MA15215 Mathematical Analysis 2
Introductory description
Mathematical Analysis is the heart of modern Mathematics. This module is the second in a series of modules where the subject of Analysis is rigorously developed.
Module aims
The principal aim is to develop Analysis in dimension 1, with much greater precision and rigour than the students had at school. While the highschool Analysis is focusing on problem solving methods, the universitylevel Analysis is switching the focus to the mathematical concepts and clarity of thought.
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.
 Differentiability
 Higher order derivatives
 Taylor's Theorem
 Taylor's Series
 Riemann Integration
 Fundamental Theorem of Calculus
 Improper integrals
Learning outcomes
By the end of the module, students should be able to:
 learn differentiability, including higher derivatives and properties of differentiable functions
 develop the working knowledge of Taylor's series and theorem, ultimately understanding representability of a function by a power series
 develop a good working knowledge of the construction of the Riemann integral
 understand and apply the fundamental properties of the integral such as integrability of continuous functions on bounded intervals or the Fundamental Theorem of Calculus
Indicative reading list
M. Hart, Guide to Analysis, Macmillan.
M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011)
L. Alcock, How to think about Analysis, Oxford University Press (2014)
View reading list on Talis Aspire
Subject specific skills
Analysis gives firstyear undergraduates a first excursion in to pure mathematics. The students will gain a new perspective and a deeper understanding of familiar mathematics which they have seen in school (e.g. real numbers, functions and differentiation). In Analysis, these concepts are developed with mathematical rigour, which characterises much of university mathematics to follow.
Transferable skills
Students will acquire key reasoning and problem solving skills, empower them to address new problems with confidence.
Study time
Type  Required 

Lectures  30 sessions of 1 hour (77%) 
Online learning (independent)  9 sessions of 1 hour (23%) 
Total  39 hours 
Private study description
Working on assignments, going over lecture notes, text books, exam revision.
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 D
Weighting  Study time  

Assignments  15%  20 hours 
Inperson Examination  85%  39 hours 

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100%  

Feedback on assessment
Marked homework (both assessed and formative) is returned and discussed in smaller classes. Exam feedback is given.
Courses
This module is Core for:

UMAAGV17 Undergraduate Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy
 Year 1 of GV17 Mathematics and Philosophy

UPXAGF13 Undergraduate Mathematics and Physics (BSc)
 Year 1 of GF13 Mathematics and Physics
 Year 1 of GF13 Mathematics and Physics

UPXAFG31 Undergraduate Mathematics and Physics (MMathPhys)
 Year 1 of FG31 Mathematics and Physics (MMathPhys)
 Year 1 of FG31 Mathematics and Physics (MMathPhys)
 Year 1 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)

USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of GG14 Mathematics and Statistics
 Year 1 of GG14 Mathematics and Statistics