School of Maths and Statistics

Course outline

MATH2400

Finite Mathematics

Term 2, 2021

Staff

Position	Name	Email	Room
Lecturer-in-charge	Igor Shparlinski	[email protected]	RC-5112

Please refer to your Timetable on MyUNSW for your Lecture Tut, Lab enrolment days and times.

Administrative Contacts

Please visit the School of Mathematics and Statistics website for a range of information on School Policies, Forms and Help for Students.

For information on Courses, please go to “Current Students” and either Undergraduate and/or Postgraduate”, Course Homepage” for information on all course offerings,

The “Student Notice Board” can be located by going to the “Current Students” page; Notices are posted regularly for your information here. Please familiarise yourself with the information found in these locations. The School web page is: https://www.maths.unsw.edu.au

If you cannot find the answer to your queries on the web you are welcome to contact the Student Services Office directly by phone.

By email       Undergraduate    [email protected]

By phone:    9385 7011 or 9385 7053

Should we need to contact you, we will use your official UNSW email address of in the first instance. It is your responsibility to regularly check your university email account. Please state your student number in all emails.

Course Aims

Since the introduction of digital computers, the importance of discrete and thus finite problems in mathematics has become apparent. For this reason this course, which introduces students to some basic ideas on Finite Mathematics, should prove useful to future Computer Scientists and Software Engineers while at the same time providing Mathematics students with an introduction to ideas in Number Theory, the theory of finite fields, cryptography and Algebraic Coding Theory. There is a follow-on course, MATH3411, Information, Codes and Ciphers, which develops the ideas in greater depth.

Course Description

This is an introduction to those areas of Mathematics which underpin parts of computing. The main topics are integer and modulo arithmetic (including tests for primeness of integers), polynomial algebra (including factorization of polynomials and creation of new fields) and an introduction to cryptography and error correcting codes.

Note: MATH1081 Discrete Mathematics is recommended.

Assessment and Deadlines

Assessment	Week	Weighting %	Due date if applicable
Test 1	4	20
Test 2	9	20
Final Exam	Exam Period	60

Late Submission of Assessment Tasks

No late submissions will be accepted. (Where "late" in this context means after any extensions granted for Special Consideration or Equitable Learning Provisions.)

Course Schedule

The course will include material taken from some of the following topics. This is should only serve as a guide as it is not an extensive list of the material to be covered and the timings are approximate. The course content is ultimately defined by the material covered in lectures.

Weeks	Topic	Reading (if applicable)
1	Introduction. Natural Numbers: Algebraic properties; Primes; Division; Divisibility
2	Representation of Numbers: Integers; Rationals; Reals; Continued fractions
3	Modular Arithmetic: Congruences; Divisibility tests
4	Solving Linear Equations: In integers and modulo $n$; Chinese Remainder Theorem
5	Powers and Roots: Fermat's theorem; Euler's theorem
7	Applications: Arithmetic of Large Numbers; Primality testing; Cryptography; Error-correcting codes
8	Polynomials: Arithmetic; common divisors; factorisation; modular arithmetic; Polynomial Equations; Factorising over fields
9	Finite Fields: General yheory; Properties of finite fields; Primitive elements; Minimal polynomials
10	Error Correcting Codes: Hamming codes; BCH codes for one and two errors

Textbooks

Recommended Reading: L. Childs, A Concrete Introduction to Higher Algebra, Springer-Verlag, 1984 (P512/84).

Course Learning Outcomes (CLO)

CLO1 demonstrate an understanding of the basic concepts of basic number theory, particularly divisibility and congruence as well as the basic theory of finite fields.

CLO2 use finite field arithmetic in application such as cryptography, coding, number theory and theoretical computer science

CLO3 demonstrate increased competency in mathematical presentation and written skills. 

Moodle

Log in to Moodle to find announcements, general information, notes, lecture slide, classroom tutorial and assessments etc. https://moodle.telt.unsw.edu.au

Computing lab

The main computing laboratory is Room G012 of the Red Centre. You can get to this lab by entering the building through the main entrance to the School of Mathematics (on the Mezzanine Level) and then going down the stairs to the Ground Level. A second smaller lab is Room M020, on the mezzanine level of the Red Centre.

For more information, including opening hours, see the computing facilities webpage: https://www.maths.unsw.edu.au/currentstudents/computing-facilities

Remember that there will always be unscheduled periods when the computers are not working because of equipment problems and that this is not a valid excuse for not completing tests on time.

School and UNSW Policies

The School of Mathematics and Statistics has adopted a number of policies relating to enrolment, attendance, assessment, plagiarism, cheating, special consideration etc. These are in addition to the Policies of The University of New South Wales. Individual courses may also adopt other policies in addition to or replacing some of the School ones. These will be clearly notified in the Course Initial Handout and on the Course Home Pages on the Maths Stats web site.

Students in courses run by the School of Mathematics and Statistics should be aware of the School and Course policies by reading the appropriate pages on the Maths Stats web site starting at: https://www.maths.unsw.edu.au/currentstudents/assessment-policies

The School of Mathematics and Statistics will assume that all its students have read and understood the School policies on the above pages and any individual course policies on the Course Initial Handout and Course Home Page. Lack of knowledge about a policy will not be an excuse for failing to follow the procedure in it.

Academic Integrity and Plagiarism

UNSW has an ongoing commitment to fostering a culture of learning informed by academic integrity. All UNSW staff and students have a responsibility to adhere to this principle of academic integrity. Plagiarism undermines academic integrity and is not tolerated at UNSW. Plagiarism at UNSW is defined as using the words or ideas of others and passing them off as your own.

The UNSW Student Code provides a framework for the standard of conduct expected of UNSW students with respect to their academic integrity and behaviour. It outlines the primary obligations of students and directs staff and students to the Code and related procedures.

In addition, it is important that students understand that it is not permissible to buy essay/writing services from third parties as the use of such services constitutes plagiarism because it involves using the words or ideas of others and passing them off as your own. Nor is it permissible to sell copies of lecture or tutorial notes as students do not own the rights to this intellectual property.

If a student breaches the Student Code with respect to academic integrity, the University may take disciplinary action under the Student Misconduct Procedure.

The UNSW Student Code and the Student Misconduct Procedure can be found at: https://student.unsw.edu.au/plagiarism

An online Module “Working with Academic Integrity” (https://student.unsw.edu.au/aim) is a six-lesson interactive self-paced Moodle module exploring and explaining all of these terms and placing them into your learning context. It will be the best one-hour investment you’ve ever made.

Plagiarism

Plagiarism is presenting another person's work or ideas as your own. Plagiarism is a serious breach of ethics at UNSW and is not taken lightly. So how do you avoid it? A one-minute video for an overview of how you can avoid plagiarism can be found https://student.unsw.edu.au/plagiarism.

Additional Support

ELISE (Enabling Library and Information Skills for Everyone)

ELISE is designed to introduce new students to studying at UNSW.

Completing the ELISE tutorial and quiz will enable you to:

■  analyse topics, plan responses and organise research for academic writing and other assessment tasks

■  effectively and efficiently find appropriate information sources and evaluate relevance to your needs

■  use and manage information effectively to accomplish a specific purpose

■  better manage your time

■  understand your rights and responsibilities as a student at UNSW

■  be aware of plagiarism, copyright, UNSW Student Code of Conduct and Acceptable Use of UNSW ICT Resources Policy

■  be aware of the standards of behaviour expected of everyone in the UNSW community

■  locate services and information about UNSW and UNSW Library

Some of these areas will be familiar to you, others will be new. Gaining a solid understanding of all the related aspects of ELISE will help you make the most of your studies at UNSW.

The ELISE training webpages: https://subjectguides.library.unsw.edu.au/elise/aboutelise

Equitable Learning Services (ELS)

If you suffer from a chronic or ongoing illness that has, or is likely to, put you at a serious disadvantage, then you should contact the Equitable Learning Services (previously known as SEADU) who provide confidential support and advice.

They assist students:

●  living with disabilities

●  with long- or short-term health concerns and/or mental health issues

●  who are primary carers

●  from low SES backgrounds

●  of diverse genders, sexes and sexualities

●  from refugee and refugee-like backgrounds

●  from rural and remote backgrounds

●  who are the first in their family to undertake a bachelor-level degree.

Their web site is: https://student.unsw.edu.au/els/services

Equitable Learning Services (ELS) may determine that your condition requires special arrangements for assessment tasks. Once the School has been notified of these, we will make every effort to meet the arrangements specified by ELS.

Additionally, if you have suffered significant misadventure that affects your ability to complete the course, please contact your Lecturer-in-charge in the first instance.

Academic Skills Support and the Learning Centre

The Learning Centre offers academic support programs to all students at UNSW Australia. We assist students to develop approaches to learning that will enable them to succeed in their academic study. For further information on these programs please go to: http://www.lc.unsw.edu.au/services-programs

Applications for Special Consideration for Missed Assessment

Please adhere to the Special Consideration Policy and Procedures provided on the web page below when applying for special consideration. https://student.unsw.edu.au/special-consideration

Please note that the application is not considered by the Course Authority, it is considered by a centralised team of staff at the Nucleus Student Hub. The School will contact you (via student email account) after special consideration has been granted to reschedule your missed assessment, for a lab test or paper-based test only.

For applications for special consideration for assignment extensions, please note that the new submission date and/or outcome will be communicated through the special consideration web site only, no communication will be received from the School.

For Dates on Final Term Exams and Supplementary Exams please check the “Key Dates for Exams” ahead of time to avoid booking holidays or work obligations. https://student.unsw.edu.au/exam-dates

If you believe your application for Special Consideration has not been processed, you should email [email protected] immediately for advice.

Course Evaluation and Development (MyExperience)

Student feedback is very important to continual course improvement. This is demonstrated within the School of Mathematics and Statistics by the implementation of the UNSW online student survey myExperience, which allows students to evaluate their learning experiences in an anonymous way. myExperience survey reports are produced for each survey. They are released to staff after all student assessment results are finalised and released to students. Course convenor will use the feedback to make ongoing improvements to the course.