Undergraduate - UnitMTH2132 - The nature and beauty of mathematics

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

Synopsis

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.

Outcomes

On completion of this unit, students will have an appreciation of the beauty and the power of mathematics; understand the fundamental concepts of number theory and geometry; appreciate the notion of proof in mathematics and be able to carry out basic proofs; appreciate the historical interplay between mathematics and attempts to understand the physical world; know of some of the great unsolved problems in modern mathematics.

Assessment

Weekly problem sheets: 30%
Essay: 30%
Final exam: 40%

Chief examiner(s)

Dr Burkard Polster

Contact hours

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

Prerequisites

24 points of university studies