Mathematics Workshop: the Art of Discovery

Mate Balogh, Oliver Janzer and Peter Simon

MathsMathematics is arguably the greatest human invention. It is the oldest formalised science, and the best practitioners of this purest form of thought have become towering figures whose achievements shine through the centuries. The same exhilaration can be shared by the most humble students, if they are allowed to roam free and unconstrained in multiple planes of thought that are opened up in front of them by their own creative thinking. Unimpeded by the cruel reality of the world, the intellectual experience that mathematics offers nevertheless conditions the mind, and prepares it well for the occasional giant leap in all other walks of life.

This intensive “practical” course revolves around problem solving and both playing and analysing mathematical games in the areas of number theory, geometry, combinatorics and graph theory. Topics include infinities, algorithms, existence and non-existence results.

This course is aimed at: Non-mathematicians who nevertheless have a strong interest in problem solving, logical and creative thinking, games and puzzles.

Pre-requisite knowledge required:The course has no pre-requisite requirements beyond an interest in problem solving and creative thinking. It is, however, recommended that students familiarise themselves with the general topics and principles of mathematics before beginning the course.

Transferable knowledge and skills:You will develop problem solving skills, inductive and deductive thinking processes. You will learn how to analyse models and theories, evaluate mathematical hypotheses and develop analytical skills that will be valuable in many walks of life. An understanding of these principles of mathematics will be of great use to anybody interested in the fields of natural sciences, medicine, economics, engineering and technology.

Teaching Methodology: Continuing guidance is given by Cambridge scholar Mate Balogh, who has had first-hand experience in such “discovery-based” learning in Hungary, where this style of teaching has a long tradition. The approach is unique and different from the usual style of mathematics teaching in that students discover most of the results themselves, while the guides (elsewhere known as teachers) help connect the dots and draw the big picture that relates the various topics together.

Assessment

Participation: 20%

Exam: 80%

The Mathematics Workshop is a non-standard course, i.e. its teaching schedule does not fit within any of the standard modular timetable groups and, because of this, is subject to the bespoke course combination constraints outlined below.

The Mathematics Workshop takes place within Module 1, but unlike the standard Module 1 courses it is timetabled between Saturday 9 and Saturday 16 July 2016 (inclusive), with the exam on Wednesday 20 July 2016.

For timetabling reasons, students taking this course cannot also choose:

  • A Module 1 Yellow timetable group course in combination with a Module 3 Green timetable group course
  • A Module 1 Blue timetable group course in combination with a Module 3 Orange timetable group course
  • A Module 1 Pink timetable group course in combination with a Module 3 Maroon timetable group course