Module Catalogues, Xi'an Jiaotong-Liverpool University
Module Code:
MTH109
Module Title:
Real Analysis
Module Level:
Level
1
Module Credits:
5.00
Academic Year:
2014/15
Semester:
SEM1
Originating Department:
Mathematical Sciences
Pre-requisites:
N/A
Aims
To provide a basic understanding of the principles of Real Analysis.
Learning outcomes
After completing this module students should be able:
State definitions and theorems in real analysis;
Present proofs of the main theorems;
Apply these definitions and theorems to simple examples;
Construct their own proofs of simple unseen results.
Method of teaching and learning
This module will be delivered by a combination of formal lectures and tutorials.
Syllabus
Mathematical language and symbols. Definitions, theorems and proofs.
The language of set theory.
Suprema and Infima, Maxima and Minima.
Real numbers: the Completeness Axiom.
Sequences of real numbers and their limits.
Algebra-of-limits theorems.
Bounded sequences and monotone sequences.
Open and closed subsets of R. Neighborhoods.
Cauchy sequences.
Subsequences.
Limit Superior and Limit Inferior.
Bolzano-Weierstrass Theorem. Compact subsets of the real line.
Sequences of partial sums of series; convergence of series.
Conditional and absolute convergence; rearrangements.
Functions, Limits and Continuity.
Epsilon-delta definition of continuity.
Continuity in terms of convergence of sequences.
Continuous images of compact and connected sets.
Brief discussion of convergence of sequences of functions.
Delivery Hours
Lectures
Seminars
Tutorials
Lab/Prcaticals
Fieldwork / Placement
Other(Private study)
Total
Hours/Semester
39
13
52
Assessment
Sequence
Method
% of Final Mark
1
Formal Examination
80.00
2
Class Test1
10.00
3
Class Test2
10.00
Module Catalogue generated from SITS
CUT-OFF: 12/16/2019 7:29:53 AM