Program Overview

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Overview

This unit introduces students to the language and key methods of the area of Discrete Mathematics. The focus is on mathematical concepts in discrete mathematics and their applications, with an emphasis on computation. For instance, to specify a computational problem precisely one needs to give an abstract formulation using mathematical objects such as sets, functions, relations, orders, and sequences. In order to prove that a proposed solution is correct, one needs to apply the principles of mathematical logic, and to use proof techniques such as induction. To reason about the efficiency of an algorithm, one often needs to estimate the growth of functions or count the size of complex mathematical objects. This unit provides the necessary mathematical background for such applications of discrete mathematics. Students will be introduced to mathematical logic and proof techniques; sets, functions, relations, orders, and sequences; counting and discrete probability; asymptotic growth; and basic graph theory.

Unit details and rules

• Academic unit: Mathematics and Statistics Academic Operations
• Credit points: 6
• Prerequisites: None
• Corequisites: None
• Prohibitions: MATH1004 or MATH1904
• Assumed knowledge: Coordinate geometry, basic integral and differential calculus, polynomial equations and algebraic manipulations, equivalent to HSC Mathematics
• Available to study abroad and exchange students: Yes

Teaching staff

• Coordinator: Jonathan Spreer
• Lecturer(s): Jonathan Spreer
• Tutor(s): Behrouz Taji

Assessment

• Type:
  • Final exam (Record+): 60%
  • Assignment: 5%
  • Online task: 10%
  • Online task: 10%
  • Assignment: 5%
  • Assignment: 10%
• Description:
  • Final exam: multiple choice and written answers
  • Assignment: written calculations
  • Online task: multiple choice or written answer
• Weight:
  • Final exam: 60%
  • Assignment: 5%
  • Online task: 10%
  • Online task: 10%
  • Assignment: 5%
  • Assignment: 10%
• Due:
  • Final exam: Formal exam period
  • Assignment: Week 04
  • Online task: Week 06
  • Online task: Week 10
  • Assignment: Week 11
  • Assignment: Weekly
• Length:
  • Final exam: 2 hours
  • Assignment: 10 days
  • Online task: 40 minutes
  • Online task: 40 minutes
  • Assignment: 10 days
  • Assignment: 1 week

Assessment summary

• Assignments: There are two assignments. Each 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. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
• Quizzes: Two quizzes will be held online through Canvas. Each quiz is 40 minutes and has 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 quiz so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that 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.
• Online WebWork Quizzes: There are 11 weekly online quizzes. Each online quiz consists of a set of randomized questions. The best 10 of your 11 quizzes will count, making each worth 1%. You cannot apply for special consideration for the quizzes. The better mark principle will apply for the total 10% - i.e. if your overall exam mark is higher, then your 10% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is 23:59 on Friday (starting in week 2). The precise schedule for the quizzes is found on Canvas.
• Final Exam: 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.

Assessment criteria

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

• Result name:
  • High distinction: 85 - 100
  • Distinction: 75 - 84
  • Credit: 65 - 74
  • Pass: 50 - 64
  • Fail: 0 - 49
• Description:
  • High distinction: Representing complete or close to complete mastery of the material.
  • Distinction: Representing excellence, but substantially less than complete mastery.
  • Credit: Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.
  • Pass: Representing at least routine knowledge and understanding over a spectrum of topics and important ideas in the course.
  • Fail: When you don’t meet the learning outcomes of the unit to a satisfactory standard.

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.

Weekly schedule

Week	Topic	Learning activity	Learning outcomes
Week 01	Logic: prepositional and first order	Lecture (3 hr)	LO1 LO2 LO3 LO4
Week 02	Inference and proofs	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 03	Sets, functions, and sequences	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 04	Number theory	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 05	Asymptotic growth	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 06	Induction and recursion	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 07	Counting (Basics)	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 08	Counting (Advanced)	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 09	Discrete probability	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 10	Relations	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 11	Graphs	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 12	Modelling computation: regular languages and DFAs	Lecture and tutorial (5 hr)	LO1 LO2 LO3 LO4
Week 13	Revision	Lecture and tutorial (5 hr)	LO1 LO2 LO3 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 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Required readings

• Recommended textbook: Discrete Mathematics and Its Applications (Eigth Edition) by Kenneth H. Rosen

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.

• Outcomes:
  • LO1: construct logically correct and mathematically sound proofs
  • LO2: apply concepts of logic, set theory, relations, induction, principles of counting, probability, algebraic structures, elementary number theory and asymptotic growth to mathematical and computational problems in more advanced courses
  • LO3: demonstrate an understanding and well-founded knowledge of the mathematics presented in this course and thus be able to apply techniques from this course to solve both familiar and novel problems
  • LO4: understand some applications of mathematics to relevant fields, such as computer programming and logic.

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
• GQ2: Critical thinking and problem solving
• GQ3: Oral and written communication
• GQ4: Information and digital literacy
• GQ5: Inventiveness
• GQ6: Cultural competence
• GQ7: Interdisciplinary effectiveness
• GQ8: Integrated professional, ethical, and personal identity
• GQ9: Influence

Outcome map

Learning outcomes | Graduate qualities ---|--- 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.

Additional information

• Science student portal
• Mathematics and Statistics student portal

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.

This unit of study outline was last modified on 23 Jul 2021.