EC119: Mathematical Analysis
Nicholas Jackson
Module Leader
Introduction
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 Aims
To give students a more rigorous understanding of the mathematics of real-valued functions. Students will acquire an understanding of basic properties of the field of real numbers, convergence of sequences and series, limits of functions and methods for calculating them, continuity, differentiation, integration, Taylor series, and differential equations.
Principal Learning Outcomes
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.
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, R2L5 - Year 1, R4LA - Year 1, R1L5 - Year 1, L1CA - Year 1
- Pre or Co-requisites
- A-level Mathematics or the equivalent
Assessment
- Assessment Method
- Coursework (30%) + Centrally-timetabled examination (On-campus) (70%)
- Coursework Details
- Centrally-timetabled examination (On-campus) (70%) , Problem Set 1 (10%) , Problem Set 2 (10%) , Quiz (10%)
- Exam Timing
- Summer
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
Exam Rubric
Time Allowed: 2 Hours
Read all instructions carefully - and read through the entire paper at least once before you enter your answers.
A formula sheet is provided at the end of the exam paper.
There is ONE section in this paper. Answer THREE questions (25 marks each).
Use a GOLD booklet.
You must write the number(s) of the question(s) you have answered on the front cover of each booklet. Make sure the numbers are clearly visible and correspond to the questions you completed inside that booklet.
Do not submit answers to more than the required number of questions. If you do, only the first answers (in the order they appear) will be marked, up to the required number for each section.
Approved scientific (non-graphical) pocket calculators are allowed.
Previous exam papers can be found in the University’s past papers archive. Please note that previous exam papers may not have operated under the same exam rubric or assessment weightings as those for the current academic year. The content of past papers may also be different.