The below is a list of presentations appropriate for senior high school classes, in alphabetical order. If you would like us to come and give any of these presentations in your classroom for free, please use the contact form on the School Visits page.

Cryptography
Grade: 12
Why are prime numbers so important? How is our credit card information kept secret when we make purchases online? By introducing modular arithmetic we will answer these questions and look at the evolution of cryptography.
Outcomes:
 Understand the basic setting of cryptography.
 Understand why digital security is so important.
 Understand the different aspects of digital security.
 Use life knowledge to solve math problems.

Eulerian Circuits
Grade: 1011
In this talk, students will be asked to find a route through the historic city of Königsberg so that they cross every bridge exactly once. This problem spawned an area of mathematics called graph theory, which makes this problem (and many others) much easier to solve! This talk serves as a gentle introduction to graph theory and its applications.
Outcomes:
 Solve problems using graphs.
 Learn definitions involving graphs.
 Look into different types of graphs.
 Try to deduce mathematical theorems.
 Understand why graph theory is so important in real life.

Fibonacci & the Golden Ratio
Grade: 10Calculus
In this talk students discover the relationship between the Golden Ratio and Fibonacci numbers. We also learn why the Golden Ratio is found throughout nature and listen to Fibonacci number inspired music.
Outcomes:
 What can happen when you sum numbers with a certain pattern.
 Look into a spatial math sequence and a special number, that appears in nature a lot and is now used in everyday life.
 Math and art.
 Math and music.
 Count the number of solutions to a problem.

Fractals
Grade: 11Calculus
Through artwork and the self similarity of nature, we will investigate the mathematical structure of fractals. Fractals are presented through active play of the Chaos game. The class is asked to work as a team to make decisions that drive the movements of volunteers at the front of the room. The class then records this activity on their own sheets and continues the game, resulting in a fractal pattern, on their own sheets.
Outcomes:
 What is Pascal's Triangle and an application of it.
 How to construct fractals.
 Where we find fractals in nature.
 Manipulate linear and quadratic polynomials, to understand complex number computations.

Graph Colouring
Grade: 1011
This talk introduces students to graph theory. We look at the four colour problem, how graph colouring can be used to solve scheduling problems and even lead students through an activity that will classify what graphs can be coloured with 2 colours.
Outcomes:
 Solve problems using graphs.
 Look into different types of graphs.
 Try to deduce mathematical theorems.
 Understand why graph theory is so important in real life.
 Look into the known problem of map colouring.
 Applications to scheduling problems.

Infinity
Grade: 11advCalculus
While the topic of Infinity can be an intimidating one for many, the attempt was to approach it through reallife situations that are extrapolated into the infinite. We start by telling students that we have a hotel with an infinite number of rooms, and every room is full. We thenask, can we fit 1 more person? 10 more people? An infinite number of people? In this talk we explore the infinite and by answering these questions, introduce students to transfinite arithmetic
Outcomes:
 Get a better understanding of the notion of infinity.
 Look at the famous problem of Hilbert's motel.

Jury Duty
Grade: 1011
A crime has been committed! By exploring various areas of mathematics, such as logic, graph theory, geometry and more we will see if we can put the guilty party behind bars!
Outcomes:
 Use math to solve problems that seem to have unpredictable solutions.
 Attempt to think outside the box to solve math problems.
 Determine and explain strategies for solving problems or winning games.
 Understand that a problem might not have a solution and being capable of explaining why.
 Apply logic to solve problems.
 Learn how to eliminate possible solutions to a problem.
 Introduction the mathematical areas that are currently studied: graph theory, cryptography, logic, geometry, algebra and number theory.

Logic and Reasoning
Grade: 1011
In this talk we will introduce students to formal logic, apply it to some fun activities like the "wolf, goat, cabbage" problem, introduce the idea of 'proof' in a nonthreatening way and learn that math is not all numbers!
Outcomes:

Mathemagic
Grade: 1012
Can you always correctly guess someones birthday, magically untie yourself from ropes or read someones mind? You should be able to! It is not magic, it's math!
Outcomes:
 Use math to solve problems that seem to have unpredictable solutions.
 Introduction to binary representation of numbers.
 Review of mental math skills and applying these to concrete problems.
 The role of each digit in a sum.
 Factorization of large numbers.
 What can happen when you sum numbers with a certain pattern.
 Different properties of different 2D shapes.

Million Dollar Hat Problem
Grade: 1112
Suppose you are at a party and everyone in the room is randomly given a red or black hat. On the count of 3 you can either guess your hat colour or pass. If everyone who guesses their hat colour guesses correctly, you all win 1 million dollars! We will look at the mathematics behind this problem and connections it has to binary numbers.
Outcomes:
 Determine strategies to a game, and figure out the probability of winning.
 Introduction to binary numbers.
 Change the rules of addition and get interesting results.
 Use the problem to understand computer security.

Nim
Grade: 11advCalculus
The game of Nim is presented as an introduction to impartial game theory. Students enjoy the manipulation of tokens and often get so involved in the fun of “playing” that they do not realize that they are, in fact, doing mathematics. Binary notation is hidden behind the joy of problem solving.
Outcomes:
 Play games and analyze their strategies.
 Generalize solutions to a game.
 Recognize equivalent games.
 Try to deduce mathematical theorems.
 Introduce binary numbers.

Numeral Systems
Grade: 10Calculus
Take a journey that will take you to the very first systems of numerals in ancient civilizations. Learn the needs that lead the Egyptians to develop clever arithmetic methods to fill their everyday needs, the origin of our system for measuring time and much more!
Outcomes:
 Get a better understanding of the notion of infinity.
 Look at the famous problem of Hilbert's motel.

Permutations & Combinations
Grade: 1112
How many winning poker hands are there? What is the probability in a room of 25 people that two people will share the same birthday? In this talk we will explore permutations and combinations through fun problem solving activities.
Outcomes:
 Learn to count the number of possibilities for a situation.
 Understand situations where order matters and where it doesn't.
 Use counting to understand probabilities.
 Develop fast math calculation skills.

Pi
Grade: 1012
We all know Pi is the ratio of a circles circumference to its diameter and that mathematicians around the world celebrate Pi day, but why else is this number so important and interesting? In this talk we will do some activities that will generate Pi in a surprising way and see why else people love Pi
Outcomes:
 Why do we care and keep looking for pi.
 How we historically estimated pi.

Prime Numbers
Grade: 1011
Learn how ancient Greeks found prime
numbers, and how huge primes today are the
secret to internet encryption! We will learn some divisibility "tricks",
prove that there are an infinite number of primes, and explore one of the
oldest unsolved problems in mathematics: the Goldbach Conjecture!
Outcomes:
 Understand divisibility, factorization and prime numbers.
 Find solutions to problems by sieving.
 Why prime numbers are so important.

Tessellations
Grade: 1011
We will explore geometry in artwork and nature through tessellations. We will look at the work of artist who used mathematics to enhance their work and even create some of our own tessellation artwork!
Outcomes:
 Counting possible solutions to a problem.
 Finding repeated patterns.

Toads & Frogs
Grade: 10Calculus
Toads & Frogs is a game that has been utilized at Math Circles for several years. This year, we created supporting material to go handinhand with the game and revive its content. The game involves six student volunteers at the front of the room, being controlled (under game rule sets) by the rest of the class. The students making move decisions are asked one by one what move should be made next; the volunteers then make the corresponding move. Not only is this game excellent for use in classes that need an energy boost, but it also serves to get everyone involved and still allow for exploration of topics such as pattern recognition, difference sequences, solving equations using substituion and elmination and more.
Outcomes:
 Study the mathematics behind the strategies to a game.
 Introduction to polynomials.

Tower of Hanoi
Grade: 1012
The Tower of Hanoi is a very old and very popular problem, it has even been referenced in shows like Survivor and movies like Planet of the Apes. According to Ancient priests there was a temple, which contained a large room with a Tower of Hanoi with 64 golden disks. It was believed that when the last move of the puzzle is completed, the world would end!
In this talk we will explore recurrence relations and use them to solve the Tower of Hanoi problem.
Outcomes:
 Study a classical game.
 Usage of graphs to solve problems.

If there is a topic you'd like to see a presentation on, but we do not have it in our list yet, just let us know and we will create one!
Contact us for ideas on how we can best serve your needs!
Contact: Svenja Huntemann (Program Director) at mathcircles@dal.ca 