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