## What is FAM?

"FAM" is an acronym for an undergraduate course, "Foundations of Abstract Mathematics", offered by the Department of Mathematical Sciences of Stellenbosch University (FAM I and FAM II, respectively) since 2012/2011. The course consists of two year-long modules, FAM I (Mathematics 278) and FAM II (Mathematics 378), offered at the second and the third year, respectively. It is possible to enroll for only one of the two modules. Neither of the modules has any prerequisites, although note that admission to the third-year module is subject to approval by the Department of Mathematical Sciences. The course aims to let the students experience mathematical research, at the level corresponding to students' mathematical skills, and in this process, to uplift those skills.

## A bit of history

## FAM assignments

## How do students find the experience?

- Reading and understanding equations. We knew about logical operators, but now we know how to use them more effectively to get actual results. This equips one with a toolbox to use in other math modules. Reading and interpreting equations in other modules specifically.
- A philosophical look at mathematics: instead of being given a problem and asked to solve it, now we look at the mechanics of how we can solve the problem and what really encompasses mathematical activity. Comparison with language is fascinating. It is a good life skill to understand logic, which this term contributed to.
- Originally, I thought of this like every other math course: numbers and calculations. Now I view this course more as a course in logic which teaches you how to think. This was very cool, very unlike to what I have done before. Excellent pacing: it was important not to go fast to get a good understanding of what we are working on.
- This term gave me a deeper understanding of mathematics - it was not just about learning a method and solving problems. It was nice that in the beginning more emphasis was placed on effort rather than accuracy. Instead of trying to get it right, one had the opportunity to engage deeper and learn more about the subject, than in other modules where the emphasis is to learn something to get it right. In this module, you learn to understand. The focus was more on understanding concepts rather than grasping the language used to interpret the concept.
- Usually, the student is on the receiving end - now it is the student who was expected to produce a precise mathematical statement that others would be able to interpret correctly.
- The concept of breaking things down and unpacking in proofs. A cool skill to learn. Mathematics is neither invented or discovered. Mathematics is rather something that is within every human being.
- How anything can be turned into math. Mathematics can be made from a normal conversation. How to write down logical reasoning through mathematical steps.
- How mathematics is really so broad around us. I kind of new this, but I did not realise the actual broad extent if this.
- The seminar does not force you to parrot learn - it is much more understanding based. It is a nice thing that the focus is on understanding the work.
- Instead of repetitive information, the lecturer gives us information and lets us build on it while learning from each other. I wish other modules were like that too.
- This is probably the only course that brings thought into it. After the lecture, instead of being happy that the lecture is done, you are still thinking about the lecture. Assessments reflect this too. Putting in extra thought and creativity gives you marks. So assessments allow thought input. You also have the freedom to interpret things in your own way.
- This module teaches you how to formulate your thoughts and structure them in terms of assumptions and conclusions. You must think carefully and understand the process, rather than go through everything step by step or parrot learning, as is often the case in other math modules.

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