For Teachers – Katherine E. Stange

If you use or adapt any of my resources, I would appreciate you letting me know. It makes me feel useful.

General Resources

My Resources for Students – Graduate and undergraduate.
My Experience with Standards-Based Grading
My Youtube Videos

Advice on Studying Mathematics

Proof of Concept, a blog for math majors
Homework Strategies – Advice for my students.
Textbook Strategies – Advice for my students.
Study Math by Speaking It – Study suggestions inspired by language learning.

Introduction to Graduate School

My Graduate Proof Grading Rubric – From my Algebra 1 course (intro for grad students).
Studying in Graduate School – Advice to first year graduate students.

Introduction to Proof

Intro to Proof Gradesheet – This is my grading rubric for a first proofs course.
Proof of Concept – My YouTube channel of math videos.
Why you should not use Right-Side-Left-Side – Why Right-Side-Left-Side proofs are a creation of the devil.
Handout about Writing Definitions
Worksheet to Introduce Mathematical Exploration (investigating polyhedra) and the polyhedron pictures
A first proof (if n is even, then n squared is even), and a video of me talking through it
A 2 minute video that addresses the issue of nested sets.
Set game instructions and cards (this is a card game for practicing set notation)
Worksheet on Cartesian products
Worksheet on Subsets vs. Elements
Worksheet on Setting up Contradiction
Wason Selection Task
Worksheets on negation: Negation I (shoes and hats) and Negation II (numbers) and solutions to the latter.
My video on if-then statements.
My video on the Dystopian Perspective on negation of statements, particularly if-then statements.
SPQR Logic Game (my own version): cards and instructions. Card game for practicing boolean algebra.
Basic Truth Tables for filling in, and a filled version.
Example problem on Pigeonhole
Logical Equivalence Worksheet
Four-Colour/Graph Intro Warmup
Graph Definition and Handshake Lemma
PDF Presentation of Trees having n-1 edges and my accompanying video
Proof by Contrapositive Setup Sheet and solutions
Proof by Induction Setup Sheet
Functions Worksheet (Introduction to Functions)
Proof that a function has an inverse if and only if it is bijective (with slots, and filled).
Worksheet on relations
First Counting Worksheet
Combinatorial Proof Worksheet and Solutions for First Two

LaTeX

Latex Tutorial (self-directed worksheet for all ability levels)

Cryptography

Number Theory

Sage Workshop (self-directed worksheet for an introduction to number theory)
Motivational questions in number theory (for undergrad or grad): questions and answers
Visualizations for Elementary Number Theory (Chinese Remainder Theorem, Diffie-Hellman etc.)
Worksheet on solving Linear Diophantine Equations (I advocate the “cards” method, which is a more intuitive formulation of the magic box).
Summary of Linear Diophantine Equations (via “cards”, a more intuitive formulation of the magic box for students who already know the Euclidean algorithm), and a typeset example.
Worksheet Introducing Linear Congruences
Worksheet on Modular Dynamics (discover Fermat’s Little Theorem, inspired by An Illustrated Theory of Numbers)
Axioms of the Integers
Geogebra notebook on rational rays and their relationship to Farey fractions
My Math 3110 (Introduction to Number Theory) website

Multivariable Calculus

MAA Mathematical Sciences Digital Library – I collected an extensive personal catalogue of computer demos for multivariable calculus, which was then incorporated into this digital library as part of my involvement with the project.
Math 317 Website (from when I taught at UBC; many resources incl. old exams etc.)

Linear Algebra

Linear Algebra Demo Links – Sorely out of date now.