Here is the official site from the department.

Time and place: Mon 11-12 in MS.01; Tue 17-18 in MS.01; Thu 16-17 in MS.02.

* Review session * Friday 8 January 2-3pm in MS.01.
The common exam Analysis/Foundations will take place Monday 11 January 1:30-5pm (I think!)

Assessment: Material from this half of the course is examined in the first week of Term 2, probably Monday.

Description:

• Inequalities: rules for manipulating inequalities; inequalities and powers; inequalities and absolute values; Bernoulli's inequality; triangle inequality.

• Sequences: monotonic sequences; bounded sequences; subsequences; tending to infinity; null sequences (and algebra of); convergent sequences (and algebra of, boundedness, uniqueness of limit); sandwich theorems; shift rules; standard limits; ratio test; limits and inequalities; recursively-defined sequences.

• The real numbers: infinitely many rationals/irrationals in any open interval; rationals/irrationals and terminating/recurring/non-recurring decimals; numbers with more than one decimal representation; sets and upper/lower bounds; supremum and infimum; completeness axiom (in the form "every non-empty set bounded above has a supremum"); consequences of completeness; existence of k-th roots; Bolzano-Weierstrass theorem; Cauchy sequences (contracting sequences as example).

• Series: partial sums; convergence and divergence; sum rule; shift rule; null sequence test, epsilon as a series and the limit of a sequence.

  • Series with positive terms: boundedness condition, comparison tests, ratio test, integral test.
  • Alternating series: alternating series test, absolute convergence, absolute value form of ratio test, conditional convergence, rearrangements.

Module material:

Here are lecture notes. This is a draft, expect many modifications before the end of the term!
I occasionally put comments on my facebook page; but anything of importance can also be found here.

• Week 1, assignment (due 12 October)

• Week 2, assignment (due 19 October)

• Week 3, assignment (due 26 October)

• Week 4, assignment (due 2 November)

• Week 5, assignment (due 9 November)

• Week 6, assignment (due 16 November) Problems 1, 2, 3, 7 only!

• Week 7, assignment (due 23 November)

• Week 8, assignment (due 30 November)

• Week 9, assignment (due 7 December)

• Week 10, assignment

References:

• Mary Hart, Guide to Analysis, Macmillan Mathematical Guides, 2001, ISBN: 0333794494.

• G. H. Hardy, A Course of Pure Mathematics, Cambridge Mathematical Library, 1993, ISBN: 0521092272.

• Michael Spivak, Calculus, Publish Or Perish, 1994, ISBN: 0914098896.

• David S. G. Stirling, Mathematics Analysis and Proof, Horwood Publishing, 1997, ISBN: 1898563365.