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: 8/20/2019 6:18:55 PM