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Faculty Handbook 2022-2023

# Module Description

Please ensure you check the module availability box for each module outline, as not all modules will run each academic year.

## Department: Mathematical Sciences

### MATH1031: DISCRETE MATHEMATICS

Type Level Credits Availability Module Cap Open 1 20 Available in 2022/23 Durham

#### Prerequisites

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

• None.

• None.

#### Aims

• To provide students with a range of tools for counting discrete mathematical objects.
• To introduce students to graph theory and its varied applications.
• To develop the students' ability in group working, written and oral skills.

#### Content

• Principles of counting: permutations and combinations, combinatorial vs arithmetical proof.
• Pigeonhole principle, inclusion and exclusion, mathematical induction.
• Recurrence relations, Fibonacci numbers, generating functions, and partitions.
• Basic concepts of graphs.

#### Learning Outcomes

Subject-specific Knowledge:
• Ability to solve a range of predictable and less predictable problems in Discrete Mathematics.
• Awareness of some fundamental mathematical concepts applicable in this field.
• A broad knowledge and basic understanding of Discrete Mathematics.
Subject-specific Skills:
• 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
Key Skills:
• 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

 Activity Number Frequency Duration Total/Hours Lectures 27 2 per week in weeks 1-10, 11-13, 21 (excluding collection examination) 1 Hour 27 Tutorials 12 Weekly in weeks 2-10, 12-13, 21. 1 Hour 12 ■ Seminars 6 Weekly in weeks 14-19 2 Hours 12 ■ Preparation and Reading 149 Total 200

#### Summative Assessment

Component: Examination Component Weighting: 70%
Element Length / duration Element Weighting Resit Opportunity
Written examination 2 hours 100% Yes
Component: Coursework Component Weighting: 30%
Element Length / duration Element Weighting Resit Opportunity
Presentation in Week 19 33% Yes
Written Report 67% Yes

#### Formative Assessment:

Weekly written assignments during term 1. Normally, each will consist of solving problems and will typically be one to two pages long. Students will have about one week to complete each assignment. 45 minute collection paper in the beginning 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