Unit of study_

# MATH1004: Discrete Mathematics

## Overview

This unit provides an introduction to fundamental aspects of discrete mathematics, which deals with 'things that come in chunks that can be counted'. It focuses on the enumeration of a set of numbers, viz. Catalan numbers. Topics include sets and functions, counting principles, discrete probability, Boolean expressions, mathematical induction, linear recurrence relations, graphs and trees.

### Unit details and rules

Unit code MATH1004 Mathematics and Statistics Academic Operations 3 MATH1904 or MATH1064 None None HSC Mathematics or MATH1111. Students who have not completed HSC Mathematics (or equivalent) are strongly advised to take the Mathematics Bridging Course (offered in February). Yes

### Teaching staff

Coordinator Andrew Mathas, andrew.mathas@sydney.edu.au Anna Aksamit Andrew Mathas

## Assessment

Type Description Weight Due Length
Final exam (Record+) Final Exam
multiple choice and written calculations
65% Formal exam period 1.5 hours
Outcomes assessed:
Assignment Assignment 1
written calculations
5% Week 04
Due date: 02 Sep 2021 at 23:59

Closing date: 12 Sep 2021
10 days
Outcomes assessed:
12.5% Week 06
Due date: 16 Sep 2021 at 23:59

Closing date: 16 Sep 2021
40 minutes
Outcomes assessed:
12.5% Week 10
Due date: 21 Oct 2021 at 23:59

Closing date: 21 Oct 2021
40 minutes
Outcomes assessed:
Assignment Assignment 2
written calculations
5% Week 11
Due date: 28 Oct 2021 at 23:59

Closing date: 07 Nov 2021
10 days
Outcomes assessed:
= Type B final exam

### Assessment summary

• 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. 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. Detailed information for each assignment 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.

### 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
Week 01 Introduction to the unit; The Catalan numbers Lecture (2 hr)
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)
Week 05 Unordered selections; Multinomial coefficients Lecture and tutorial (3 hr)
Week 06 The inclusion–exclusion principle Lecture and tutorial (3 hr)
Week 07 Boolean expressions Lecture and tutorial (3 hr)
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)
Week 11 Generating functions Lecture and tutorial (3 hr)
Week 12 Linear recurrence relations Lecture and tutorial (3 hr)
Week 13 Revision Lecture and tutorial (3 hr)

### 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.

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

## 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. 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. solve linear recurrence relations by using generating functions or characteristic equations.

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.