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Favorite things I learned from each course

First Year

• MAT157: Calculus from scratch, starting from axioms of ordered field satisfying least upper-bound property.
• MAT240/7: Vector spaces.
• CSC148: Basic python and how to think about recursion.
• CSC240: Regular languages and how to prove programs correct.
• MAT327: Topological spaces.
• MAT315: Natural numbers.

Second Year

• MAT257: Multivariable calculus and Stoke's theorem on submanifolds of Rn
• MAT267: Uniqueness and existence of solutions to ODEs.
• MAT309: Completeness and incompleteness of FOL, along with some model theory.
• MAT347: Groups, rings, and modules.
• CSC265: Designing data structures is hard.
• CSC463: Turing machines.
• STA257: Probability spaces.

Third Year

• MAT409: Some basic set theory, infinite combinatorics, and something about forcing.
• MAT354: Holomorphic functions.
• MAT482: Fast Fourier Transform and Rabin-Miller.
• MAT357: Metric spaces and Lesbegue integration.
• MAT367: What an abstract manifold is and how to integrate/differentiate on it.
• MAT495: BPP and the PCP theorem.
• CSC373: Greedy, dynamic programming, and approximation algorithms.
• CSC448: Context-free language and Turing machines.
• PHL354: Structualism, Quine, and fictionalism.
• CSC324: Recursion and semantics of programming languages.

Fourth Year

• MAT457: Measures, integration, some basic things about Banach spaces.
• CSC369: Operating systems: memory management, file systems, scheduling.
• APM461: Probabilisitic method, linear algebra method, and brutally estimating quantities using concentration inequalities.
• MAT495: Back and forth constructions, daily application of the compactness theorem, stability theory.