M1F: Foundations of Analysis Clore Lecture Theatre, M 2-3, T 4-5, Th 9-10 Problem classes: M 3-4, Huxley 340, 341, 342 Department: Mathematics Office: Huxley 668. Office Hours: M 5-6pm.

News Third assessed coursework is due on Wednesday December 5th at noon. General department information about the arrangements for assessed coursework: Page 1, Page 2, Page 3.

Homework Assignments Problem sheet 1. Reading: Liebeck Chapters 1 and 2 Solutions to problem sheet 1. Problem sheet 2 (First assessed coursework due noon Friday Oct 26th). Reading: Liebeck Chapter 2, 3, and 4 Solutions to problem sheet 2. Problem sheet 3. Reading: Liebeck Chapters 4, 5 and 6 Solutions to problem sheet 3. Problem sheet 4. Reading: Liebeck Chapters 6 and 7 Solutions to problem sheet 4. Problem sheet 5 (Second assessed coursework due noon Weds Nov 14th). Reading: Liebeck Chapter 8 Solutions to problem sheet 5. Problem sheet 6. Reading: Liebeck Chapters 11 and 12 Solutions to problem sheet 6. Problem sheet 7. Reading: Liebeck Chapters 13 and 14 Solutions to problem sheet 7. Problem sheet 8 (third and final assessed coursework due noon Weds Dec 5th). Reading: Liebeck Chapter 10 Solutions to problem sheet 8. Problem sheet 9. Reading: Liebeck Chapters 18, 19 and 20 Solutions to problem sheet 9. Problem sheet 10. Reading: Liebeck Chapters 17, 20 and 22 Solutions to problem sheet 10.

About the course First Day Handout

Texts Martin Liebeck: A Concise Introduction to Pure Mathematics, Chapman & Hall.

Syllabus The official syllabus for the course can be found in the First Year Course Guide which also gives information about exams and marking. A more detailed syllabus will be given below as we progress through the course. WEEK DATES TOPICS READING 2 Oct 8-12 Sets and Proofs Chapter 1 3 Oct 15-19 The Real Numbers: Rationals, Irrationals and Decimals Chapters 2 and 3 4 Oct 22-26 The Real Numbers: Inequalities, nth roots and rational powers. Complex numbers. Chapters 4, 5, 6 5 Oct 29-Nov 2 Complex numbers: De Moivre's Theorem and applications, exponential notation, nth roots of unity, the Fundamental Theorem of Algebra, relations between roots. Chapters 6, 7 6 Nov 5-Nov 9 Induction. Chapter 8 7 Nov 12-Nov 16 The integers: Euclid's algorithm, highest common factor, the Fundamental Theorem of Arithmetic. Chapters 11,12 8 Nov 19-Nov 23 Congruence of integers. Chapters 13,14 9 Nov 26-Nov 30 Greatest lower bounds, least upper bounds and nth roots. Chapter 10 10 Dec 3-7 More set theory: unions, intersections, cartesian products, subsets of finite sets, equivalence relations. Functions. Chapters 18, 19, 20 11 Dec 10-14 Countable and uncountable sets. Counting: binomial coefficients, binomial theorem and multinomial coeffiecients and theorem. Chapters 17, 20, 22

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