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Module

MAS8854 : Advanced Concepts of Applied Mathematics (Inactive)

  • Inactive for Year: 2024/25
  • Module Leader(s): Dr Paul McFadden
  • Lecturer: Professor Paul Bushby
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters

Your programme is made up of credits, the total differs on programme to programme.

Semester 2 Credit Value: 15
ECTS Credits: 8.0
European Credit Transfer System

Aims

To introduce students to a selection of advanced applied mathematical topics that underpin current internationally-recognised research at Newcastle.

Outline of Syllabus: The module involves discussion of current research in Applied Mathematics at Newcastle. The anticipated syllabus is given below, although there may be changes to reflect recent developments.

Outline Of Syllabus

The module involves discussion of current research in Applied Mathematics at Newcastle. This module will introduce students to TWO of the areas that are described below.

Mathematical Biology:
Mathematical Biology is an important application of mathematics to biology. Students are introduced to the concepts and techniques involved in developing mathematical models of biological systems. Students will learn how to analyse the resulting models and interpret their results in the context of the biological questions being asked. In particular, topics considered include population dynamics, delay differential equations and their analysis and networks of biochemical reactions.

Asymptotic and Perturbation Methods:
A universal theme in Applied Mathematics research is the search for a "good" approximation to the solution of a problem that cannot be solved exactly. If the problem features a small parameter, then often this can be achieved by constructing a sequence of increasingly accurate approximations, with an error that vanishes as the parameter tends to zero (the Taylor series for f(x-epsilon) is a familiar example). This module will introduce a range of asymptotic techniques that can be used to obtain such approximations. We will illustrate their usage with examples taken from current Applied Mathematics research.

Introduction to Quantum Field Theory:
Combining special relativity and quantum mechanics, quantum field theory is a cornerstone of modern theoretical physics. Providing a common language for particle physics, cosmology and condensed matter, its predictions are some of the most accurate and highly tested in all of science. In this course, we aim to introduce key concepts in quantum field theory in an introductory and self-contained manner. Topics to be covered include: (i) the canonical quantisation of scalar fields, (ii) perturbation theory and Feynman diagrams, (iii) symmetry and the path integral.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture341:0034:00Formal lectures
Guided Independent StudyAssessment preparation and completion118:0018:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:302:30Unseen exam
Guided Independent StudyIndependent study151:3051:30Studying, practising, and gaining understanding of course material
Guided Independent StudyIndependent study63:0018:00Review of coursework assignments and course test
Guided Independent StudyIndependent study64:0024:00Preparation for coursework assignments
Total150:00
Jointly Taught With
Code Title
PHY8034Advanced Concepts of Applied Mathematics
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Tutorials (within lectures) are used to discuss the course material, identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1502A90N/A
Exam Pairings
Module Code Module Title Semester Comment
2N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M10Coursework assignments
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments are expected to consist of six written assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The coursework assignments and allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists

Timetable