This page contains selections from a recent course syllabus, with annotations, additional description, and commentary. Please drop me an email if you have any questions.
Examination of mathematical methods commonly used in physics, their application to the solution of physical problems through numerical methods and algorithm development, and modern computational methods. The goal of this course is to give an introduction to methods for solving difficult mathematics problems that arise in physics. This requires the combination of applied mathematics with the intelligent use of numerical algorithms and computers. We will survey tools developed from probability and statistics (statistical analysis of physical data, modeling using stochastic processes, etc.) and progress toward more challenging and applied topics including Monte Carlo, stochastic optimization, and molecular dynamics.
Prerequisites: MATH 2215 (Multivariate Calculus) and PHYS 2212K (Principles of Physics II) with a C or higher, as well as basic familiarity with a programming language.
Suggested Reference: Jacobs, K. Stochastic Processes for Physicists: Understanding Noisy Systems. Cambridge: Cambridge University Press (2010). doi:10.1017/CBO9780511815980. ISBN-13: 9780521765428, ISBN-10: 0521765420
Credit Hours: 3
At the completion of this course, students will be able to:
select a satisfactory mathematical method to solve a given physics problem.
evaluate what error is introduced by a mathematical approximation, and what error is introduced by a numerical method.
understand when a result is statistically relevant.
compare different methods for solving physical equations.
understand the difference between a stochastic and deterministic method.
The course syllabus provides a general outline for the course; deviations may be necessary, and will be announced on iCollege.
| Week | Date | Topic |
|---|---|---|
| 1 | 1/14 | Introduction to Probability |
| 2 | 1/18 | Randomness and Random Number Generators |
| 3 | 1/25 | Random Sampling |
| 4 | 2/1 | Noise and Stochastic Processes in Physics |
| 5 | 2/8 | Brownian Motion & Diffusion |
| 6 | 2/15 | Random Walks, Stochastic Differential Equations |
| 7 | 2/22 | Monte Carlo Methods |
| 8 | 3/1 | Ising Model |
| 9 | 3/8 | ————- Take-Home Midterm Exam ————- |
| 10 | 3/15 | ————- Spring Break ————– |
| 11 | 3/22 | Stochastic Optimization |
| 12 | 3/29 | Molecular Dynamics |
| 13 | 4/5 | Granular Materials |
| 14 | 4/12 | Special Functions |
| 15 | 4/19 | Oral Final Exams |
Reading assignments and problems will be given regularly. Assignments will be announced on the iCollege page for this course. There will be one midterm and one final exam. The midterm exam will be an open-book take-home exam, and students will be given one week to complete it. The final exam will be conducted as a class project.
Final grades will be assigned on a curve. Different components of the coursework will be weighted:
| Assignments | 40% |
| Take-home midterm | 30% |
| Final project | 30% |
General
This class will be run as an advanced undergraduate course.
Assignments
Reading assignments and problems will be given regularly.
It is the student’s responsibility to understand the reading, to engage with the material on iCollege, to solve the problems assigned, to turn in all work associated with those problems, and to understand the solutions.
Attendance and Absences
In accordance with GSU policies, attendance is not required.
Course Feedback
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