# Current students

Unit of study_

## Overview

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 frame- work 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

Unit code MATH2923 Mathematics and Statistics Academic Operations 6 MATH2023 or MATH2962 or MATH3068 [(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 None Yes

### Teaching staff

Coordinator Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au

## Assessment

Type Description Weight Due Length
Final exam (Take-home short release) Final exam
Written calculations
60% Formal exam period 2 hours
Outcomes assessed:
Tutorial quiz Quiz 1
Quiz
15% Week 06 40 minutes
Outcomes assessed:
Assignment Assignment
Assignment
10% Week 10 2 weeks
Outcomes assessed:
Tutorial quiz Quiz 2
Quiz
15% Week 12 40 minutes
Outcomes assessed:
= Type D final exam

### Assessment summary

Detailed information for each assessment can be found on Canvas.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material;

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery;

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge

and understanding, but less than excellence;

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and

important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Multiple weeks Tutorial Tutorial (1 hr)
Revision of Topics Practical (1 hr)
Week 01 Introduction Lecture (3 hr)
Week 02 Sequences and convergence Lecture (3 hr)
Week 03 Sequences and convergence Lecture (3 hr)
Week 04 Number series Lecture (3 hr)
Week 05 Number series Lecture (3 hr)
Week 06 Power series: part 1 Lecture (3 hr)
Week 07 Functions Lecture (3 hr)
Week 08 Sequences of functions Lecture (3 hr)
Week 09 Power series: part 2 Lecture (3 hr)
Week 10 Contour integration Lecture (3 hr)
Week 11 Contour integration Lecture (3 hr)
Week 12 Residue and singularities Lecture (3 hr)
Week 13 Revision Lecture (3 hr)

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

• Daniel Daners, Real and Complex Analysis, which is available from Kopystop.

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

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

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

No changes have been made since this unit was last offered.