Phys-197: Analytical Methods in Physics 2022

Course Assistants

Oğuz Alp Ağırbaş, Anıl Ata, Ahmet Baysan, Yağmur Bülbül, Eren Demirci, Umut Nuri Erdoğan, Tuğba Hırlı, Recep Semih Kanber, Ahmet Berk Kavruk, Zehra Özcan, Ali Mert Yetkin, Reyhan Yumuşak, Sena Zorla

Homeworks

  • HW1
  • HW2
  • HW3 (deadline 31.10.2022)
  • HW4 (deadline 12.12.2022)

Projects

Projects will involve studying a paper of interest, writing a 3 – (infinity) page report, and making a brief oral online presentation (10-15 minutes). Below are project suggestions, each group of students (3 students in a group) is supposed to prepare one project. Please, try to decide on your project topic by October 22, 2022.

  1. Starrett, J. (2007). Solving differential equations by symmetry groups, The American Mathematical Monthly, 114(9), 778-792. [pdf]
  2. Aharonov, D., Beardon, A., & Driver, K. (2005). Fibonacci, Chebyshev, and orthogonal polynomials, The American Mathematical Monthly, 112(7), 612-630. [pdf]
  3. Louis Zulli, Charting the 3-Sphere–An Exposition for Undergraduates, The American Mathematical Monthly , Mar., 1996, Vol. 103, No. 3, pp. 221-229 [pdf]
  4. Roger B. Nelsen, Elementary Proofs of the Trigonometric Inequalities of Huygens, Cusa, and Wilker, Mathematics Magazine, 93:4, 276-283 (2020) [link]
  5. David Speyer & Bernd Sturmfels, Tropical Mathematics, Mathematics Magazine, 82:3, 163-173, (2009) [link]
  6. Kenneth S. Miller, Derivatives of Noninteger Order, Mathematics Magazine, 68:3, 183-1922 (1995) [link]
  7. Lorenzo David (2022), The Binomial Coefficient as an (In)finite Sum of Sinc Functions, The American Mathematical Monthly, 129:8, 734-742 [link]

Examination

The grade will be composed as follows: problem sessions 20%, homework 15%, typed notes of a project (pdf and tex-files) and presentation 15%, exams 50%. The projects will be evaluated according to the clarity of exposition, effort, and calculations.

Literature

I am not going to follow any specific book. List of some books:

  • Y. B. Zeldovich, I. M. Yaglom, Higher Math for Beginning Physicists and Engineers
  • Victor V. Prasolov, Polynomials, 1999
  • Victor V. Prasolov, Intuitive Topology, 1995
  • A. Kurosh, Higher algebra, 1975
  • Van der Waerden, Modern Algebra, 1930

Previous year papers