SHORT TOPICS

These are shorter treatments (some merely a page or two) of topics that arose in various courses. The students for which these were originally intended ranged in level from freshmen to advanced graduate students. Items marked "scanned" were converted from physical originals.

Hilbert Spaces of Functions (2 pp, 0.03 MB)
https://uchicago.box.com/s/g352or9nnncchb94mj2iedrfq60p58mk

Basis for L^2[R^n] (3 pp, 0.05 MB)
https://uchicago.box.com/s/8qa53m7reev3afhmayh00oe3xjt80djk

Adjoint of an Operator (1 pp, 0.3 MB, scanned)
https://uchicago.box.com/s/j3lfpcxsbu2etu4q1nbjgc8d6q5pxq13

Self-Adjoint and Unitary Operators (1pp, 0.1 MB)
https://uchicago.box.com/s/kpyus4lp0ruirdkv6jf1du580mqmzd60

Unbounded Operators (4 pp, 1.0 MB, scanned)
https://uchicago.box.com/s/hjy764z9m5v2poyrj0foydwstkwlqcpo

Tensor Products of Operators (1 pp, 0.08 MB)
https://uchicago.box.com/s/vz5ug9rwvho318a1u64mo4ivf9ze8o2a

Direct Sum, Tensor Product of Hilbert Spaces (2 pp, 0.7 MB, scanned)
https://uchicago.box.com/s/ytonv5bt3ahdgb91mxx5myw2rug7moa5

Ray-Evolution on Hilbert Spaces (4 pp, 0.05 MB)
https://uchicago.box.com/s/e5qbs8gfsmz0enap1cwf9tg53vvfjqyi

Traceclass Operators (2 pp, 0.1 MB)
https://uchicago.box.com/s/yjx4kdumejlcpfgzs0co7rvxq471y5u2

Spectral Theorem (3 pp, 0.4 MB, scanned)
https://uchicago.box.com/s/m34f81fobje5tbi8cglahcwf5znhhss0

Hamiltonian Evolution (4 pp, 0.5 MB, scanned)
https://uchicago.box.com/s/wonnhpu6khwpr210vld0htjjpppm6o0a

Heisenberg Formulation (2 pp, 0.3 MB, scanned)
https://uchicago.box.com/s/e0n0lvymunqvyg3f960hn83mael4hngy

Superselection Principles (2 pp, 0.6 MB, scanned)
https://uchicago.box.com/s/q35zmotsi5bahrkhfr7q1m6sjw2lsaqc

A Watched Pot Never Boils (4 pp, 0.1 MB)
https://uchicago.box.com/s/1frcnfe9k8aavhx1y7dza6jvn25m5na7

Path Integrals (19 pp, 0.2 MB)
https://uchicago.box.com/s/km50iucsjla7i5mkvrlw5iybug7vde7d

Feynmann Path-Integral Example (3 pp 0.1 MB)
https://uchicago.box.com/s/5c5ffbomzd4pnap7a4e9xeabc6w20du5

Uncertainty Relations (2 pp, 0.2 MB, scanned)
https://uchicago.box.com/s/tjfxm3aoe9vlmys55322g8diw7rpkaeo

Quantum Mechanics of a Charged Particle (3 pp, 0.1 MB)
https://uchicago.box.com/s/ixtzb3jr558cq3ui2zprztqld3hv2evj

You Can't Observe the Quantum State (4 pp, 0.1 MB)
https://uchicago.box.com/s/63rtpafsojja6pt8zxo9q0qoo0k7tqmm

Spinors (4 pp, 0.1 MB)
https://uchicago.box.com/s/6l6f1mj30hlgd07zdzzhoijth1zj9o7s

Spinor Algebra (4 pp, 1.3 MB, scanned)
https://uchicago.box.com/s/5hgtlkjv6zx0tmcto489ihomnww5c1wy

Conducting Perfect Fluid (4 pp, 0.1 MB)
https://uchicago.box.com/s/demw1x971c43qb1snqw9tbxjpojypcxq

Conducting Fluids in Space-time (3 pp, 0.03 MB)
https://uchicago.box.com/s/vugjhk7ouh1ohtm6kzvqdgka1u4s0e9f

Fibre Bundles (4 pp, 0.1 MB)
https://uchicago.box.com/s/9cb9oix3kx59ltb2cgh0xn3yie3k7iqr

Fourier Analysis (7 pp, 0.1 MB)
https://uchicago.box.com/s/4q4y63u122z6s48lqkkjngmtffpgdirp

Linear Algebra (9 pp, 1.2 MB, scanned)
https://uchicago.box.com/s/7irk8la3spnwp7okr9zfc4dqaqjb7ybw

Manifolds (5 pp, 0.5 MB, scanned)
https://uchicago.box.com/s/umit83dktxsxfjick5tngrs44k3sfah7

Nets on Topological Spaces (1 pp, 0.03 MB)
https://uchicago.box.com/s/hdwlu9k64ny91gzpn3rbug6gtffm511o

Non-Standard Analysis (6 pp, 0.1 MB)
https://uchicago.box.com/s/8u8doonyr4658d4o9gs151dtclqj80c2

Distribution Functions (10 pp, 1.2 MB, scanned)
https://uchicago.box.com/s/qv7jpusha5a43nutxvy2jvupk17qs4qm

Entropy Increase in Kinetic Theory (2 pp, 0.6 MB, scanned)
https://uchicago.box.com/s/n5j14pga40uuyhjd52lu5xlmxxz3nx6i

Regular Distributions (4 pp, 0.06 MB)
https://uchicago.box.com/s/udijko1xd1w8n5fm1o88xnutpeg4nme6

Representations of Lie Algebras (10 pp, 0.1 MB)
https://uchicago.box.com/s/rc1ai9v6dxj6hkxpb3y4ar3sdzena7nl

Classification of 3-dimensional Lie Algebras (2 pp, 1.0 MB, scanned)
https://uchicago.box.com/s/bz77oykyq5o6a987r9864ndewaqs94ve

Representations of Groups (49 pp, 5.7 MB, scanned)
https://uchicago.box.com/s/0xbt8o3pamqtet59gq8diav0d2wbcbj0

Lie Groups, Lie Algebras (10 pp, 1.4 MB, scanned)
https://uchicago.box.com/s/mf9irr1242h6dhr2k2xdwpwheqkndwtc

Thermodynamics (10 pp, 1.1 MB, scanned)
https://uchicago.box.com/s/gaiwnw1lkm8djihqkgnfvq737t32p7ko

RSA Encryption (2 pp, 0.03 MB)
https://uchicago.box.com/s/e4bt0ttxgm6m68my0h34kts0xmhztsu6

Wave Equation (2 pp, 0.03 MB)
https://uchicago.box.com/s/84qklyfcbip50hmq8ik8ayfmvhorkbgf

Spherical Harmonics; Multipoles (13 pp, 1.3 MB, scanned)
https://uchicago.box.com/s/q0gu75piech5xhgyd2z8omdifa4fnci3

Calculus in R^n (2 pp, 0.04 MB)
https://uchicago.box.com/s/uv6hcbsu0pyqczlwjmafq2hje1j849ha

Calculus of Variations (6 pp, 0.1 MB)
https://uchicago.box.com/s/55b4edbx0kjis90w4akc009ifxn6cklr

Ordinary Differential Equations (3 pp, 0.04 MB)
https://uchicago.box.com/s/ti0bkll92ev11bvlhe4luxpp147prnuv

Lagrangian and Hamiltonian Mechanics (6 pp, 0.06 MB)
https://uchicago.box.com/s/xfhp4iqqozp3opqdah32gw8q9kme3wwx

Order-of-Magnitude Estimates (11 pp, 0.08 MB)
https://uchicago.box.com/s/lehotwpe3etv3pne7lfxvooe9qxqd40o

Measure Theory (16 pp, 0.1 MB)
https://uchicago.box.com/s/j0jerrcjuhick2vgi6rnk6yj5wb28ppa

Lebesque Measure (6 pp, 0.07 MB)
https://uchicago.box.com/s/xvp1ggi0f1co979jfgpp7b7tdw7zaidq

Measure Spaces (3 pp, 0.04 MB)
https://uchicago.box.com/s/cqlthbzkrh4yzu9hr3v0xj5i5sobyghw

Probability Measures (2 pp, 0.04 MB)
https://uchicago.box.com/s/fu8li19o0qhzdbybf3lak6q33h37jqtb

Thinking About Physics (3 pp, 0.3 MB, scanned)
https://uchicago.box.com/s/lzu5q4el3xq7rql348lhjcb2tk334bxv

Mathematics (4 pp, 0.1 MB)
https://uchicago.box.com/s/i1dzevpwpno599d3sr3j77p2zftgmoe0