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A course mapper by Monash Association of Coding (MAC)
Real analysis
MTH3140
Synopsis
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.
Sourced from the Monash Handbook 2026.
Quick facts
- Credit points
- 6
- Level
- 3
- Audience
- Undergraduate
- Type
- Coursework
- School
- Faculty of Science
- Faculty
- School of Mathematics
- Handbook year
- 2026
Prerequisites (4)
What it unlocks (12)
- Theory of computationFIT2014
- Differential geometry (Advanced)MTH3115
- Topology: The mathematics of shapeMTH3130
- Metric spaces, Banach spaces, Hilbert spacesMTH3160
- Network mathematicsMTH3170
- Network mathematics (Advanced)MTH3175
- Measure theoryMTH4099
- Algebraic topologyMTH4115
- Nonlinear optimisationMTH4331
- Measure theoryMTH5099
- Algebraic topologyMTH5115
- Nonlinear optimisationMTH5331
Offerings (1)
- First semesterClayton · ON-CAMPUS
Listed in 8 areas of study
- Applied mathematicsAdditional elective unit
- Financial and insurance mathematicsFinancial and insurance mathematics elective unit
- MathematicsMathematics elective units
- MathematicsMathematics elective units
- Pure mathematicsReal analysis
- Pure mathematicsReal analysis
- Mathematical foundations of econometricsElective units
- Mathematical statisticsAdditional elective units