Fundamentals of Real Analysis
Undergraduate
Undergraduate
MATH 2027
Undergraduate
No
106054
4.5
No
School of Information Technology and Mathematical Sciences
This course aims 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 mathematical problems.
Nature of proof in analysis: direct, contrapositive, and by contradiction.
The structure of real numbers: Completeness and arquemedian properties.
Irrationality of square root of 2.
Functions: one-to-one, onto, bijections.
Cardinality: Finite, and infinite sets, Countable and uncountable sets.
Topology of the reals: open and closed intervals, structure theorem of open sets, compact sets.
Metric Spaces and normed spaces: function spaces and their general properties.
Continuous functions; definitions and properties, intermediate value for continuous functions.
Differentiable functions: intermediate value theorem for differentiable functions, Taylor development for higher order differentiable functions, and applications to global extrema.
The space of continuous functions on an interval and on a compact set, uniform convergence; Arzela-Ascoli theorem; Stone-Weierstrass theorem.
Abbott, Stephen 2015, Understanding Analysis
Common to all relevant programs | |
---|---|
Subject Area & Catalogue Number | Course Name |
MATH 1055 | Calculus 2 |
Nil
Component | Duration | ||
---|---|---|---|
INTERNAL, MAWSON LAKES | |||
Lecture | 3 hours x 13 weeks | ||
Tutorial | 1 hour x 12 weeks |
Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.
Assignment 1, Assignment 2, Examination
EFTSL*: 0.125
Commonwealth Supported program (Band 2)
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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.