Module MATH1031: DISCRETE MATHEMATICS

Department: Mathematical Sciences

MATH1031: DISCRETE MATHEMATICS

Prerequisites

• Normally, A level Mathematics at grade C or better, or equivalent.

Corequisites

• None.

Excluded Combination of Modules

• None.

Aims

• To provide students with a range of tools for counting discrete mathematical objects.
• To provide experience of a range of techniques and algorithms in the context of Graph Theory, many with every day applications.
• To develop the students' ability in group working, written and oral skills.

Content

• Principles of Counting: mathematical induction, permutations and combinations, combinatorial vs arithmetical proof.
• Pigeonhole principle, inclusion and exclusion.
• Prime numbers: density of prime numbers, modular arithmetic, public key encryption.
• Generating Functions: partitions, recurrence relations.
• Special Numbers: Fibonacci, Fermat, Mersenne, Stirling etc.
• Algorithms and Finite State Machines: elementary discussion of algorithmic complexity.
• Basic concepts of Graphs.
• In term 2, students will work in guided self-study through special topics in Graph theoretic/Combinatorial Mathematics
• In week 19, students will give a short presentation in groups based on their chosen topic to their peers.

Learning Outcomes

• By the end of the module students will: be able to solve a range of predictable and less predictable problems in Discrete Mathematics.
• have an awareness of the basic concepts of theoretical mathematics in the field of Discrete Mathematics.
• have a broad knowledge and basic understanding of these subjects demonstrated through one or more of the following topic areas:
• Principles of counting
• Recurrence relations and generating functions.
• Algorithms and finite state machines.
• Graphs.

• students will have basic mathematical skills in the following areas: Spatial awareness, Abstract reasoning, Modelling.
• students will develop the ability to write mathematical reports with rigour and precision

• students will have basic problem solving skills.
• students will further their oral and written skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Tutorials provide the practice and support in applying the methods to relevant situations as well as active engagement and feedback to the learning process.
• Weekly coursework provides an opportunity for students to consolidate the learning of material as the module progresses (there are no higher level modules in the department of Mathematical Sciences which build on this module). It serves as a guide in the correct development of students' knowledge and skills, as well as an aid in developing their awareness of standards required.
• Seminars in term 2 will develop the students ability for self-study on an extended and open-ended programme, and enhance their group working skills.
• Presentations in week 19 will develop students oral communication skills.
• The written report will train students to write an extended report with precision and rigour of expression.
• The end-of-year written examination provides a substantial complementary assessment of the achievement of the student.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

One written assignment each week in term 1. Normally it will consist of solving problems from a Problem Sheet and typically will be about 2 pages long. Students will have about one week to complete each assignment.45 minute collection paper in the first week of Epiphany term. Submission of written work in week 17 for feedback

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University