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Area/Catalogue
MATH 2027

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Course Level
Undergraduate

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Offered Externally
No

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Course ID
106054

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Unit Value
4.5

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University-wide elective course
No

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Timetable/s
First Semester
(Study Period 2)
Course owner

Course owner
School of Information Technology and Mathematical Sciences

Course aim

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.

Course content

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.

Textbook(s)

Abbott, Stephen 2015, Understanding Analysis

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number Course Name
MATH 1055 Calculus 2

Corequisite(s)

Nil

Teaching method

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.


Assessment

Task Length Weighting Duration
INTERNAL, MAWSON LAKES
Problem solving exercise 1250 word equivalent 20% N/A
Problem solving exercise 1250 word equivalent 20% N/A
Examination 2000 word equivalent 60% N/A

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
How to determine your Commonwealth Supported course fee. (Opens new window)

Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the Division offering the course. To determine the cost of this course, go to:
How to determine the relevant non award tuition fee. (Opens new window)

Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* 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

Course Coordinators

School of Information Technology and Mathematical

Degrees this course is offered in

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