MTH2132 - The nature and beauty of mathematics - 2017

6 points, SCA Band 2, 0.125 EFTSL

Undergraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.



Organisational Unit

School of Mathematical Sciences


Associate Professor Burkard Polster

Unit guides



  • First semester 2017 (Day)


This unit is intended for students with little or no mathematical background. Through the discussion of historical, practical and conceptual questions, it will emphasise the beauty and the power of mathematics. The number of topics covered will be very broad. These will include, amongst many others:

  • Symmetry (regular solids, tilings, Escher, ruler-and-compass, origami)
  • Fibonacci numbers and Golden Ratio
  • Optimal design (soap bubble maths, minimal networks)
  • Mathematical soul capturing (the maths of juggling and lacing shoes)
  • Visualising the 4th dimension
  • The shape of space (Mobius bands, Klein bottles, "pacman" spaces)
  • Infinity.


On completion of this unit students will be able to:

  1. Appreciate the beauty and power of mathematics;
  2. Understand the fundamental concepts of number theory and geometry;
  3. Understand the notion of proof in mathematics and carry out basic proofs;
  4. Appreciate the historical interplay between mathematics and attempts to understand the physical world;
  5. State some of the great unsolved problems in modern mathematics.


Weekly problem sheets: 25%

Essay: 25%

Examination: 50%

Workload requirements

Two 1-hour lectures and one 1-hour support class per week

See also Unit timetable information

Chief examiner(s)

This unit applies to the following area(s) of study


24 points of university studies