James Cook's Notes from NCSU Courses Homepage
Welcome, I include here scans of notes, assignments, tests and other study materials from courses I took at NCSU either in my undergraduate (1998-2001) or graduate (2003-2008) work. All errors are my own obviously.

Odds and Ends:

derivation of Snell's Law by minimizing time via variational calculus.

My course notes from Math 430 at NCSU. This course introduces Maxwell's Equations in terms of differential forms on Minkowski space.

Notes from a summer I read about Quantum Mechanics and Symmetries from Greiner's text:

• Chapter 3 and 4 on exponentiation of Lie algebra, Lie groups, generation of symmetries in quantum mechanics
• Chapter 5 on isospin and representations, the adjoint representation.
• Chapter 6 and 7 on hypercharge and SU(3) representations as derived from SU(2) subalgebras.
• Chapter 8 on quarks built from SU(3) representations
• my talk from graduate school on Quarks built from SU(3)

notes on magnetic monopoles (actually, this is from both SUNY Stony Brook E&M and NCSU, I think these were based on Nakahara's old edition. )

Manifold Theory:

1. part 1 outline of course, inverse function theorem,
2. part 2 examples of manifolds, atlas, topology,
3. part 3 stereographic projection, smooth maps between manifolds,
4. part 4 connected implies path connected on manifold, theorems on curves in a manifold,
5. part 5 a bit more on bumps, derivations and differentiation on manifold,
6. part 6 contrasting views of tangent vectors, the differential,
7. part 7 tangent bundle,
8. manifolds my study guide from the notes above

Lie Groups:

1. Syllabus
2. Topic Overview
3. Notes: definition, examples of matrix groups, matrix groups as manifolds, matrix exponential
4. Notes: exponential chart, Lie algebra set-up
5. Notes: left invariant vector fields, subgroups, submanifolds and their Lie subalgebras
6. Notes: (handed out p. 157-194 of Dr. Fulp notes), theory developing one parameter subgroups
7. Notes: local Lie groups comment, functorial theorems interlinking Lie groups and algebras, one parameter subgroup properties
8. Notes: from a friend, some analytical bits
9. Notes: Frobenius type arguments, preparing for integral manifolds, looks like I missing some notes here between the next one
10. Notes: representation theory, properties of integral on Lie group, trace etc.
11. Notes: Schur's Lemma, irreducible modules, G-morphism, theorems about integral on Lie group, representative function of group
12. Notes: group characters, left-invariance of integral
13. Dr. Fulp's supplemental notes on representative functions and irreducible submodules, preparing for proof of Peter-Weyl Theorem
14. Midterm and Final and study materials:
    • Review for Midterm
    • Test 1
    • Solution to in-class Test 1
    • Takehome Midterm problem solution
    • part 1 Review for Final
    • part 1 Review for Midterm
    • Final Exam
15. Homeworks (possibly not in order)
    • Homework on matrix representations
    • Homework on orthogonal matrices
    • Homework on matrix groups
    • Homework on connected nbhd of identity
    • Homework on covering manifolds
    • Homework on Lie algebras

Last modified 7-16-2025

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