Mathematics · Columbia University
Mathematical reasoning, linear algebra from an abstract point of view, emphasis on proofwriting
SURFACE, TANGENT PLANE, VECTOR, LINEAR TRANSFORMATION ...
eh, general topology and some abstract topology I guess.
Linear algebra, logical equivalencies and manipulations, and proof writing skills/strategies.
Parametric curves, partial derivatives, differential, dot/cross product, continuity, differentiability, matrix operations, linear functions, tangent planes to surface, lagrange multiplier
Point-set topology and basics of more advanced topology
How to write proofs and linear algebra in a very abstract sense.
Planes, partial derivatives, matrix multiplication, multi-variable chain rule, second partials, etc.
Topological spaces, Continuous functions on topological spaces, Point-set topology, Compactness, Hausdorff spaces, Homeomorphisms, Algebraic topology, Topological groups, Homotopy, Manifolds, Classification of surfaces, Topological gluing, some Geometric topology Skills developed: Geometric intuition, Translating pictures into proofs, Mathematical exposition (through final project)
The basics of propositional logic, how to construct rigorous arguments about sets and functions, and how to utilize basic concepts of linear functions to arrive at increasingly interesting results (basis sets are OP).