Introductory description

This module provides students with a strong background in pure mathematics, particularly the theory of sets and functions, the real number system, logic and proof, analysis of real-valued functions, and differential equations. This allows the students to develop a fluency with abstract mathematical reasoning, and gives a deeper understanding of techniques used in mathematical economics and econometrics.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

The module will typically cover the following topics: Set theory (notation, basic concepts), Real numbers (basic properties, interval notation), Functions (injectivity, surjectivity, composition), Sequences and Series (convergence, divergence, boundedness), Limits of functions (basic definitions, the Sandwich Rule, boundedness), Continuity (basic definitions, the Intermediate Value Theorem, numerical methods for solving equations), Differentiation (basic definitions and properties, Rolle’s Theorem, the Mean Value Theorem), L’Hopital’s Rule (techniques and applications), Taylor’s Theorem (generalisation of the Mean Value Theorem, polynomial approximations to functions, convergence criteria), Integration (basic properties, the Newton-Leibniz definition, the Riemann definition, the Fundamental Theorem of Calculus, integration by parts, calculation of improper integrals), Differential equations (first-order separable equations, first- and second-order linear equations)

Learning outcomes

By the end of the module, students should be able to:

• 1. Reproduce definitions and examples of core concepts, perform standard calculations, and state and prove standard facts and results in set theory and real analysis.
• 2. Interpret, generalize and apply a range of mathematical techniques, concepts and results to questions in set theory and real analysis, and understand their relevance to economics.
• 3. Use existing concepts and theorems to construct illustrative examples and counterexamples and rigorously prove further mathematical results.

Indicative reading list

Reading lists can be found in Talis

Specific reading list for the module

Subject specific skills

Abstraction
Analytical reasoning
Analytical thinking and communication
Critical thinking
Problem solving

Transferable skills

Numeracy and quantitative skills
Mathematical, statistical and data-based research skills
Oral communication
Written communication