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