Real Analysis

Subject MAST20026 (2015)

Note: This is an archived Handbook entry from 2015.

Credit Points: 12.5
Level: 2 (Undergraduate)
Dates & Locations:

This subject has the following teaching availabilities in 2015:

Semester 1, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period 02-Mar-2015 to 31-May-2015
Assessment Period End 26-Jun-2015
Last date to Self-Enrol 13-Mar-2015
Census Date 31-Mar-2015
Last date to Withdraw without fail 08-May-2015

Semester 2, Parkville - Taught on campus.
Pre-teaching Period Start not applicable
Teaching Period 27-Jul-2015 to 25-Oct-2015
Assessment Period End 20-Nov-2015
Last date to Self-Enrol 07-Aug-2015
Census Date 31-Aug-2015
Last date to Withdraw without fail 25-Sep-2015

Timetable can be viewed here. For information about these dates, click here.
Time Commitment: Contact Hours: 3 x one hour lectures per week; 2 x one hour practice classes per week.
Total Time Commitment:

Estimated total time commitment of 170 hours

Study Period Commencement:
Credit Points:
Semester 1, Semester 2

Plus one of

Study Period Commencement:
Credit Points:
Summer Term, Semester 1, Semester 2
  • MAST10013 UMEP Maths for High Achieving Students


Recommended Background Knowledge:


Non Allowed Subjects:

Students who gain credit for MAST20026 Real Analysis may not also gain credit for MAST10009 Accelerated Mathematics 2.

Core Participation Requirements:

For the purposes of considering request for Reasonable Adjustments under the Disability Standards for Education (Cwth 2005), and Students Experiencing Academic Disadvantage Policy, academic requirements for this subject are articulated in the Subject Description, Subject Objectives, Generic Skills and Assessment Requirements of this entry.
The University is dedicated to provide support to those with special requirements. Further details on the disability support scheme can be found at the Disability Liaison Unit website:


Assoc Prof Deborah King, Dr Richard Brak


Second Year Coordinator


Subject Overview:

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.

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.

Four to six written assignments due at regular intervals during semester amounting to a total of up to 50 pages (20%), and a 3-hour written examination in the examination period (80%).

Prescribed Texts:


Breadth Options:

This subject potentially can be taken as a breadth subject component for the following courses:

You should visit learn more about breadth subjects and read the breadth requirements for your degree, and should discuss your choice with your student adviser, before deciding on your subjects.

Fees Information: Subject EFTSL, Level, Discipline & Census Date
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.

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 Course(s): Doctor of Philosophy - Business and Economics
Master of Commerce (Finance)
Related Majors/Minors/Specialisations: Applied Mathematics
Applied Mathematics
B-ENG Electrical Engineering stream
Discrete Mathematics / Operations Research
Discrete Mathematics / Operations Research
Pure Mathematics
Pure Mathematics
Science-credited subjects - new generation B-SCI and B-ENG.
Selective subjects for B-BMED
Statistics / Stochastic Processes
Statistics / Stochastic Processes
Related Breadth Track(s): Mathematics and Statistics

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