Fundamentals of Real Analysis
Undergraduate
Undergraduate
To introduce the student to fundamental concepts of analysis that underpin a large number of areas of mathematics, both pure and applied. By studying the material in this course the student will learn theoretical principles and techniques of analysis and learn to apply them so as to analyse and solve mathematical problems.
A selection drawn from the following topics:
Types of proof used in analysis: direct proof, proof of a contrapositive, proof by induction, proof by contradiction. Quantifiers. Negation of a statement.
Properties of the real numbers, least upper bounds, the Axiom of Completeness and its consequences.
Cardinality of a set. One-to-one and onto functions. Finite, countable and uncountable sets.
Properties of sequences and series. Limit theorems, Monotone Convergence Theorem, Bolzano-Weierstrass Theorem, Cauchy Criterion.
Subsets of the real numbers. Open sets, closed sets, compact sets, perfect sets, connected sets. Closure of a set, unions, intersections and complements.
Properties of continuous functions and of differentiable functions. Intermediate Value Theorem, Mean Value Theorem.
Possible additional topics such as Taylor series, power series, uniform convergence, Riemann integration, metric spaces.
Abbott, Stephen 2015, Understanding Analysis, Second Edition
Common to all relevant programs | |
---|---|
Subject Area & Catalogue Number | Course Name |
MATH 1055 | Calculus 2 |
Nil
Component | Duration | ||
---|---|---|---|
INTERNAL, MAWSON LAKES | |||
Seminar | 2 hours x 13 weeks | ||
Seminar | 1 hour x 13 weeks | ||
Tutorial | 1 hour x 13 weeks |
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.
Examination, Problem solving exercise
EFTSL*: 0.125
Commonwealth Supported program (Band 1)
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Fee-paying program for domestic and international students
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* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.