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Prof Peter Allen and Dr Emilio Pierro

This course is compulsory on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. This course is available on the BSc in Actuarial Science, BSc in Business Mathematics and Statistics, BSc in Data Science and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission 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, sets and functions, relations, real numbers, infimum and supremum, sequences, limits and continuity, integers, prime numbers, greatest common divisor and modular arithmetic, complex numbers, groups and vector spaces.

This course is delivered through a combination of classes and lectures totalling a minimum of 80 hours across Michaelmas Term and Lent Term.

Students will be expected to produce 20 problem sets in the MT and LT.

Written answers to set problems will be expected on a weekly basis.

Students may wish to have one of the recommended textbooks: N L Biggs, Discrete Mathematics (2nd edn) or P J Eccles, An Introduction to Mathematical Reasoning, but these are not required. 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.

Exam (90%, duration: 3 hours) in the summer exam period.
Continuous assessment (10%) in the MT and LT.