COMPSCI 120 : Mathematics for Computer Science
2021 Summer School (1210) (15 POINTS)
This course is a core part of the Computer Science major. It focuses on laying theoretical foundations of mathematics which are further developed in COMPSCI 220, COMPSCI 225, and more advanced courses on algorithms, machine learning, and theoretical computer science. COMPSCI 120 is centered around one "big" idea: namely, the idea of a mathematical proof. In mathematics, a proof is an argument to show that something is true. In this course, we look at how we prove statements in the fields of computer science, logic, combinatorics, and graph theory. To do this, COMPSCI 120 is going to have a slightly different feel than most other courses you have had. Specifically, we are going to focus as much on the way arguments are formed as on the solutions to the problems we are studying! This course is suitable for any student who is interested in the foundations of computer science, mathematics, and logic.
Capabilities Developed in this Course
|Capability 1:||Disciplinary Knowledge and Practice|
|Capability 2:||Critical Thinking|
|Capability 3:||Solution Seeking|
|Capability 4:||Communication and Engagement|
|Capability 5:||Independence and Integrity|
- Communicate mathematically. Students should be able to read and interpret basic mathematical symbols and notation (for example, standard terminology of numbers, sets, functions, strings, trees and graphs), and be capable of translating and communicating their own ideas into mathematical language. (Capability 1, 2 and 4)
- Perform simple mathematical modelling. Students should be capable of translating simple real-life tasks into algorithms, and of describing the tasks in mathematical language and abstraction. In particular, students should be capable of using the language and ideas represented by sets, functions, strings, trees and graphs when modelling and studying real-life tasks. (Capability 3 and 5)
- Use and apply counting and probability techniques. Students should be comfortable with basic ideas in probability and counting, and applying them in easy real-life settings (for example, counting arrangements of items, computing expectation of a discrete random variable). (Capability 4 and 5)
- Critically analyse formal logic and perform elementary proofs, including inductive proofs: Students should be comfortable with elementary formal mathematical proof techniques and inductive reasoning, and be capable of using these to prove theorems, such as correctness of a simple algorithm. They should be able to formally determine validity of a logical statement, for example by truth tables. (Capability 1, 2, 3, 4 and 5)
|Tutorials||9%||Group & Individual Coursework|
|Final Exam||50%||Individual Examination|
|Assessment Type||Learning Outcome Addressed|
For more information and to find contact details for the Tuākana coordinator, please see https://www.auckland.ac.nz/en/science/study-with-us/maori-and-pacific-at-the-faculty/tuakana-programme.html
2. Sets and strings.
3. Basics of combinatorics and probability.
4. Introduction to algorithms and their running time, functions, and limit techniques.
5. Introduction to graph theory.
6. Direct proofs, proof by cases, proof by contradiction, proof by construction, and proof by induction.
This course is a standard 15 point course and students are expected to spend 150 hours in total for each 15 point course that they are enrolled in. During Summer School, this will be approximately 20 hours per week.
For this course, you can expect 6 hours of lectures, a 3 hours tutorial, 7 hours of reading and thinking about the content and 4 hours of work on assignments and/or test preparation.
Attendance is required at scheduled activities including tutorials to receive credit for components of the course.
Lectures will be available as recordings. Other learning activities including tutorials will not be available as recordings.
The course will include live online events including group discussions/tutorials if there are students approved to take the course online.
Attendance on campus is required for the test/exam.
The activities for the course are scheduled as a standard weekly timetable.
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.
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 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.
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.
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 http://disability.auckland.ac.nz
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.
Students who are approved to take this course remotely will have alternative arrangements made for all assessed components.
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 your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
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.
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.