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Introduction to Probability

Introduction Computing Probabilities Probability Trees Venn Diagrams

Chaos Theory

Introduction Mathematical Billiard The Three Body Problem Phase Space and Strange Attractors The Logistic Map

Circles and Pi

Introduction Degrees and Radians Tangents, Chords and Arcs The Circle Theorems Cyclic Polygons Spheres, Cones and Cylinders Conic Sections

Codes and Ciphers

Introduction Binary Numbers Error Detection Secret Codes The Enigma Public Key Cryptography

Combinatorics

Factorials Permutations Combinations

Complex Numbers

Introduction Complex Arithmetic Euler’s Formula Solving Polynomials De Moivre’s Theorem and Roots of Unity

Data and Statistics

Introduction Center and Spread Visualising Data Sampling Scatter Plots and Linear Models

Divisibility and Primes

Factors and Multiples Divisibility Rules Prime Numbers The Distribution of Primes Lowest Common Multiples Greatest Common Factors

Euclidean Geometry

Introduction Euclid’s Axioms Ruler and Compass Construction Even More Constructions Angles and Proofs Origami and Paper Folding

Exploding Dots

Staircase to Infinity Unusual Numbers P-adic Numbers

Exponential Functions

Carbon Dating Exponential Growth and Decay Comparing Models Compound Interest Population Dynamics

Fractals

Introduction The Sierpinski Triangle The Mandelbrot Set Space Filling Curves

Functions

Relations and Functions Graphing and Interpreting Functions Piecewise Functions Absolute Value Functions Inverse Functions Rates of Change

Game Theory

The Prisoners’ Dilemma Cards, Coins and Dice The Winning Move Random Walks

Graphs and Networks

Introduction The Bridges of Königsberg Handshakes and Dating Planar Graphs Map Colouring The Travelling Salesman Problem Scheduling Problems Graphs in Everyday Life

Linear Functions

Input, Output and Graphs Slope and Intercept Parallel and Perpendicular Lines Systems of Equations

Logic, Sets and Proof

Logic and Paradoxes Axioms and Proof Proof by Induction Infinity and Hilbert’s Hotel

Matrices

Transformations Matrix Arithmetic Determinants Matrix Inverses Cramer’s Rule and Gaussian Elimination Eigenvalues and Eigenvectors

Non-Euclidean Geometry

Spherical Geometry Map Projections Hyperbolic Geometry Metric Spaces Topology Higher Dimensions

2D Shapes and Perimeter

Introduction Attributes of 2D Shapes Using Attributes of 2D Shapes to Find Perimeter Relating Perimeter and Area

Angles and Polygons

Angles Angles in Polygons Drawing Triangles Pythagoras’ Theorem The Coordinate Plane Transformations and Congruence

Polygons and Polyhedra

Polygons Quadrilaterals Tessellations Polyhedra Nets and Cross Sections Platonic Solids

Probability

Introduction Probability Trees and Venn Diagrams Conditional Probability The Monty Hall Problem The Birthday Problem True Randomness

Quadratic Equations

Introduction Binomial Expressions Solving Quadratic Equations The Quadratic Formula Graphing Quadratics Projectile Motion More Applications

Sequences and Patterns

Introduction Arithmetic and Geometric Sequences Figurate Numbers Sequences as Functions Fibonacci Numbers Special Sequences Pascal’s Triangle Limits and Convergence

Area and Shapes

Introduction Parallelograms Triangles Polygons Circles and Circumferences Area of Circles

3D Solids

Introduction Nets and Surface Area Prisms and Pyramids Cylinders and Cones Spheres

Statistics and Data

Casino Mathematics Data Visualisation Center and Spread of Data Sampling and Estimation The Wisdom of Crowds Linear Models

Talks and Workshops

MoMath Workshop NCTM 2021 Alex Kontorovich

Transformations and Symmetry

Introduction Rigid Transformations Congruence Symmetry Symmetry Groups and Wallpapers Symmetry in Physics Dilations Similarity

Triangles and Trigonometry

Introduction Properties of Triangles Midsegments and Similarity Triangle Congruence Pythagoras’ Theorem Isosceles and Equilateral Triangles Trigonometry Sine and Cosine Rules

Vectors

Introduction Vector Arithmetic Scalar Products and Equations of Planes Cross Products and Equations of Lines Geometry Problems