Mathematical Methods in Theoretical Physics

6 EC

Semester 1, period 2

5354MMIT6Y

Owner Master Physics and Astronomy (joint degree)
Coordinator dr. V. Gritsev
Part of Master Physics and Astronomy, track Theoretical Physics, year 1Master Physics and Astronomy, track GRAPPA, year 1

Course manual 2018/2019

Course content

The course focuses on (algebraic) topological methods and group theory and their applications in theoretical physics. Subjects to be covered will be simplicial homology, homotopy, manifolds, groups, De Rham cohomology. When time permits, the basics of fibre bundles and connections may also be covered.

Study materials

Literature

  • M. Nakahara, 'Geometry, Topology and Physics'.

  • C. Nash and S. Sen, 'Topology and Geometry for Physicists'.

  • B. Schutz, 'Geometrical Methods for Mathematical Physics'.

Objectives

At the end of the course, the student will be familiar with concepts of Lie groups, manifolds and Riemann geometry, homotopy, homology and cohomology, and applications of above concepts in physics.

Teaching methods

  • Lecture
  • Seminar
  • Laptop seminar
  • Self-study

Learning activities

Activity

Number of hours

Zelfstudie

168

Attendance

Requirements concerning attendance (OER-B).

  • In addition to, or instead of, classes in the form of lectures, the elements of the master’s examination programme often include a practical component as defined in article 1.2 of part A. The course catalogue contains information on the types of classes in each part of the programme. Attendance during practical components is mandatory.

    • Assessment

    Item and weight Details

    Final grade

    40%

    Homeworks

    60%

    Exam

    Assignments

    There are three homework assignments planned for this course. The average grade for the three homework sets will count as 40 % of the final grade. Discussing the homework problems with your fellow students is allowed, but we expect every student to
    write down his or her own solutions.

    Fraud and plagiarism

    The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

    Course structure

    Weeknummer Onderwerpen Studiestof
    1 Introduction and math preliminary Nakahara, chapters 1-2 
    2 Homology Nakahara, chapter 3
    3 Homotopy Nakahara, chapter 4
    4 Homotopy and Manifolds Nakahara, chapter 5
    5 Manifolds and forms  Nakahara, chapter 5
    6 Cohomology  Nakahara, chapter 6
    7 Geometry Nakahara, chapter 7
    8 Preparation for the exam and the exam. Nakahara

    Timetable

    The schedule for this course is published on DataNose.

    Additional information

    Teaching assistant for this course is Ward Vleeshouwers (wardvleeshouwers@protonmail.com)

    Contact information

    Coordinator

    • dr. V. Gritsev

    v.gritsev@uva.nl