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Unit of study_

MATH1904: Discrete Mathematics (Advanced)

This unit is designed to provide a thorough preparation for further study in mathematics. It parallels the normal unit MATH1004 but goes more deeply into the subject matter and requires more mathematical sophistication.

Details

Academic unit Mathematics and Statistics Academic Operations
Unit code MATH1904
Unit name Discrete Mathematics (Advanced)
Session, year
? 
Semester 2, 2020
Attendance mode Normal day
Location Camperdown/Darlington, Sydney
Credit points 3

Enrolment rules

Prohibitions
? 
MATH1004 or MATH1064
Prerequisites
? 
None
Corequisites
? 
None
Assumed knowledge
? 

Strong skills in mathematical problem solving and theory, including coordinate geometry, integral and differential calculus, and solution of polynomial equations equivalent to HSC Mathematics Extension 2 or a Band E4 in HSC Mathematics Extension 1

Available to study abroad and exchange students

No

Teaching staff and contact details

Coordinator Daniel Daners, daniel.daners@sydney.edu.au
Lecturer(s) Emily Rose Cliff , emily.cliff@sydney.edu.au
Administrative staff MATH1904@sydney.edu.au Please send all email regarding MATH1904 to this address. It goes to the unit of study coordinator, the lecturers and administrative support.
Type Description Weight Due Length
Final exam (Open book) Type C final exam Final exam
multiple choice and written answers
65% Formal exam period 1.5 hours
Outcomes assessed: LO1 LO6 LO5 LO4 LO3 LO2
Assignment Assignment 1
written calculations
5% Week 04
Due date: 17 Sep 2020

Closing date: 27 Sep 2020
10 days
Outcomes assessed: LO1 LO6
Online task Quiz 1
multiple choice or written answers
12.5% Week 06
Due date: 01 Oct 2020

Closing date: 01 Oct 2020
40 Minutes
Outcomes assessed: LO1
Tutorial quiz Quiz 2
multiple choice or written answers
12.5% Week 10
Due date: 05 Nov 2020

Closing date: 05 Nov 2020
40 minutes
Outcomes assessed: LO2
Assignment Assignment 2
written calculations
5% Week 11
Due date: 12 Nov 2020

Closing date: 22 Nov 2020
10 days
Outcomes assessed: LO1 LO2 LO5 LO6
Type C final exam = Type C final exam ?
  • Quizzes : Two quizzes will be held online through Canvas. The quizzes are 40 Minutes and have to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time. The better mark principle will be used for the quizzes so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that for each quiz, the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
  • Assignments : There are two assignments. Each assignment must be submitted electronically, as one single typeset or scanned PDF file only via Canvas by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submissions will receive a penalty. Detailed information for each assessment can be found on Canvas..
  • Examination : There is one examination during the examination period at the end of Semester. Further information about the exam will be made available at a later date on Canvas.

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.

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
Week 01 Introduction to the unit; The Catalan numbers Lecture (2 hr) LO1
Week 02 Sets Lecture and tutorial (3 hr)  
Week 03 Functions Lecture and tutorial (3 hr)  
Week 04 Counting principles; Ordered selections Lecture and tutorial (3 hr) LO1
Week 05 Unordered selections; Multinomial coefficients. Lecture and tutorial (3 hr) LO1
Week 06 The inclusion–exclusion principle Lecture and tutorial (3 hr)  
Week 07 Boolean expressions Lecture and tutorial (3 hr) LO2
Week 08 Logic Lecture and tutorial (3 hr)  
Week 09 Mathematical induction Lecture and tutorial (3 hr)  
Week 10 Introduction to prime numbers. Lecture and tutorial (3 hr) LO3
Week 11 Generating functions Lecture and tutorial (3 hr) LO4
Week 12 Linear recurrence relations Lecture and tutorial (3 hr) LO4

Attendance and class requirements

  • Attendance: Students are expected to attend a minimum of 80% of timetabled activities for a unit of study, unless granted exemption by the Associate Dean. For some units of study the minimum attendance requirement, as specified in the relevant table of units or the unit of study outline, may be greater than 80%.
  • Tutorial attendance: Tutorials (one per week) start in Week 2. You should attend the tutorial given on your personal timetable. Attendance at tutorials will be recorded. Your attendance will not be recorded unless you attend the tutorial in which you are enrolled.  While there is no penalty if 80% attendance is not met we strongly recommend you attend tutorials regularly to keep up with the material and to engage with the tutorial questions. Since there is no assessment associated with the tutorials do not submit an application for Special Consideration or Special Arrangements for missed tutorials.

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 3 credit point unit, this equates to roughly 60-75 hours of student effort in total.

Required readings

  • Recommended text: K. G. Choo and D. E. Taylor. Introduction to Discrete Mathematics. Addison Wesley Longman Australia, Melbourne, Vic, Australia, 1998

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. identify combinatorial objects involved in counting problems
  • LO2. understand how to construct switching circuits representing Boolean functions
  • LO3. factor numbers using sieve methods and use the Euclidean algorithm to compute greatest common divisors
  • LO4. resolve linear recurrence relations by using generating functions or characteristic equations
  • LO5. apply mathematical logic and rigour to solving problems
  • LO6. express mathematical ideas and arguments coherently in written form.

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.

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.