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Real Analysis (MAST20026)
Undergraduate level 2Points: 12.5Dual-Delivery (Parkville)
From 2023 most subjects will be taught on campus only with flexible options limited to a select number of postgraduate programs and individual subjects.
To learn more, visit COVID-19 course and subject delivery.
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable(opens in new window)
Contact information
Semester 1
Semester 2
Overview
Availability | Semester 1 - Dual-Delivery Semester 2 - Dual-Delivery |
---|---|
Fees | Look up fees |
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: 11 April 2024
Eligibility and requirements
Prerequisites
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10006 | Calculus 2 |
Semester 1 (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
Summer Term (Dual-Delivery - Parkville)
|
12.5 |
MAST10021 | Calculus 2: Advanced | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
MAST10019: Calculus Extension Studies
AND
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10007 | Linear Algebra |
Summer Term (Dual-Delivery - Parkville)
Semester 2 (Dual-Delivery - Parkville)
Semester 1 (Dual-Delivery - Parkville)
|
12.5 |
MAST10008 | Accelerated Mathematics 1 | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
MAST10022 | Linear Algebra: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
MAST10018: Linear Algebra Extension Studies
Corequisites
None
Non-allowed subjects
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10009 | Accelerated Mathematics 2 | Semester 2 (Dual-Delivery - Parkville) |
12.5 |
MAST20033 | Real Analysis: Advanced | Semester 1 (Dual-Delivery - Parkville) |
12.5 |
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: 11 April 2024
Assessment
Description | Timing | Percentage |
---|---|---|
Four to six written assignments due at regular intervals amounting to a total of up to 50 pages
| During the teaching period | 20% |
A written examination
| During the examination period | 80% |
Last updated: 11 April 2024
Dates & times
- Semester 1
Coordinator Christopher Duffy Mode of delivery Dual-Delivery (Parkville) Contact hours 3 x one hour lectures per week; 2 x one hour practice classes per week. Total time commitment 170 hours Teaching period 28 February 2022 to 29 May 2022 Last self-enrol date 11 March 2022 Census date 31 March 2022 Last date to withdraw without fail 6 May 2022 Assessment period ends 24 June 2022 Semester 1 contact information
- Semester 2
Coordinator Gufang Zhao Mode of delivery Dual-Delivery (Parkville) Contact hours 3 x one hour lectures per week; 2 x one hour practice classes per week. Total time commitment 170 hours Teaching period 25 July 2022 to 23 October 2022 Last self-enrol date 5 August 2022 Census date 31 August 2022 Last date to withdraw without fail 23 September 2022 Assessment period ends 18 November 2022 Semester 2 contact information
Time commitment details
Estimated total time commitment of 170 hours
Last updated: 11 April 2024
Further information
- Texts
Prescribed texts
None
- Subject notes
This subject is available for science credit to students enrolled in the BSc (both pre-2008 and new degrees), BASc or a combined BSc course.
Previously known as MAST20026 Real Analysis with Applications.
- Related Handbook entries
This subject contributes to the following:
Type Name Course Master of Commerce (Finance) Informal specialisation Science Discipline subjects - new generation B-SCI Informal specialisation Discrete Mathematics / Operations Research Informal specialisation Applied Mathematics Informal specialisation Physics Informal specialisation Pure Mathematics Major Discrete Mathematics / Operations Research Major Physics Informal specialisation Statistics / Stochastic Processes Major Applied Mathematics Major Pure Mathematics Major Statistics / Stochastic Processes Breadth Track Mathematics and Statistics - Breadth options
This subject is available as breadth in the following courses:
- Bachelor of Arts
- Bachelor of Commerce
- Bachelor of Design
- Bachelor of Environments
- Bachelor of Fine Arts (Acting)
- Bachelor of Fine Arts (Animation)
- Bachelor of Fine Arts (Dance)
- Bachelor of Fine Arts (Film and Television)
- Bachelor of Fine Arts (Music Theatre)
- Bachelor of Fine Arts (Production)
- Bachelor of Fine Arts (Screenwriting)
- Bachelor of Fine Arts (Theatre)
- Bachelor of Fine Arts (Visual Art)
- Bachelor of Music
- Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 11 April 2024