# MA140 Mathematical Analysis 1

**Lecturer:** Joel Moreira

**Term(s):** Term 1

**Status for Mathematics students:** This module is not available to Maths students

**Commitment:** 30 lectures, written assignments

**Assessment:** 15% from assignments and 85% from January exam

**Formal registration prerequisites: **None

**Assumed knowledge: **Grade A in A-level Further Maths or equivalent

**Synergies: **

**Leads to: **The following modules have this module listed as **assumed knowledge** or **useful background:**

**Aims: **

This module gives a rigorous introduction to some of the principles of mathematical analysis that are essential in most aspects of modern mathematics.

**Content:**

- The real numbers: Supremum and infimum, completeness axiom, rational and irrational numbers
- Sequences: Convergence, algebra of limits, Cauchy sequences, monotonicity, subsequences, Bolzano-Weierstrass Theorem
- Series: Convergence and divergence, tests, absolute convergence, rearrangements, the number e
- Continuity: Functions, formal definition of continuity, continuity and limits, algebra of continuous functions, the intermediate value theorem and the extreme value theorem

**Objectives:**

In addition to mastering the contents listed above, by the end of the module students will be able to understand and write formal mathematical sentences (aided by symbolic quantifiers).

**Books:**

D. Stirling, *Mathematical Analysis and Proof*, 1997

M. Spivak, *Calculus*, Benjamin

M. Hart, *Guide to Analysis*, Macmillan. (A good traditional text with theory and many exercises)

G.H. Hardy, *A Course of Pure Mathematics*, CUP