MTH3140 Real analysis
Faculty of Science
MTH3140 Real analysis is a level 3, 6-credit-point, undergraduate unit from the Faculty of Science, offered in 2027 in Semester 1 at Clayton. It has no prerequisites and unlocks 9 units, leading on to 19 units in all.
- Credit points
- 6
- Offered in 2027
- Semester 1
- Clayton
- Assessment
- Exam 50%
- and 1 other task
Reviews
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Requisites
Before MTH3140
No prerequisites or corequisites besides the enrolment rules below.
After MTH3140
9 units list MTH3140 as a prerequisite or corequisite.
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Enrolment rules
PROHIBITION: MTH2111, MTH3111, MTH2140
PREREQUISITE: You must have passed one unit from MTH1030 or MTH1035or ENG1005 or ETC2440, or be enrolled in the Master of Mathematics or the Master of Financial Mathematics.
Equivalent units
The same content under another code. Only one of them counts.
Overview
An introduction to real analysis with a special focus on sequences of real numbers and functions. Topics covered include properties of real numbers (infima/suprema and the axiom of completeness), sequences and series of real numbers (order limit theorem, Cauchy sequences and completeness, compactness), properties of functions over the reals (intermediate value theorem, mean value theorem), sequences and series of functions (pointwise and uniform convergence, the Weierstrass M-test, continuity and differentiability of the limit). Emphasis will be on rigorous mathematical proof and examples will be provided to show how intuition can be misleading.
Offerings in 2027
| Teaching period | Campus | Mode |
|---|---|---|
| First semester | Clayton | On campus |
Assessment
- Continuous assessmentDemonstration50%
- Final assessment - Exam (3 hours and 10 minutes)Examination50%
Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.
Learning outcomes
When you finish this unit, you should be able to:
- 1
Apply core concepts of real analysis to study sequences, series, and functions of real variables;
- 2
Develop and justify rigorous mathematical proofs in the context of real analysis;
- 3
Analyse continuity, differentiability, and convergence with an emphasis on logical reasoning and counterexamples;
- 4
Communicate mathematical arguments effectively, both orally and in writing, and collaborate to solve analysis problems;
- 5
Extend and deepen understanding of real analysis through advanced proofs, generalisations, and applications, demonstrating higher levels of rigour and independence.
Workload and teaching
- Seminars36 hours
- Applied sessions22 hours
- Three 1-hour seminars;
- One 2-hour applied class (in weeks 2-12) and
- 7 hours of independent study per week.
Where it fits
MTH3140 is part of 1 area of study in the 2027 handbook.
Contacts
- Unit Coordinators
- Dr Ngan Le
- Chief Examiners
- Dr Yann Bernard
Common questions
What are the prerequisites for MTH3140?
MTH3140 has no prerequisites, but enrolment rules apply.
What can I take after MTH3140?
MTH3140 is a prerequisite or corequisite for 9 units, including FIT2014, MTH3115, MTH3130, MTH3160, MTH3170 and MTH3175. Those lead on to 19 units in all.
When is MTH3140 offered?
In 2027, MTH3140 runs in Semester 1 at Clayton.
Does MTH3140 have an exam?
Yes. The exam is worth 50% of the final mark, alongside 1 other task.
Which majors and minors include MTH3140?
MTH3140 is part of Mathematical foundations of econometrics.