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Module

MAS8814 : Advanced Concepts of Applied Mathematics

  • Offered for Year: 2021/22
  • Module Leader(s): Dr Graeme Sarson
  • Lecturer: Dr Paul McFadden
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus
Semesters
Semester 1 Credit Value: 10
Semester 2 Credit Value: 10
ECTS Credits: 10.0

Aims

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

Module Summary: 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

This module will introduce students to the two 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.

Introduction to Quantum Field Theory:

Combining special relativity and quantum mechanics, quantum field theory is a cornerstone of modern theoretical physics. It provides a common language for particle physics, cosmology and condensed matter, and its predictions are 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 dynamics of classical fields; (ii) Noether's theorem connecting symmetries to conservation laws; (iii) canonical quantisation for a scalar field; (iv) the energy of the vacuum.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture91:009:00Synchronous On-Line Material
Structured Guided LearningLecture materials361:0036:00Non-Synchronous Activities
Guided Independent StudyAssessment preparation and completion301:0030:00N/A
Scheduled Learning And Teaching ActivitiesLecture91:009:00Present in Person (S2)
Structured Guided LearningStructured non-synchronous discussion181:0018:00N/A
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Office Hour or Discussion Board Activity
Guided Independent StudyIndependent study941:0094:00N/A
Total200:00
Jointly Taught With
Code Title
PHY8048Advanced Concepts of Applied Mathematics
Teaching Rationale And Relationship

Non-synchronous online materials are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on assessed work. Present-in-person and synchronous online sessions are used to help develop the students’ abilities at applying the theory to solving problems and to identify and resolve specific queries raised by students, and to allow students to receive individual feedback on marked work. Students who cannot attend a present-in-person session will be provided with an alternative activity allowing them to access the learning outcomes of that session. In addition, office hours/discussion board activity will provide an opportunity for more direct contact between individual students and the lecturer: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Student’s should consult their individual timetable for up-to-date delivery information.

Assessment Methods

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

Other Assessment
Description Semester When Set Percentage Comment
Written exercise1M10written exercises
Written exercise2M10written exercises
Written exercise2M80Alternative Assessment
Assessment Rationale And Relationship

A substantial formal examination / alternative assessment is appropriate for the assessment of the material in this module. The course assessments will consist of five assignments of approximately equal weight and will 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