Fall 2026
Michael Kiessling
Course Description:
In a nutshell, this course is about Hilbert's 6th problem, in updated form.
More to the point, in this course classical physics is done not only mathematically rigorously in the sense of ``supplying epsilons and deltas'' whenever we can, while the working physicist tends to be more cavalier about these. More importantly, we emphasize conceptual clarity: how fundamental (microscopic) physical theories aim to explain the physical world in which we live, how the motion of atoms and the evolution of fields gives rise to the ``everyday'' phenomena. The classical universe according to Newton, and according to Einstein, are covered --- though of course in updated versions!
Text:
Professor Kiessling's extensive lecture notes
Prerequisites:
to be a graduate student of mathematics or physics; others by permission from the instructor
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Fall 2025
Michael Kiessling
Course Description:
In this course classical physics is done mathematically rigorously. This not only implies ``supplying epsilons and deltas'' where the working physicists tends to be cavalier, we also emphasize conceptual clarity. After all, we want to understand what our physical theories say about the world, don't we? The universe according to Newton, and according to Einstein, are covered in this course. Mathematically we will see how physical problems pushed algebra and analysis, and how the evolution of those fields informed physics --- via the theories of ODEs, PDEs, probabiiity and statistics, functional analysis, group theory, etc etc.
There will be no exams, and only suggested HW, but essentially regular attendance and active participation during the lectures is required.
Text:
Professor Kiessling's extensive lecture notes (200+ pages)
Prerequisites:
Being a graduate student in mathematics or physics; undergraduates with special permission
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Fall 2024
Ian Jauslin
Course Description:
In this course, we will discuss the mathematical structure of Classical Mechanics. We will start with a brief discussion of the Newtonian formulation, and then discuss the Lagrangian and Hamiltonian formulations. We will then use these formulations to discuss the properties of many-body systems and introduce the fundamentals of classical statistical mechanics. Attention will be spent on the mathematical structures involved in these theories, and will take us to discuss topics in symplectic geometry, functional analysis and probability theory. This course does not require pre-existing knowledge in these fields, as we will cover what we need.
Text:
Lecture notes
Prerequisites:
None
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Fall 2023
Michael Kiessling
Course Description:
The course covers Newton's mechanics, Maxwell's electromagnetic field theory, and Einstein's special theory of relativity, with only a brief outlook on the general theory of relativity (that is offered by Prof. Tahvildar-Zadeh in its own course). The presentation is unlike in any textbook and contains as of yet unpublished results.
Text:
Prof. Kiessling's lecture notes will be handed out in class.
Prerequisites:
Advanced calculus / a desire to discover the mathematical secrets of the universe
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Fall 2022
Ian Jauslin
Course Description:
In this course, we will discuss the mathematical structure of Classical Physics. We will discuss Classical Mechanics, both in the Newtonian formulation, as well as the equivalent Lagrangian and Hamiltonian formulations. We will also cover topics in electromagnetism, and Special Relativity. We will not cover Quantum Physics, which is the subject of the follow-up course 562, but the topics covered here form the basis on which Quantum Mechanics and Quantum Field Theory are built.
The aim of this course is to develop an understanding of these topics in a mathematically rigorous way.
Text:
Michael Kiessling's lecture notes
Prerequisites:
501 or special permission by instructor
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Fall 2021
Michael Kiessling
Course Description:
The course offers a mathematically rigorous treatment of the so-called classical theories of physics, i.e. non-quantum physics (which will be covered in the follow-up course 562). Topics: Newton's non-relativistic model of the world (space and time; N point particles in space which move according to Newton's laws of motion; from atoms to stars), and its Langrangian, Hamiltonian, and Hamilton-Jacobian reformulations. Maxwell's theory of electromagnetic fields and recent developments; Einstein's special (and a bit of his general) relativity theory.
Text:
Professor Kiessling's lecture notes
Prerequisites:
501 or special permission by instructor
Schedule of Sections:
Previous Semesters:
- Fall 2019 Prof. Kiessling
- Fall 2018 Prof. Kiessling