MTH3140 · Real analysis

Overview

An introduction to real analysis with a special focus on sequences of real numbers and functions. Topics covered include properties of real numbers (infima/suprema and the axiom of completeness), sequences and series of real numbers (order limit theorem, Cauchy sequences and completeness, compactness), properties of functions over the reals (intermediate value theorem, mean value theorem), sequences and series of functions (pointwise and uniform convergence, the Weierstrass M-test, continuity and differentiability of the limit). Emphasis will be on rigorous mathematical proof and examples will be provided to show how intuition can be misleading.

Areas of study: Applied mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

Learning outcomes

1. Apply core concepts of real analysis to study sequences, series, and functions of real variables;
2. Develop and justify rigorous mathematical proofs in the context of real analysis;
3. Analyse continuity, differentiability, and convergence with an emphasis on logical reasoning and counterexamples;
4. Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve analysis problems;
5. Extend and deepen understanding of real analysis through advanced proofs, generalisations, and applications, demonstrating higher levels of rigour and independence.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12) and • 7 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.