# EC119: Mathematical Analysis

15 CATS - Department of Economics
Summer Module
Autumn Module

### Principal Aims

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.

### Principal Learning Outcomes

Subject knowledge and understanding: … demonstrate an understanding of basic properties of real numbers, functions, and finite and infinite sets. The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets, online quizzes and independent study. The assessment methods that measure the achievement of this learning outcome are: Problem sheets, online quizzes and unseen examination.

Subject knowledge and understanding: … demonstrate an understanding of basic topics in the analysis of real-valued functions, including convergence of sequences and series, limits, continuity, differentiation, Taylor-MacLaurin series, and integration. The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets, online quizzes and independent study. The assessment methods that measure the achievement of this learning outcome are: Problem sheets, online quizzes and unseen examination.

Key skills: …understand formal mathematical definitions and theorems, and apply them to prove statements about real-valued functions. The teaching and learning methods that enable students to achieve this learning outcome are: Lectures, tutorials, problem sheets, online quizzes and independent study. The assessment methods that measure the achievement of this learning outcome are: Problem sheets, online quizzes and unseen examination.

### Syllabus

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)

### Context

Optional Module
L100 - Year 1, L116 - Year 1, LM1D (LLD2) - Year 1, V7ML - Year 1, L1L8 - Year 1, LA99 - Year 1, R9L1 - Year 1, R3L4 - Year 1, R4L1 - Year 1, R2L4 - Year 1, R1L4 - Year 1
Pre or Co-requisites
A-level Mathematics or the equivalent

### Assessment

Assessment Method
Coursework (30%) + Online Examination (70%)
Coursework Details
Online Examination (70%) , Problem Set 1 (5%) , Problem Set 2 (5%) , Problem Set 3 (5%) , Problem Set 4 (5%) , Test 1 (2%) , Test 2 (2%) , Test 3 (2%) , Test 4 (2%) , Test 5 (2%)
Exam Timing
Summer

### Exam Rubric

Time Allowed: 2 Hours