# Current students

Unit of study_

### 2024 unit information

Analysis grew out of calculus, which leads to the study of limits of functions, sequences and series. It is one of the fundamental topics underlying much of mathematics including differential equations, dynamical systems, differential geometry, topology and Fourier analysis. This advanced unit introduces the field of mathematical analysis both with a careful theoretical framework as well as selected applications. This unit will be useful to students with more mathematical maturity who study mathematics, science, or engineering. Starting off with an axiomatic description of the real numbers system, this unit concentrates on the limiting behaviour of sequences and series of real and complex numbers. This leads naturally to the study of functions defined as limits and to the notion of uniform con-vergence. Special attention is given to power series, leading into the theory of analytic functions and complex analysis. Besides a rigorous treatment of many concepts from calculus, you will learn the basic results of complex analysis such as the Cauchy integral theorem, Cauchy integral formula, the residues theorems, leading to useful techniques for evaluating real integrals. By doing this unit, you will develop solid foundations in the more formal aspects of analysis, including knowledge of abstract concepts, how to apply them and the ability to construct proofs in mathematics.

## Unit details and rules

#### Science

 Prerequisites: ? [(MATH1961 or MATH1971 or (a mark of 65 or above in MATH1061)) and (MATH1962 or MATH1972 or (a mark of 65 or above in MATH1062))] or ([(MATH1921 or MATH1931 or MATH1901 or MATH1906) or (a mark of 65 or above in MATH1021 or MATH1001)] and [MATH1902 or (a mark of 65 or above in MATH1002)] and [(MATH1923 or MATH1933 or MATH1903 or MATH1907) or (a mark of 65 or above in MATH1023 or MATH1003)]) None MATH2023 or MATH2962 or MATH3068 None

At the completion of this unit, you should be able to:

• LO1. Demonstrate a conceptual understanding of limit, continuity, differentiation, and integration as well as a thorough background in variety of techniques and applications of mathematical analysis.
• LO2. assess problems in the framework of mathematical analysis, to choose among several potentially appropriate mathematical methods of solution, and persist in the face of difficulty
• LO3. present complete and mathematically rigorous solutions for problems in mathematical analysis that include appropriate justification for their reasoning
• LO4. recognise problems in mathematics, science, engineering and real life that are amenable to mathematical analysis, and to formulate models for such problems and apply the techniques of mathematical analysis in solving them
• LO5. apply mathematical logic and rigor to solving problems, and express mathematical ideas coherently using precise mathematical language
• LO6. understand new mathematical concepts beyond routine methods and calculations

## Unit availability

This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.

The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

Session MoA   Location Outline
Semester 2 2024
Normal day Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote
Semester 2 2023
Normal day Camperdown/Darlington, Sydney

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### Modes of attendance (MoA)

This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.