# 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, sets and functions, graphs, codes, and finite automata.

### Course Overview

On one hand, COMPSCI 225 is an incredibly content-rich course. Our diverse range of topics are listed below. On the other, COMPSCI 225 is best to be thought of not as a smorgasbord of disparate concepts, but rather as a paper centred around one "big" idea: 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, or Logic.

### Course Requirements

Prerequisite: COMPSCI 120 or MATHS 120 Restriction: MATHS 254

### Capabilities Developed in this Course

 Capability 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 4: Communication and Engagement

### Learning Outcomes

By the end of this course, students will be able to:
1. Apply 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. Display the mastery of basic mathematical results about properties of graphs. (Capability 1 and 3)
7. Display mastery of 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
Mid-Semester Assessment 15% Individual Coursework
Final Exam 55% Individual Examination
1 2 3 4 5 6 7
Assignments
Mid-Semester Assessment
Final Exam

### Tuākana

Tuākana Science is a multi-faceted programme for Māori and Pacific students providing topic specific tutorials, one-on-one sessions, test and exam preparation and more. Explore your options at
https://www.auckland.ac.nz/en/science/study-with-us/pacific-in-our-faculty.html
https://www.auckland.ac.nz/en/science/study-with-us/maori-in-our-faculty.html

### Key Topics

• Propositional and first-order logic
• Integers and factorization algorithms
• Graph theory
• Equivalence relations and posets
• Functions and cardinality
• Combinatorics and enumeration problems
• Coding theory
• Finite automata

### Special Requirements

A total of 100 points is awarded for this course:
• 55 points for final exam;
• 15 points for midterm test;
• 30 points for written assignments.
To pass this course, you need to satisfy two conditions:
• You must obtain at least 50 of the 100 points available.
• You must also obtain at least 35 of the 70 points available for midterm test + final examination.

This course is a standard 15-point course; as such, 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 to spend:

• 3 hours per week at the lectures
• 1-2 hours per week at the drop-in tutoring sections and your lecturer's office hours
• Alongside this, you can expect to spend 1-2 hours per week revising the material from lectures
• 4-5 hours per week working on assignments

### Delivery Mode

Lectures will be available as recordings. Other learning activities (e.g. the drop-in clinics) will not be available as recordings. The activities for the course are scheduled as a standard weekly timetable.

The assignments can be completed online. The mid-semester assessment and exam will follow the current University of Auckland test and exam policies.

This course may be taken remotely if you meet Ministry of Health guidelines and receive an exemption or cannot attend because of border restrictions.

### Learning 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.

Coursebook:

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

### 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.

Feedback suggested we give students more problems to practice. We will do that during the coming semesters

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.

With the above said, collaboration is allowed (and indeed encouraged) on the homework sets! Mathematics and Computer Science at the research level is a collaborative activity, and there is no reason that it should not also be this way in a classroom.

The only things that we ask of you are the following:
• You must write up your work separately, write up solutions in your own words, and only write up solutions you understand fully.
• When writing up your own work, you can directly cite and use without proof anything proven in class or in the class notes posted online. For anything else - i.e., results from textbooks, Wikipedia, etc. - you need to both cite in your write-up, and reprove the results you're using from those sources carefully in your own words. Simply copying solutions over directly is plagiarism/cheating/otherwise poor academic form; it is passing off the ideas of others as your own work (which is bad!)
• With that said: you are certainly welcome (indeed, encouraged) to read and learn what other people have thought about the concepts that we're covering in this class! All I am asking you to do here is to not claim the ideas of others as your own work and to rephrase and present any such ideas you encounter in a new way so that it is clear that you have actually learned something.
If you have any questions on the collaboration policy, please email your lecturer and they will be happy to clarify any possible edge cases.

### Class Representatives

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.

### 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

### 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 .

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

### Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.

### 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 .

### 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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 06/03/2023 08:13 a.m.