Philip K Schwartz

Teaching

Here you find a selection of material from my teaching. If you want to share or re-use any of the material listed on this page, please contact me first—but please feel free to cite it for scientific purposes without asking! A full list of my teaching activities may be found in my CV.

University teaching

Newton–Cartan gravity
Leibniz University Hannover, academic years 2021/22, 2022/23, and 2024/25
A course on Newton–Cartan gravity, i.e. geometrised Newtonian gravity, aimed at advanced students with background knowledge in differential geometry and general relativity. It consists of an introductory course in the winter semester and a more advanced course on gauge-theoretic aspects in the summer semester. For students not familiar with principal bundles, I offered an extra ‘crash course’ of four-and-a-half lecture sessions.
Lecture notes (6+93 pages)
Handwritten transcript of the principal bundle ‘crash course’
Exercises: Sheet 1, Sheet 2, Sheet 3, Sheet 4, Sheet 5, Sheet 6, Sheet 7, Sheet 2.1, Sheet 2.2, Sheet 2.3

A significantly extended version of the lecture notes from these courses has been published as a volume in Springer’s Lecture Notes in Physics:
Newton–Cartan Gravity: A Modern Introduction to Geometrised Newtonian Gravity
Lecture Notes in Physics 1044 (Springer, Cham, 2026)
Repetitorium Theoretical Electrodynamics and Theoretical Physics B
Leibniz University Hannover, summer semester 2021
Two one-week refresher ‘crash courses’ on classical electrodynamics, aimed at second-semester students in the physics bachelor’s programme (‘Electrodynamics’) or in the physics teaching degree programme (‘Theory B’). Due to the COVID-19 pandemic, they were given as online courses, recordings of which (in German) are available on request.
Repetitorium Mathematical Methods of Physics and Theoretical Physics A
Leibniz University Hannover, winter semester 2020/21
Two one-week refresher ‘crash courses’ on mathematical methods of physics and basic Newtonian mechanics, aimed at first-semester students in the physics bachelor’s programme (‘Mathematical Methods’) or in the physics teaching degree programme (‘Theory A’). Due to the COVID-19 pandemic, they were given as online courses, recordings of which (in German) are available on request.

Courses given at academies of the Club der Ehemaligen der Deutschen SchülerAkademien e. V.

I am a member of the Club der Ehemaligen der Deutschen SchülerAkademien e. V., the alumni organisation of the Deutsche SchülerAkademien. At the academies organised by this club, I have given several courses on physics and mathematics. For two mathematics courses, I have prepared lecture notes, which are available here.
Differential Forms and basics of Symplectic Geometry
CdE-SommerAkademie 2022
A one-week course on differential forms, with an outlook on the basic notions of symplectic geometry.
Lecture notes (4+84 pages, in German), Exercises (in German)
Introduction to Differential Geometry
CdE-WinterAkademie 2018/19
A one-and-a-half-week course on differential geometry, joint with Benjamin Haake.
Lecture notes (86 pages, in German), Exercises (in German)