### University Lower Division and Below

All Mathematics, Physics, Statistics, and Computer Science

### University Upper Division

#### Mathematics

##### Calculus:

Single variable, Multivariable

##### Algebra:

Linear, Abstract, Commutative, Homological

##### Number Theory:

Foundations, Modular Arithmetic, Quadratic Reciprocity, Applications to Cryptography

##### Analysis:

Real, Complex, Functional

##### Topology:

Point-set, Algebraic

##### Geometry:

Formal, Differential, Algebraic

##### Logic/Foundations:

Proofs, Mathematical Logic, Set Theory, Order Theory, Category Theory

##### Probability:

Combinatorics, Discrete Probability, Random Variables, Stochastic Processes

#### Statistics

##### Description:

Classic descriptive methods, Exploratory analysis, visualization

##### Inference:

Parametric and Non-parameteric Estimation, Hypothesis Testing, Confidence Regions, Bootstrap

##### Models and Methods:

Linear and Logistic Regression

#### Computer Science

##### Foundations^{2}:

Discrete Math, Set Theory, Proofs, Logic, Induction, Recursion, Algebraic Structures, Enumeration and Randomness

##### Programming:

Fundamentals, Functional, Object-Oriented

##### Algorithms and Data Structures:

Complexity and Asymptotic Analysis, Abstract Data Types, Searching, Sorting, Graphs

##### Languages and Tools^{3}:

Python (I), SQL (B), C++ (B), HTML & CSS (B), Git (B), Jupyter Notebook (B)

#### Machine Learning