Statistical Methods - Prerequisites: None
184: Enumerative combinatorics - Prerequisites: None
188: Algebraic Combinatorics (credit not offered for 184 if 188 is taken) - Prerequisites: None
194: Mathematics of Finance - Prerequisites: 180A
To read the course descriptions and see additional courses I didn't mention: Mathematics Course Catalog

I really appreciate the help, thank you all!

 

[Qui-Gon]

In a lot of ways your course selection will depend on whether your intended grad school route is an MFE or PhD. That said, in the (pure) math realm, your Real Analysis sequence (140A-C) will be of the utmost importance. Try to take a course in functional analysis after you finish 140C, I think you'll be ripe for a measure theory-based treatment also because 140C seems to have elements of measure theory introduced. Functional analysis is the lifeblood of mathematical finance. This combined with taking your stochastic processes sequence 180B and C, and 146 (ODEs) and 148(PDEs) will leave you in a good position to begin learning stochastic analysis and subsequently mathematical finance. With this, of course you should also gain exposure to programming -- the extent to which you go is a function of what "kind" of quant you want to be -- and applied math e.g. numerical analysis, optimization, etc.

 

[Daniel Duffy]

Real and Functional Analysis are core skills.

 

[isaiahtx]

In a lot of ways your course selection will depend on whether your intended grad school route is an MFE or PhD. That said, in the (pure) math realm, your Real Analysis sequence (140A-C) will be of the utmost importance. Try to take a course in functional analysis after you finish 140C, I think you'll be ripe for a measure theory-based treatment also because 140C seems to have elements of measure theory introduced. Functional analysis is the lifeblood of mathematical finance. This combined with taking your stochastic processes sequence 180B and C, and 146 (ODEs) and 148(PDEs) will leave you in a good position to begin learning stochastic analysis and subsequently mathematical finance. With this, of course you should also gain exposure to programming -- the extent to which you go is a function of what "kind" of quant you want to be -- and applied math e.g. numerical analysis, optimization, etc.

This is perfect, and exactly what I was looking for. I just want to express how much I appreciate this response and you taking the time to look through the classes available to me for a mere internet stranger. Thanks!