# MA3K7 Content

**Aims**: We will examine the process of mathematical problem solving, with the use of Python as an exploratory tool. Problem-solving skills will be developed through a system of rubrics, which allow each problem to be approached systematically in distinct phases. Python will used not just as a tool to perform elaborate calculations, but also for visualisation and simulation, hence allowing each problem to be explored more freely, deeply and efficiently than the pen-and-paper approach. .

You will work both individually and in groups on mathematical problems that are challenging, unfamiliar and often open-ended. The problem-solving, critical-thinking and programming skills learnt in this course are highly desirable and transferrable, whether you go on to further study or into the job market.

**Content**: Mathematicians are used to solving problems, but few have really thought about what the problem-solving process really involves. The great mathematician George Pòlya was one of the pioneers who regarded problem solving as a subject worthy of studying on its own. He subsequently developed what he called heuristics (i.e. a recipe) for problem solving, and this was further refined by mathematicians over the past decades.

In this module, we will not only explore these problem-solving strategies in detail, but we will also learn how even a basic knowledge of Python can be used to greatly enhance these strategies and make problem solving an enjoyable and mathematically enriching experience.

Indicative syllabus:

- The phases of problem-solving according to Pólya, Mason and others

- Using Python to enhance the problem-solving phases

- Writing a problem-solving rubric

- Making conjectures and dealing with being stuck

- Justifying and convincing

- Asking question and extending a given mathematical problem

**Objectives**:

- Use an explicit scheme to organise your approach to solving mathematical problems.
- Use Python for calculations and visualisation of problems, aiding and enriching your solution.
- Critically evaluate your own problem-solving practice

**Books:**

- Mason, Burton and Stacey,
*Thinking Mathematically*, 2nd ed., Pearson (2010) - Linge and Langtangen,
*Programming for Computations - Python,*2nd ed ., Springer (2019) - Pólya,
*How To Solve It*, 2nd ed., (1990) - Grieser,
*Exploring Mathematics: Problem-Solving and Proof*, Springer (2018) - Chongchitnan,
*Exploring University Mathematics with Python,*Springer (2023)