Undergraduate - UnitMTH2132 - The nature and beauty of mathematics

This unit entry is for students who completed this unit in 2013 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

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6 points, SCA Band 2, 0.125 EFTSL

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Level	Undergraduate
Faculty	Faculty of Science
Organisational Unit	School of Mathematical Sciences
Offered	Clayton Second semester 2013 (Day)
Coordinator(s)	Dr Burkard Polster

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 be able to:

Appreciate the beauty and power of mathematics;

Understand the fundamental concepts of number theory and geometry;

Understand the notion of proof in mathematics and carry out basic proofs;

Appreciate the historical interplay between mathematics and attempts to understand the physical world;

State some of the great unsolved problems in modern mathematics.

Assessment

Weekly problem sheets: 25%
Essay: 25%
Final exam: 50%

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