Real Analysis (MAST20026)

Undergraduate level 2Points: 12.5On Campus (Parkville)

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Overview

Availability
Semester 1
Semester 2
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This subject introduces the field of mathematical analysis both with a careful theoretical framework as well as selected applications. Many of the important results are proved rigorously and students are introduced to methods of proof such as mathematical induction and proof by contradiction.

The important distinction between the real numbers and the rational numbers is emphasized and used to motivate rigorous notions of convergence and divergence of sequences, including the Cauchy criterion. These ideas are extended to cover the theory of infinite series, including common tests for convergence and divergence. A similar treatment of continuity and differentiability of functions of a single variable leads to applications such as the Mean Value Theorem and Taylor's theorem. The definitions and properties of the Riemann integral allow rigorous proof of the Fundamental Theorem of Calculus. The convergence properties of sequences and series are explored, with applications to power series representations of elementary functions and their generation by Taylor series. Fourier series are introduced as a way to represent periodic functions.

Intended learning outcomes

On completion of this subject students should



  • Acquire an appreciation of rigour in mathematics, be able to use proof by induction, proof by contradiction, and to use epsilon-delta proofs both as a theoretical tool and a tool of approximation;
  • Understand the theory and applications of the Riemann integral and improper integrals;
  • Be able to determine the convergence and divergence of infinite series;
  • Have a good knowledge of the theory and practice of power series expansions and Taylor polynomial approximations; and
  • Understand the role of Fourier series in representing periodic functions.

Generic skills

In addition to learning specific skills that will assist students in their future careers in science, they will have the opportunity to develop generic skills that will assist them in any future career path. These include:

  • problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
  • analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
  • collaborative skills: the ability to work in a team;
  • time management skills: the ability to meet regular deadlines while balancing competing commitments.

Last updated: 20 March 2025

Eligibility and requirements

Prerequisites


One of

Code Name Teaching period Credit Points
MAST10006 Calculus 2 No longer available
MAST10021 Calculus 2: Advanced No longer available

MAST10019: Calculus Extension Studies

AND


One of

Code Name Teaching period Credit Points
MAST10007 Linear Algebra No longer available
MAST10008 Accelerated Mathematics 1 No longer available
MAST10022 Linear Algebra: Advanced No longer available

MAST10018: Linear Algebra Extension Studies

Corequisites


Non-allowed subjects

Code Name Teaching period Credit Points
MAST10009 Accelerated Mathematics 2 No longer available
MAST20033 Real Analysis: Advanced No longer available

Inherent requirements (core participation requirements)

The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.

Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home

Last updated: 20 March 2025

Assessment

DescriptionTimingPercentage

Four to six written assignments due at regular intervals amounting to a total of up to 50 pages

  • 50 pages
During the teaching period20%

A written examination

  • 3 hours
During the examination period80%

Last updated: 20 March 2025

Dates & times

  • Semester 1
    CoordinatorChristian Haesemeyer
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week; 2 x one hour practice classes per week.
    Total time commitment170 hours
    Teaching period26 February 2024 to 26 May 2024
    Last self-enrol date 8 March 2024
    Census date 3 April 2024
    Last date to withdraw without fail 3 May 2024
    Assessment period ends21 June 2024

    Semester 1 contact information

    christian.haesemeyer@unimelb.edu.au

  • Semester 2
    CoordinatorBrian Krummel
    Mode of deliveryOn Campus (Parkville)
    Contact hours3 x one hour lectures per week; 2 x one hour practice classes per week.
    Total time commitment170 hours
    Teaching period22 July 2024 to 20 October 2024
    Last self-enrol date 2 August 2024
    Census date 2 September 2024
    Last date to withdraw without fail20 September 2024
    Assessment period ends15 November 2024

    Semester 2 contact information

    brian.krummel@unimelb.edu.au

Time commitment details

Estimated total time commitment of 170 hours

What do these dates mean

Visit this webpage to find out about these key dates, including how they impact on:

  • Your tuition fees, academic transcript and statements.
  • And for Commonwealth Supported students, your:
       -  Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
     

    Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.

Last updated: 20 March 2025

Further information

Last updated: 20 March 2025