Welcome to CM101, an introduction to what competitive mathematics is about, and how you can get started with it.

What is Competitive Mathematics?

Competitive Mathematics is an activity where participants attempt to solve mathematical problems across a wide range of topics, usually under a time limit. Usually, participants either provide answers or give complete mathematical proofs to each problem.

Many people enjoy participating in mathematics competitions for the challenging and unique problems they encounter and also for the fun of it. They are also a great practice for university maths courses, technical interviews such as for trading firms and to develop problem-solving skills more generally in real-world scenarios.

Why do Competitive Mathematics?

Competitive mathematics differs from high-school and university mathematics since the difficulty of the problems lies in the fact that known concepts must be applied in clever and unique ways to solve them, even though not a great amount of theoretical knowledge is typically required. As such, doing competitive mathematics helps develop strong problem solving skills, which are often seeked by employers (e.g. Optiver sponsors the Australian Maths Olympiad Program). Hence, it can assist in a future career that relies on mathematical ability, and more generally helps improve mathematical thinking. And of course, as mentioned earlier, it’s just plain fun!

Competitive Mathematics at UNSW

CPMSoc’s mathematics team runs regular workshops and occasional contests, suitable for all levels of students from beginner to advanced. We are always happy to give advice and help out.

The most notable university maths competition in Australia is the Simon Marais Mathematics Competition. The contests consist of two periods of exactly three hours each (including reading time), with a 90-minute break between the two sessions.

You can also sign up to various other international mathematics competition, some notable ones include International Mathematics Competition for University Students. Though the registration process will be a lot more complicated than the SMMC.

Getting started

High School CM

If you have experience with mathematics competitions in high school and scored high results in them (such as the AMC, AIMO or AMO), feel free to skip this sub-section.

If you don’t have much CM experience, trying high school contest problems, even problems in junior or intermediate levels is a great starting point. This is by no means “starting off easy” as high school problems can still challenge your skills of problem solving and thinking outside of the box. High school maths competitions typically don’t require much university level mathematics knowledge such as calculus, linear algebra or analysis. The most difficult and notable maths competition for high school students is the International Mathematical Olympiad, which is of comparable difficulty to the most notable university mathematics competition Putnam.

Some of the important topics to study after you get a hang of what mathematics competitions are like will be geometry, number theory, algebra, combinatorics etc. Check out our slides and notes!

University CM

The difference between high school CM and university CM is that university CM covers a broader area of study. University competitions may include additional topics such as calculus, linear algebra or analysis.

Non-exhaustive list of resources:

1. This is a really good book (Putnam and Beyond) to get started , and it is enough to get you to a decent level when you’ve first started.
2. Course Materials would do for Introductory level University CM too, the books mentioned in the list are complementary to the University courses.
3. A beginner recommendation will be Art of Problem Solving.
4. Once you get the beginner level stuff down you can move onto doing past papers from Putnam Archive.

Training and contests

The best way to practice is to solve problems. There maybe times that you are not making progress with your problem, however, don’t be disheartened as this is normal and to be expected, otherwise this wouldn’t be called competition!

We hope to see you at a CPMSoc workshop or event in the near future! If you have any concerns, reach out to one of us either on discord or in person!