## Math 405: Mathematical Physics: Summer 2018

This is a modern mathematical physics course focusing on mathematical physics techniques used in theoretical physics.  We will use many examples from high energy physics

Marking

Anybody who understands this course, does the homework, and comes to class very regularly, should get a very good grade.  The marking has to be according to BRACU rules, as far as I know.  This means

• Attendance: 5%,
• Homework & Quizzes: 25%,
• Midterm 20%,
• Final 50%.

You need to try to attend EVERY lecture.    I will be happy with students who attend all the lectures and are not late.

Class structure

You will be expected to write up summaries of the topics we cover in class to turn is as homework. You will also be expected to complete all of the homework.

Course Book:

• Riley & Hobson, “Mathematical Methods for Physics & Engineering,” Cambridge University Press, 3rd Edition.
• Stephonson & Radmore, “Advanced Mathematical Methods for Engineering and Science Students,” Cambridge University Press, 1st Edition.
• Cahill, “Physical Mathematics,” Cambridge University Press, 1st Edition.
• Polchinski, “String Theory: Volume 1,” Cambridge University Press, 1st Edition
• Tong, “Lectures on String Theory,” https://arxiv.org/abs/0908.0333

Some background material for the course on special relativity and generating functions are

A wonderful popular science introduction to the place of modern mathematical physics is

This should be the first book you read before coming to class.

## Mathematical Physics

BRACU ClassDateTimeRoom
Phy 405Su, Tue2pm-3:20pmUB3502

Slides

Lecture Notes

Tutorials

1. Summary of Quantum Mechanics:
1. Advanced Linear Algebra, by Yang
2. Harmonic Oscillator & Hermite Polynomials
1. Shankar
3. Index notation
1. Physical Mathematics, by Cahill, Chap 11.1-11.9
2. Primer on Index Notation
3. Special Relativity by Rindler, Chapter 4 and Chapter 5, Special Relativity by Woodhouse
4. Homework: Index manipulation
5. Homework Solutions
4. Lagrange Multipliers
5. Lagrangian Mechanics
6. Symmetry Transformations: