Introduction to Abstract Mathematics
This information is for the 2012/13 session.
Professor Martin Anthony, COL 3.13 and Professor Graham Brightwell, COL 3.03
This course is available to students on the following programmes: BSc Business Mathematics and Statistics, BSc Actuarial Science, BSc Mathematics and Economics, BSc Mathematics with Economics and BSc Statistics with Finance. Students on other degrees may take this course provided they satisfy the pre-requisites. Available as an outside option and to General Course students.
Students should have taken, or be taking concurrently, the course Mathematical Methods (MA100).
The course is an introduction to the use of formal definitions and proofs in mathematics, and to basic results of elementary set theory, number theory, linear algebra, algebra and analysis.
Specific topics covered are as follows: Logic, integers, sets and functions, prime numbers, relations, real and complex numbers, greatest common divisor and modular arithmetic, infimum and supremum, sequences, limits, continuity, groups and vector spaces.
40 lectures (MA103) and 20 classes (MA103.A) (for BSc Mathematics and/with Economics students: MA103.B) in MT and LT. Revision lectures in ST. 20 additional 'Extra Examples Sessions' are also available to students on this course, one hour per week in the MT and LT.
Weekly exercises are set and marked.
Students are expected to have one of the recommended textbooks: N L Biggs, Discrete Mathematics (2nd edn) or P J Eccles, An Introduction to Mathematical Reasoning. Further background reading can be found in R Allenby, Numbers and Proofs; M Liebeck, A Concise Introduction to Pure Mathematics; V Bryant, Yet Another Introduction to Analysis; R Bartle & D Sherbert, Introduction to Real Analysis and H Anton, Elementary Linear Algebra.
A three-hour formal examination in the ST (100%).