Upper Division Math Courses

Proofs-based courses for Math majors and other highly technical majors

Reading by Lecture

Book Sections Coordinated with Lecture Schedule

Topology Introduction

Open Balls are Open

Reading by Lecture

Book Sections Coordinated with Lecture Schedule

Notes: Chapter 2 Rewrite - FDVS

Revised Notes on Finite Dimensional Vector Spaces

Notes: Section 3F Rewrite - Duality

Revised Notes on Duality to Supplement Chapters 6 and 7

3F - Duality

Revised Notes on Duality to Supplement Chapters 6 and 7

SVD Example

An example of how Singular Value Decomposition works

7A - Self-adjoint and Normal Operators

Notes for Section 7A

7B - Spectral Theorem

Notes for Section 7B

7C - Positive Operators

Notes for Section 7C

7D - Isometries, Unitary Operators, and QR Factorization

Notes for Section 7D

Roots of Complex Numbers

Visualizing the Regular Polygon of Roots and Principal Roots

Limits that Do Not Exist

Figures that help demonstrate an argument from board in class

Real Powers of Complex Numbers

Real Powers of Complex Numbers and the Golden Ratio Spiral

Triangle Axiom

Constructing an Isometry given two congruent triangles