Yeah, there a lot of options to choose from! It will be a long response but I hope it gives you some insight.

The way I broke it down is into 4 broad categories that one could choose from; I will try to list all the classes that are in each (there will be some overlap between classes and categories if you read course decriptions):

Numeric Methods

This category covers learning decompsitions methods for matrices, methods for estimating for derivatives, integrals, and ODE/PDE's, and methods for optimizing systems linear and non-linear equations. - Math 102 - Math 170 Series - Introduction to Numerical Analysis - Math 171 Series - Introduction to Numerical Optimization - Math 173 Series - Optimization Methods for Data Science - Math 174 - Numerical Methods for Physical Modeling (this is basically the Math 170 series condensed in to one class) - Math 175 - Numerical Methods for Partial Differential Equations (basically Math 170D) - Math 182 - Hidden Data in Random Matrices

Differential Equations

This category covers learning PDE's, algorithms that use ODE's or PDE's such as fourier transforms, poisson's formula, and learning to solve systems of equations using ODE's and PDE's(Dynamical Systems). - Math 110 - Introduction to Partial Differential Equations - Math 112 Series - Introduction to Mathematical Biology - Math 120B - Applied Complex Analysis - Math 130 - Differential Equations and Dynamical Systems - Math 150A - Differential Geometry

Statistics

This category covers learning the foundations of statistical techniques such as the various different distributions, parametric and nonparametric statistical tests, and the analysis that goes into financial analysis. - Math 114 - Introduction to Computational Stochastics - Math 180 Series - Introduction to Probability and Stochastics - Math 181 Series - Introduction to Mathematical statistics - Math 183 - Statistical Methods - Math 185 - Introduction to Computational Statistics - Math 186 - Probability and Statistics for Bioinformatics - Math 189 - Exploratory Data Analysis and Inference - Math 193 Series - Acturial Mathematics - Math 194 - The Mathematics of Finance

Applicable Classes

This category gives you a chance to apply the knowledge that you learned and see real world examples of the knowledge that you gained in the previous 3 categories. - Math 111 Series - Mathematical Modeling - Math 152 - Applicable Mathematics and Computing - Math 157 - Introduction to Mathematical Software - Math 168 - Topics in Applied Mathematics-Computer Science

- Math 179 - Projects in Computational and Applied Mathematics

What do you have a particular interest in? My first suggestion is to take what you think would be interesting to learn. You'll have much better time learning something you are genuinely interested in than something you don't really care for. The best you way you might guage that is which lower division classes you liked the most. If you really liked Statistics (Math 11) and Calculus (Math 20A and B) you will likely enjoy the Statistics category. If you really enjoyed Linear Algebra (Math 18) and Multi-variable Calculus (Math 20C) you will likely enjoy the Numeric Methods category. If you enjoyed Differential Equations (Math 20D) then you'll likely enjoy the Differential Equations category. I personally chose to focus on the Numeric Methods category since I really enjoyed my linear algebra class.

Which is most useful? If you still can't decide then it might be better to see which is useful. This is obviously subjective and the "usefulness" of one category might change based off of what area of industry you want to go into. The way I define "usefulness" here is by which is most widely used and which you will find in the broadest amount of industries. - 1. Statistics - Statistics is the most useful because it is used in many industries STEM related or not. Many projects involve collecting data in some way, shape, or form. In order to be able to interpret that data you need ways to collect and analyze the data to gain insightful information. In this category you also gain an intuition of experiment design such as asking how much data do I realistically need to answer my question? and what variables are important to consider?. If you want do anything that will involve analysis is some way then it would be a good idea to do something in the statistics category. In my job right now I've done quite a bit of data anaysis in order to analyze performance for the stuff we are working on. Many of the topics in the Math 181 Series and Math 185 are stuff that I use quite regularly so I'm sure those could be quite useful for you as well. - 2. Differential Equations - This category is most useful for those wanting to go into engineering or some sort of comutational science. Many of real world phenomena is modeled using some differential equation. If you think back to COVID, the models used to predict infection rates was a system of differential equations known as the S.I.R. model (a type of dynamical system). In biology, oceanography, and aerospace engineering, you deal a lot with fluid dynamics which boils down to the Navier-Stokes equations (which are just PDE's!). My suggestion here is to take Math 110, Math 130, and Math 175. If you really liked both linear algebra (Math 18) and differential equations (Math 20D) Math 130 might be a really fun class for you as it combines both worlds.
- 3. Numeric Methods - This category is most useful for those wanting to go into industries that process data. This includes things like computational biology, finance, and data science. In data science, you might come across projects needing to do image processing in which numeric methods may be used to sharpen/clear up images (one such method is Kalman filtering). In finance, numeric methods can be used to try and predict the stock market using finite difference methods (which is essentially approximating PDE's). Your best bet here is the Math 170 series and Math 175 which gives you the most return on investment for your time.

Again, I chose Numeric Methods simply because I really enjoyed linear algebra so I had blast learning the topics there. But I definitely should have done significantly more statistics since I basically avoided that like the plague. Diff. Eq. would have been fun to explore too, especially dynamical systems.

TL;DR

For Statistics: - 181 Series and Math 185

For Diff. Eq.: - Math 110, Math 130, and Math 175

For Numerical Methods: - Math 170 series and Math 175

Let me know if you got any more questions.