EC11915 Mathematical Analysis
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 realvalued 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 aims
To give students a more rigorous understanding of the mathematics of realvalued 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.
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 NewtonLeibniz definition, the Riemann definition, the Fundamental Theorem of Calculus, integration by parts, calculation of improper integrals), Differential equations (firstorder separable equations, first and secondorder linear equations)
Learning outcomes
By the end of the module, students should be able to:
 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 realvalued functions, including convergence of sequences and series, limits, continuity, differentiation, TaylorMacLaurin 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 realvalued 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.
Indicative reading list
Please see Talis Aspire link for most up to date list.
View reading list on Talis Aspire
Subject specific skills
Students will have the opportunity to develop skills in:
Analytical thinking and communication
Analytical reasoning
Critical thinking
Problemsolving
Abstraction
Transferable skills
Students will have the opportunity to develop skills in:
Numeracy and quantitative skills
Written communication
Oral communication
Mathematical, statistical and databased research skills
Study time
Type  Required 

Lectures  20 sessions of 1 hour (13%) 
Seminars  9 sessions of 1 hour (6%) 
Private study  121 hours (81%) 
Total  150 hours 
Private study description
'Private study will be required in order to prepare for seminars/classes, to review lecture notes, to prepare for forthcoming assessments, tests, and exams, and to undertake wider reading around the subject.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Students can register for this module without taking any assessment.
Assessment group D3
Weighting  Study time  

Problem Set 1  5%  
Take home problem set 

Problem Set 2  5%  
Take home problem set 

Problem Set 3  5%  
Take home problem set 

Problem Set 4  5%  
Take home problem set 

Test 1  2%  
Online quiz worth 2% or 0 depending on whether student achieves 80% 

Test 2  2%  
Online quiz worth 2% or 0 depending on whether student achieves 80% 

Test 3  2%  
Online quiz worth 2% or 0 depending on whether student achieves 80% 

Test 4  2%  
Online quiz worth 2% or 0 depending on whether student achieves 80% 

Test 5  2%  
Online quiz worth 2% or 0 depending on whether student achieves 80% 

Online Examination  70%  
A paper which examines the course content and ensures learning outcomes are achieved. ~Platforms  AEP

Assessment group R1
Weighting  Study time  

Online Examination  Resit  100%  
A paper which examines the course content and ensures learning outcomes are achieved. ~Platforms  AEP

Feedback on assessment
The Department of Economics is committed to providing high quality and timely feedback to students on their assessed work, to enable them to review and continuously improve their work. We are dedicated to ensuring feedback is returned to students within 20 University working days of their assessment deadline. Feedback for assignments is returned either on a standardised assessment feedback cover sheet which gives information both by tick boxes and by free comments or via free text comments on tabula, together with the annotated assignment. For tests and problem sets, students receive solutions as an important form of feedback and their marked assignment, with a breakdown of marks and comments by question and subquestion. Students are informed how to access their feedback, either by collecting from the Undergraduate Office or via tabula. Module leaders often provide generic feedback for the cohort outlining what was done well, less well, and what was expected on the assignment and any other common themes. This feedback also includes a cumulative distribution function with summary statistics so students can review their performance in relation to the cohort. This feedback is in addition to the individualspecific feedback on assessment performance.
Prerequisites
Alevel Mathematics or the equivalent
Courses
This module is Core optional for:
 Year 1 of UIPAL1L8 Undergraduate Economic Studies and Global Sustainable Development
This module is Optional for:

UECA3 Undergraduate Economics 3 Year Variants
 Year 1 of L100 Economics
 Year 1 of L100 Economics
 Year 1 of L100 Economics
 Year 1 of L116 Economics and Industrial Organization
 Year 1 of L116 Economics and Industrial Organization

UECALM1D Undergraduate Economics, Politics and International Studies
 Year 1 of LM1D Economics, Politics and International Studies
 Year 1 of LM1D Economics, Politics and International Studies

UPHAV7ML Undergraduate Philosophy, Politics and Economics
 Year 1 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 1 of V7ML Philosophy, Politics and Economics (Tripartite)
 Year 1 of V7ML Philosophy, Politics and Economics (Tripartite)
This module is Option list A for:
 Year 1 of UIPAL1L8 Undergraduate Economic Studies and Global Sustainable Development