UWC Math Circle
Tuesday 3:15pm  4:30pm @ D624
The UWC Math Circle is the main mathematical learning and research community in our school (UWCSEA East). Each week, students from grades 912 gather to learn intriguing math topics and work on yearlong projects.
Sign up!
Please fill out this form to sign up for Math Circle 202223. We will get back to you within a few days.
Signups close on Saturday, September 10th, 11:59 pm.
What is Math Circle?
Each Math Circle session will be centered around a key motivating question, like "how do zip files work?" Then, in answering this question, mathematical theories and tools are introduced, like "expected values". Below are some of the topics covered in the 202223 Math Circle Syllabus.
Topics:
Can we prove that there is no riskfree strategy in the stock market/casino?

Stochastic processes & random walks

Probability spaces

Martingales

Fundamental theorem of Asset Pricing
How does raytracing work?

Trigonometry

Vectors

Dot product

Snell's law
What do quantum computers do?

Quantum algorithms

Bloch Spheres and Hilbert Spaces

Superposition and Entanglement

Quantum Machine Learning and Encryption
How do rates of reaction relate to exponential decay?

Probability density functions (PDFs)

Cumulative distribution functions (CDFs)

Memoryless property

Functional equations
How do computers learn?
How do doctors analyze data from clinical trials?

Differential calculus

Gradient Descent

Neural networks

Bayes' theorem & hypothesis testing

Regression

Least Squares

Matrices
How does the internet securely transmit information?
How do mathematicians communicate?
(great preparation for a STEM EE!)

Number theory

Publickey cryptography

RSA algorithm

The formatting language ‘LaTeX’

Math writing tips

Proof techniques
In a typical school curriculum, these topics are usually covered in IB or undergraduate classes. But that doesn’t mean much prior knowledge is needed.
Difficulty:
Each Tuesday, two Math Circle classes are held at the same time: a “core” class, and an “extension” class. They focus on the same topic, but:

The core class will be oriented around building intuition and understanding.

The extension class will go above and beyond to clarify details and build rigor.
You can choose to attend either, and switch between them anytime. So, there will always be a class suitable for your level of experience.
Projects:
In Math Circle, you also will work on a yearlong project that either:

Focuses on a particular mathematical topic you find intriguing, or

Applies your acquired knowledge to a realworld problem, such as helping your GC decide product prices.
As your project progresses, you will get additional support from the wider Project 0 Lab, such as:

Alumni & expert support

Funding (eg. for purchasing materials, software, food)
At the end of the year, you will have a chance to publish your work to our school community (through conferences, websites, science fairs), as well as exchange ideas with other students in Singapore (from Dover, SAS, SAIS…).
Your project will be a great addition to your own portfolio, which will come in handy when showcasing your passion and aptitude in STEM to others, like in university applications.
FAQs:

How will Math Circle be different from math tuition/SEAMC?

In Math Circle, there is less focus on practicing foundational skills. Instead, more emphasis will be put on exposure to new concepts and applying them. For example, when learning trig, we won’t do practice problems on calculating side lengths of triangles. Rather, we’ll learn how graphics engines use cosine to render images.

This will also allow a more diverse range of topics to be covered (than math tuition/SEAMC).


Are classes the only learning resource provided by Math Circle?

There will be a variety of other resources for each topic covered, such as:

 Accompanying slides:
 Summary notes :
 Resource compilations
 Class recordings
 Network of peers & teachers.

What’s special about the classes? Why can’t I just watch YouTube videos about those topics?

Most online resources are either overly systematic & rigorous, like MIT OpenCourseware Lectures, or too standalone & introductory, like Numberphile. The former looks like 30 hour long playlists of professors writing on blackboards, while the latter are fun bitesized videos that don't provide enough opportunities for further practice and investigation into the underlying math.

Math Circle, however, provides a balance. It presents a diverse range of topics with medium amounts of detail, which allows students to later choose particular areas to delve into deeper.

Math Circle also features a variety of other perks:

The chance to work on a yearlong project with support from experts.

Guest speakers & special exclusive events/conferences.

A variety of resources in different forms (eg. lectures, notes, videos, slides) for all types of learners.

A community of peers to discuss with.

Tons of prizefilled competitions.
