# COMPSCI 225 : Discrete Structures in Mathematics and Computer Science

## Science

### Course Prescription

An introduction to the foundations of computer science, mathematics and logic. Topics include logic, principles of counting, mathematical induction, recursion, relations and functions, graphs and trees, and algorithms.

### Course Overview

On one hand, COMPSCI 225 is an incredibly content-rich course. In this paper, you'll study the following concepts:

1) Propositional and first-order logic

2) Integers and factorization algorithms

3) Graph theory

4) Equivalence relations and posets

5) Functions and cardinality

6) Combinatorics and enumeration problems

7) Coding theory

8) And more!

COMPSCI 225 is a paper centred around one "big" idea: namely, the idea of mathematical proof. In mathematics, a proof is an argument we use to show that something is true. In this class, we're going to study what proofs are, and look at how we prove things in the fields of computer science, logic, combinatorics, and graph theory. To do this, our course is going to have a slightly different feel than most other classes you've had --- we're going to focus as much on the way arguments are formed as on the solutions to the problems we're studying! This course is suitable for any student who is interested in the foundations of computer science, mathematics and logic.

### Course Requirements

Prerequisite: 15 points from COMPSCI 120, MATHS 120, 150, 153 Restriction: MATHS 255

### Capabilities Developed in this Course

 Capability 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 4: Communication and Engagement
Graduate Profile: Bachelor of Science

### Learning Outcomes

By the end of this course, students will be able to:
1. Use the basic notation and terminology of relations, functions, trees, graphs, and strings. (Capability 1 and 3)
2. Translate problems stated in ordinary language (e.g. counting problems or graph problems) into the language of discrete structures. (Capability 1, 2, 3 and 4)
3. Apply proof methods (e.g. direct proof, proof by cases) to simple mathematical statements and analyse a simple format of the statements using logic (e.g. propositional logic). (Capability 1, 2, 3 and 4)
4. Apply propositional logic to find truth values of statements given in ordinary language. (Capability 1, 2, 3 and 4)
5. Apply induction and recursion principles to analysis of algorithms and proving simple mathematical statements (that involve integers). (Capability 1, 2, 3 and 4)
6. Know basic mathematical results about properties of graphs. (Capability 1 and 3)
7. Know the basics of finite automata (e.g. design automata recognizing the language of strings that contain the substring 'aba'). (Capability 1 and 3)

### Assessments

Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 15% Individual Test
Final Exam 55% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7
Assignments
Test
Final Exam

### Learning Resources

A coursebook containing the lecture notes will be available from Canvas.

### Special Requirements

In addition to achieving a passing mark overall for this course, students will need to have at least a 35% mark on the weighted average of their test+exam to pass this class. For example: a student who scored a 40% on the test and a 30% on the exam would have a ((40% * 15) + (30% * 55))/(15+55) = 32.14% weighted average of their test and exam, and thus would be unable to pass the course, regardless of their performance on the assignments.

Note that this condition is an "if" statement, not an "equivalence" statement. That is: while you need to have at at least a 35% mark on the weighted average of your test+exam to pass, it is not sufficient to have a 35% mark if you want to pass. Passing requires both an overall passing mark and at least a 35% mark on the weighted average of their test+exam. To give a second example: a student with a 0% on the assignments, a 60% on the test and a 60% on the exam would have a mark of (0% * 30) + (60% * 15) + (60% * 55) = 42%, and thus still fail the course even though their test+exam average was above the 35% threshold.

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, you can expect 3 hours of lectures, a 1-hour tutorial, 3 hours of reading and thinking about the content and 3 hours of work on assignments and/or test preparation.

### Digital Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.

You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.

### Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website at http://disability.auckland.ac.nz

### Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

This should be done as soon as possible and no later than seven days after the affected test or exam date.

### Student Feedback

During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.

At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.

Your feedback helps to improve the course and its delivery for all students.

### Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).

### Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.

Published on 23/02/2020 10:00 a.m.