Thomas Bury

Teaching Materials

Calculus

Lecture notes - for Math 127 (Fall 2018) at the University of Waterloo


Examples with guided solutions - for Math 117 (Fall 2016) tutorials at the University of Waterloo
• Inequalities, Exponentials and Logarithms, Inverses
• Composite Functions, Piecewise Functions, Partial Fractions
• Trigonometric Functions, Hyperbolic Functions
• Limits and Continuity
• Differential Calculus
• Differentials, L’Hopital’s Rule, and Curve Sketching
• Riemann Integrals, The Fundamental Theorem of Calculus and Integration Techniques
• Further Integration Techniques and Applications
• Improper Integrals, Polar Coordinates and Complex Numbers

External resources

• "Early Transcendentals" by Lyryx Learning - comprehensive open source textbook
• "Intuitive infinitesimal calculus" by Victor Blasjo - insightful, concise and packed full of intriguing examples

Stochastic processes

Miscellaneous
• Notes on extinction times and Gillespie's algorithm
• Mathematica notebook implementing Gillespie's algorithm

External resources
• "Physical Applications of Stochastic Processes" - Lecture series by Prof. V. Balakrishnan at the Department of Physics, IIT Madras.
• "Applied Stochastic Processes in science and engineering" - Lecture notes by Prof. M. Scott at the Department of Applied Mathematics, University of Waterloo.

Pedagogy

I am interested in the development of active learning techniques for undergraduate mathematics classes. Below is a literature review and perspective of cooperative learning as teaching technique in mathematics.