Here is the official site from the department.

Time and place: Tue 17-19 in L3; Thu 16-17 in MS.02.

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

Revision material:

- From the MORSE Society's: Mock exam; exams description.
- Past exams from a university web site.
- Last year's exam with solutions.

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.

- 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**:

I occasionally put comments on my facebook page; but anything of importance can be found here.

Week 1, assignment due 10 October

Week 2, assignment due 17 October

Week 3, assignment due 24 October

Week 4, assignment due 31 October

Week 5, assignment due 7 November

Week 6, assignment due 14 November

Week 7, assignment due 21 November

Week 8, assignment due 28 November

Week 9, assignment due 5 December

**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.