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Math Circle Presentations

Math Circles is a weekly enrichment activity for grade 6 to 12 students organized by the Faculty of Mathematics of the University of Waterloo.

Information about the audience, dates and location.

Listed below are summaries of previous weekly presentations and related student exercises for the Grade 11/12 classes. These resources are provided for both students and teachers. Please use them!

Grade 11/12


Fall 2022 Winter 2023
Special Relativity 1 [pdf]
Special Relativity 2 [pdf]
Special Relativity 3 [pdf]
The Mathematics of Climate Change 1 [pdf, solns]
The Mathematics of Climate Change 2 [pdf, solns]
The Mathematics of Climate Change 3 [pdf, solns]
The Mathematics of Climate Change 1,2,3 [slides]
Generating Functions 1 [pdf, prob set, solns]
Generating Functions 2 [pdf, prob set, solns] 		The Insolvability of the Quintic 1 [prob set, solns]
The Insolvability of the Quintic 2 [prob set, solns]
The Insolvability of the Quintic 3 [prob set, solns]
Dynamical Systems and Fractals 1 [pdf, prob set, solns]
Dynamical Systems and Fractals 2 [pdf, prob set, solns]
Introduction to Machine Learning 1 [pdf, prob set, solns]
Introduction to Machine Learning 2 [pdf, prob set, solns]
Introduction to Machine Learning 3 [pdf, prob set, solns]

Fall 2021 Winter 2022
Game Theory [pdf, solns]
Game Theory II [pdf, solns]
Irrationality [pdf, solns]
Transcendental Numbers [pdf, solns]
Circles, Ellipses and Astrophysics I [pdf, solns]
Circles, Ellipses and Astrophysics II [pdf, solns] 		Cryptography I [pdf, prob set, solns]
Cryptography II [pdf, prob set, solns]
Cardinality I [pdf, prob set, solns]
Cardinality II [pdf, prob set, solns]

Fall 2020 Winter 2021
Polar Coordinates [pdf, solns]
Crocodiles [pdf, solns]
Polar Curves [pdf, solns]
Mathematical Games [pdf, solns]
Partitioning Puzzles [pdf, solns]
Dwellings with Many Doors [pdf, solns] 		Symmetrical Equations [pdf, solns]
Proof by Contradiction [pdf, solns]
Trugs and Falths [pdf, solns]
Greedy Algorithms [pdf, solns]
Comparison Machine [pdf, solns]
Silly Square Roots [pdf, solns]

Fall 2019 Winter 2020
Graph Theory I [pdf, solns, video]
Graph Theory II [pdf, solns, video]
Graph Theory III [pdf, solns, video]
Number Theory I [pdf, prob set, solns, video]
Number Theory II [pdf, prob set, solns, video]
Number Theory III [pdf, prob set, solns, video]
Mathematics of Climate Change I
[pdf, prob set, solns, video]
Mathematics of Climate Change II
[pdf, prob set, solns, video]		 Axioms and Sets I [pdf]
Axioms and Sets II [pdf, solns]
Axioms and Sets III [pdf]
Special Relativity I [pdf, slideshow]
Special Relativity II [pdf]
Special Relativity III [pdf, slideshow]

Fall 2018 Winter 2019
Games & The Mathematical Process I [pdf, video]
Games & The Mathematical Process II [pdf, video]
Games & The Mathematical Process III [pdf, video]
Algebraic Number Theory I
[pdf, prob set, solns, video]
Algebraic Number Theory II
[pdf, prob set, solns, video]
Algebraic Number Theory III
[pdf, prob set, solns, video]
Cellular Automata I [pdf, prob set, solns, video]
Cellular Automata II [pdf, prob set, solns, video]
 Euclidean Geometry I [pdf , video]
Euclidean Geometry II [pdf , video]
Order Chaos I [pdf, video]
Order Chaos II [pdf, prob set, video]
Groups I [pdf, prob set, solns, video]
Groups II [pdf, prob set, solns, video]
Groups III [pdf, prob set, solns, video]

Fall 2017 Winter 2018
Logic I [pdf, prob set, solns, video]
Logic II [pdf, prob set, solns, video]
Logic III [pdf, prob set, solns, video]
A Brief History of Math I [pdf, prob set, solns, video]
A Brief History of Math II [pdf, prob set, solns, video]
A Brief History of Math III [pdf, prob set, solns, video]
Set Theory I [pdf, prob set, solns, video]
Set Theory II [pdf, prob set, solns, video]
Primes I [pdf, solns, video]
Primes II [pdf, solns, video]
Cryptography I [pdf, prob set, solns, video]
Cryptography [Bridges Lecture video]
Cryptography II [pdf, prob set, solns, video]
Complex Numbers I [slides, slide solns, video]
Complex Numbers II [slides, slide solns, video]
Complex Numbers III [slides , video]

Fall 2016 Winter 2017
Forecasting [pdf, prob set, solns, video]
Statistics [pdf, prob set, solns, video]
Compound Interest [pdf, prob set, solns, video]
Optimization I [pdf, prob set, solns, video]
Optimization II [pdf, prob set, solns, video
Optimization III [pdf, prob set, solns, video
Number Theory I [pdf, prob set, video]
Number Theory II [pdf, prob set, solns, video] 		Special Relativity I [pdf, prob set, video]
Special Relativity II [pdf, solutions, video]
Special Relativity III [pdf, solutions, video]
Geometry I [pdf, prob set, solutions, video]
Geometry II [pdf, prob set, solutions, video]
Graph Theory I [pdf, prob set, solutions, video]
Graph Theory II [pdf, prob set, solutions, video]
Graph Theory III [pdf, prob set, solutions, video]

Fall 2015 Winter 2016
Sets & Languages
[pdf, prob set, solns, slideshow, video]
Regular Languages
[pdf, prob set, solns, slideshow, video]
Beyond Regular Languages
[pdf, prob set, solns, video]
Congruent Number Problem
[pdf, prob set, solns, slideshow, video]
Curves I [pdf, prob set, solns, slideshow, video]
Curves II [pdf, prob set, solns, slideshow, video]
Conics & Applications I [pdf, prob set, solns, video]
Conics & Applications II [pdf, prob set, solns, video] 		Surfaces [pdf, prob set, solns, video]
Surfaces 2 [pdf, prob set, solns, video]
Surfaces 3 [pdf, prob set, solns, video]
Patterns in Words 1 [pdf, prob set, solns, video]
Patterns in Words 2 [pdf, solns, video]
Patterns in Words 3 [pdf, solns, video]
Complex Numbers [pdf, prob set, solns, video]
Complex Numbers & e [pdf, prob set, solns, video]

Fall 2014 Winter 2015
Number Theory I [pdf, prob set, solns]
Number Theory II [pdf, prob set, solns]
Number Theory III [pdf, prob set, solns]
Recurrences I [pdf, prob set, solns, slideshow]
Recurrences II [pdf, prob set, solns, slideshow]
Recurrences III [pdf, prob set, solns, slideshow]
Optimization & OR I [pdf, prob set, solns, slideshow]
Optimization & OR II [pdf, prob set, solns, slideshow] 		Group Theory I [pdf, prob set, solns]
Group Theory II [pdf, prob set, solns]
Group Theory III [pdf, prob set, solns]
Game Theory I [pdf, prob set, solns]
Game Theory II [pdf, prob set, solns]
Game Theory III [pdf, prob set, solns]
Paradoxes [pdf, prob set, solns]
Infinite Series [pdf, prob set, solns]

Fall 2013 Winter 2014
Problem Solving I [prob set, solns, slideshow]
Problem Solving II [prob set, solns, slideshow]
Problem Solving III [prob set, solns, slideshow]
Surfaces I [pdf-combined, prob set I , solns]
Surfaces II [prob set II, solns]
Surfaces III [prob set III, solns]
Sequences and Series I [pdf]
Sequences and Series II [pdf]		 Cryptography I [pdf, solns]
Cryptography II [pdf, solns]
Cryptography III [pdf, solns]
Linear Recurrence Relations [pdf, solns]
Linear Recurrence Relations II [pdf, solns]
Linear Recurrence Relations III [pdf, solns]
Math Modeling [pdf]

Fall 2012 Winter 2013
Basics of Set Theory [pdf]
Infinite Sets [pdf, prob set]
Equivalence Relations and Infinite Sets [pdf, prob set]
Symbolic Logic I [pdf, prob set, solns]
Symbolic Logic II [pdf, prob set, solns]
Mathematical Induction [pdf, prob set, solns]
Iterated Functions I [pdf, prob set]
Iterated Functions II [pdf, prob set]		 Inversive [pdf, prob set]
Inequalities [pdf, prob set, solns]
Graph Theory I [slides, prob set, solns]
Graph Theory II [slides, solns]
Graph Theory III [pdf]
Number Theory [pdf, solns]

Fall 2011 Winter 2012
Finite Machines [pdf, prob set]
Regular Languages [pdf, prob set]
Regular Languages & Beyond [pdf, prob set]
Geometry I [pdf]
Geometry II [pdf]
Geometry III [pdf]
Solid Geometry I [pdf]
Solid Geometry II [pdf, solns]		 Combinatorics [pdf]
Combinatorics II Set Theory [pdf]
Combinatorics III [pdf, solns]
Probability, Statistics, and Bayes' Theorem I [pdf]
Probability, Statistics, and Bayes' Theorem II [pdf]
Probability, Statistics, and Bayes' Theorem III [pdf]
Elementary Knot Theory [pdf]

Fall 2010 Winter 2011
Induction and Sequences I [pdf, tutorial]
Limits of Sequences I [pdf]
Limits of Sequences II [pdf]  
Series [pdf]
Linear Programming I [pdf]
Linear Programming II [pdf]
Length, Area & Volume [pdf, problem set]		 Probability I [pdf, prob set]
Probability II [prob set]
Number Theory I [prob set]
Number Theory II [prob set]
Number Theory III [prob set]
Invariants I [prob set]
Invariants II [prob set]

Fall 2009 Winter 2010
Infinite Series I [pdf]
Infinite Series II [pdf]
Infinite Series III [pdf]
History of Equations I [pdf]
History of Equations II [pdf]
History of Equations III [pdf]
Graph Theory I [pdf]
Graph Theory II [pdf] 		Game Theory I [pdf]
Game Theory II [pdf]
Game Theory III [pdf]
Probability and Expectation [pdf]
Counting Techniques and Probability [pdf]
Distribution and Probability [pdf]

Fall 2008 Winter 2009
Number Theory I [pdf]
Number Theory II [pdf]
Number Theory III [pdf]
Trigonometry I [pdf]
Trigonometry II [pdf]
Trigonometry III [pdf]
Probability I [pdf]
Probability II [pdf]		 Conics I [pdf]
Conics II [pdf]
Conics III [pdf]
Geometry I [pdf]
Geometry II [pdf]
Geometry III [pdf]
Equations [pdf]


Previous Weekly Presentations and Related Student Exercises


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