Summary report for the 2020/2021 school year
Math Circles 2020/2021 Year End Summary Report
Online Math Circles events at Dal during the 2020/2021 school year
Below is our schedule of past (virtual) events at Dalhousie for the 2020/2021 school year.
October 28
Speaker: Justin Makary (Dalhousie University)
Topic: Wonders of the Infinite
The concept of infinity has both interested, and bewildered mathematicians over the course of history.
We explore some interesting properties of infinity that are not so obvious.
For example, a hotel with infinitely many rooms all which are filled, can still accommodate new guests (Known as Hilbert's Hotel). A lab with infinitely many monkeys typing on keyboards,
would eventually produce all of the works of Shakespeare. We consider these interesting properties through the use of examples, in an interactive work session.
November 25
Speaker: Tom Potter (Dalhousie University)
Topic: Interactive Problem Solving
Problem solving is central to mathematics. In this presentation we will interactively tackle a series of fun problems,
and students will be encouraged to attempt their own solutions and share their ideas with us.
We will also very briefly discuss the recent history of approaches to problem solving, including concepts like: can you become a better problem solver?
what are common pitfalls? what constitutes a real problem? and what about problem posing?
These problems will be geared toward a junior high level audience. Have your pencil and paper ready!
December 16
Speaker: Heesung Yang (Dalhousie University)
Topic: Pascal's Triangle
Pascal's triangle is an array of numbers arranged in a triangular shape which, upon closer inspection, contains fascinating patterns.
In this presentation we will explore what information Pascal's triangle contains and discover that it has connections to combinatorics ("art of counting"),
number theory, geometry and even fractals.
We will end with an idea that seems true, intuitively, but is surprisingly not yet proven.
January 27
Speaker: Sarah Meng Li (Dalhousie University)
Topic: Logic and Puzzles
In school, we learned that math is a set of rules, and we were trained to become human calculators.
Admittedly, number sense is important, but math is not just computation. Mathematical thinking is a way of observing and understanding the world.
Math allows us to see hidden order in real world chaos!
This workshop will introduce you to another aspect of Mathematics, logic.
We will show you how to use mathematical thinking to solve problems, identify the hidden patterns, and think like a mathematician.
From solving math puzzles, you will develop your logical reasoning and critical thinking skills.
February 24
Speaker: Dr. Frank Fu (Dalhousie University)
Topic: Fun with Cryptography
How do we communicate through the internet without being eavesdropped?
How can we login to a remote computer without using a password? How does the remote computer know it is really me?
In this talk, we will learn a few cryptographic concepts and encryption methods.
Hopefully, by the end of the talk, we gain some insights into how modern cryptography is safegarding the digital world.
March 31, 7-8pm
Speaker: Dr. Asmita Sodhi (Dalhousie)
Topic: Exploding Dots
Imagine you have constructed a curious mathemagical machine, which consists of several boxes in a row.
When you put one dot in the first box, nothing happens.
But when you add another dot to the box... BOOM! These two dots explode, and form a new dot in the second box.
When we put a second dot in that box to join the first... BOOM! These dots explode too, and form a new dot in the third box.
What will happen if we make some changes to our machine, so now we need to add three dots for an explosion? Or more?
What mathematics can we learn from this strange machine?
In this talk, we'll learn about different ways of counting and arithmetic ideas while playing with Exploding Dots.
This talk will make use of the online Mathigon Polypad so that you can interact with the dots yourself.
If you can, please make sure you can either access the Polypad from the same device you're using to join the talk, or a different one!
Links to pre-made Polypads to play on will be shared during the talk.
April 28, 7-8pm
Speaker: Dr. Matthew Amy (Dalhousie)
Topic: The Secret of Nim
Can mathematics help us to win games? Quite unlike the NIMH from the 1980's animated fantasy film after which this workshop is named, Nim is an ancient game with a deep mathematical theory.
In this workshop we will explore the game of Nim and learn to use the mathematics of binary numbers to outsmart our opponents.
Next we will look at the even more devious hat game where we can stack the odds in our favour, again through the magic of binary numbers.
Finally, we will learn how these principles are used to protect our precious data from harmful rays of sunlight and other sources of errors.
May 26, 7-8:30pm
Speaker: Sarah Li (Dalhousie)
Topic: Math and Coding
Believe it or not, coding is full of math. In real life, coding is used to implement an algorithm,
a recipe to solve a logical and mathematical problem. But coding can do more than that. It is an engaging way to learn math and it
will help you develop an intuition for abstract theories.
In this workshop, let's think and experience math in a hands-on, dynamic, and engaging way!
You will soon be amazed by the project you have developed with your friends and how much you have learned from it.
We will use Scratch, a block-based visual programming language and website developed by MIT Media lab.
On this platform, you will develop your first Scratch project such as
Lattice Multiplication, Calculator, Geometric Kaleidoscope, and Drawing Shape with Math.
You can even program an interactive animation to teach some interesting math problems.
At the end of the workshop, you are welcomed to share your work. If you wish, you could also share it on the Scratch platform with people around the world!
June 9, 7:00 - 8:30pm
Speakers: Sarah Li and Mozhgan Saeidi (Dalhousie)
Topic: Problem Solving with Algorithms
Abstract: An algorithm is a series of step-by-step instructions to carry out a task or solve a problem. For example, a cake recipe is an algorithm to make a cake.
At school, you have learned algorithms such as the procedures for adding, subtracting, multiplying, and dividing numbers.
You could also observe more algorithms in everyday life!
Beyond just solving a problem, we always hope to optimize ways to get to the answers. Algorithmic thinking allows us to resolve a problem creatively, and math helps us design efficient algorithms.
In this workshop, you will see some interesting and well-known problems about graph coloring, numbers, and computing.
Then we will navigate the algorithmic approach to tackle these problems!
Tentative itinerary:
- Divide-and-conquer algorithm
- Four-colourability of the world map [7:00 ~ 7:30]
- Circular maximum sum subarray problem. [7:30 ~ 7:45]
- Euclidean algorithm
- Continued fractions [7:45 ~ 8:00]
- Karatsuba's algorithm
- Multiplication of integers [8:00 ~ 8:20]
- Lattice multiplication [8:20 ~ 8: 35]
Topic Ideas?
If you have a request for topics, please contact us. If you have a topic or idea that appeals to you, let us help you explore it! Email our team at mathcircles@dal.ca and we will work it into our repertoire.
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