MATU9KC - Special Topics II

SCQF Level: 10
Availability: Spring, Advanced module
Course Prerequisite: MAT9K4
Credit Value: 20 (1 module)

Aims

The first part of this module introduces students to conics and transformations. The second part describes the fundamental concepts underlying the construction of number systems.

Learning Outcomes

Students should be able to recognize circles and conics, and interpret linear fractional transformations. They should understand how the different number systems can be constructed, and be able to prove properties of these systems.

Content

A1: Circles and conics.
A2: Transformations.
A3: Inversion in a circle.
B1: Sets, relations, functions, axiomatic systems.
B2: Construction of the natural numbers, the integers, the rationals, the reals and the complex numbers.
B3: Countability, cardinality, Schroder-Bernstein theorem.

Transferable Skills

Logical thinking.

Bibliography

D.A.Brannan, M.F.Esplen and J.J.Gray , "Geometry", CUP 1999.
I. Stewart and D. Tall, "The Foundations of Mathematics", OUP, 1977.

Teaching Format

3 one-hour lectures and a 1 hour tutorial per week.

Assessment

1/3 coursework and 2/3 examination.

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