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Unit of study_

MATH2023: Analysis

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 unit introduces the field of mathematical analysis both with a careful theoretical framework as well as selected applications. It shows the utility of abstract concepts and teaches an understanding and construction of proofs in mathematics. This unit will be useful to students of mathematics, science and engineering and in particular to future school mathematics teachers, because we shall explain why common practices in the use of calculus are correct, and understanding this is important for correct applications and explanations. The unit starts with the foundations of calculus and the real numbers system. It goes on to study 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 convergence. Returning to the beginnings of calculus and power series expansions leads to complex variable theory: elementary functions of complex variable, the Cauchy integral theorem, Cauchy integral formula, residues and related topics with applications to real integrals.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH2023
Unit name Analysis
Session, year
? 
Semester 2, 2021
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 6

Enrolment rules

Prohibitions
? 
MATH2923 or MATH3068 or MATH2962
Prerequisites
? 
(MATH1X21 or MATH1931 or MATH1X01 or MATH1906) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907) and (MATH1XX2 or a mark of 65 or above in MATH1014)
Corequisites
? 
None
Available to study abroad and exchange students

Yes

Teaching staff and contact details

Coordinator Milena Radnovic, milena.radnovic@sydney.edu.au
Type Description Weight Due Length
Final exam (Take-home short release) Type D final exam Final exam
Final exam
70% Formal exam period 2 hours
Outcomes assessed: LO1 LO4 LO3 LO2
Tutorial quiz Quiz
Quiz
15% Week 06 40 minutes
Outcomes assessed: LO1 LO2
Assignment Assignment
Assignment
15% Week 10 1 week, late submissions not accepted
Outcomes assessed: LO1 LO2 LO3 LO4
Type D final exam = Type D final exam ?

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.

For more information see sydney.edu.au/students/guide-to-grades.

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.

This unit has an exception to the standard University policy or supplementary information has been provided by the unit coordinator. This information is displayed below:

Late submissions are not allowed.

Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

Academic integrity

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

WK Topic Learning activity Learning outcomes
Multiple weeks Tutorial Tutorial (1 hr) LO1 LO2 LO3 LO4
Revision of Topics Practical (1 hr) LO1 LO2 LO3 LO4
Week 01 Numbers Lecture (3 hr) LO2 LO4
Week 02 Sequences and convergence Lecture (3 hr) LO1 LO2 LO3 LO4
Week 03 Sequences and convergence Lecture (3 hr) LO1 LO2 LO3 LO4
Week 04 Number series Lecture (3 hr) LO1 LO2 LO3 LO4
Week 05 Number series Lecture (3 hr) LO1 LO2 LO3 LO4
Week 06 Power series: part 1 Lecture (3 hr) LO1 LO2 LO3 LO4
Week 07 Functions Lecture (3 hr) LO1 LO2 LO3 LO4
Week 08 Sequences of functions Lecture (3 hr) LO1 LO2 LO3 LO4
Week 09 Power series: part 2 Lecture (3 hr) LO1 LO2 LO3 LO4
Week 10 Contour integration Lecture (3 hr) LO1 LO2 LO3 LO4
Week 11 Contour integration Lecture (3 hr) LO1 LO2 LO3 LO4
Week 12 Residue and singularities Lecture (3 hr) LO1 LO2 LO3 LO4
Week 13 Revision Lecture (3 hr) LO1 LO2 LO3 LO4

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.

Required readings

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

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.

Graduate qualities

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

Learning outcomes Graduate qualities
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9
No changes have been made since this unit was last offered.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

  • No eating or drinking is allowed in any laboratory under any circumstances 

  • A laboratory coat and closed-toe shoes are mandatory 

  • Follow safety instructions in your manual and posted in laboratories 

  • In case of fire, follow instructions posted outside the laboratory door 

  • First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory 

  • As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.