Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH109
Module Title: Real Analysis
Module Level: Level 1
Module Credits: 5.00
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