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Working through Evan Chen's
An Infinitely Large Napkin
, chapter by chapter.
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1
Starting Out
0/3
2
Basic Abstract Algebra
0/3
3
Basic Topology
0/3
4
Linear Algebra
0/7
5
More on Groups
0/3
6
Representation Theory
0/4
7
Quantum Algorithms
0/3
8
Calculus 101
0/5
9
Complex Analysis
0/4
10
Measure Theory
0/5
11
Probability
0/3
12
Differential Geometry
0/4
13
Riemann Surfaces
0/6
14
Alg NT I: Rings of In…
0/6
15
Alg NT II: Galois and…
0/5
16
Alg Topology I: Homot…
0/3
17
Category Theory
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18
Alg Topology II: Homo…
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19
Alg Geometry I: Class…
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20
Alg Geometry II: Affi…
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21
Set Theory I: ZFC, Or…
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22
Set Theory II: Model…
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A–E
Appendix
0/5
Ch 0: Sales pitches (not started)
0
Sales pitches
Ch 1: Groups (not started, 0/9 exercises)
1
Groups
Ch 2: Metric spaces (not started, 0/6 exercises)
2
Metric spaces
Ch 3: Homomorphisms and quotient groups (not started, 0/8 exercises)
3
Homomorphisms and quotie…
Ch 4: Rings and ideals (not started, 0/8 exercises)
4
Rings and ideals
Ch 5: Flavors of rings (not started, 0/9 exercises)
5
Flavors of rings
Ch 6: Properties of metric spaces (not started, 0/5 exercises)
6
Properties of metric spa…
Ch 7: Topological spaces (not started, 0/8 exercises)
7
Topological spaces
Ch 8: Compactness (not started, 0/9 exercises)
8
Compactness
Ch 9: Vector spaces (not started, 0/9 exercises)
9
Vector spaces
Ch 10: Eigen-things (not started, 0/7 exercises)
10
Eigen-things
Ch 11: Dual space and trace (not started, 0/4 exercises)
11
Dual space and trace
Ch 12: Determinant (not started, 0/8 exercises)
12
Determinant
Ch 13: Inner product spaces (not started, 0/8 exercises)
13
Inner product spaces
Ch 14: Bonus: Fourier analysis (not started, 0/2 exercises)
14
Bonus: Fourier analysis
Ch 15: Duals, adjoint, and transposes (not started, 0/8 exercises)
15
Duals, adjoint, and tran…
Ch 16: Group actions overkill AIME problems (not started, 0/5 exercises)
16
Group actions overkill A…
Ch 17: Find all groups (not started, 0/5 exercises)
17
Find all groups
Ch 18: The PID structure theorem (not started, 0/5 exercises)
18
The PID structure theorem
Ch 19: Representations of algebras (not started, 0/5 exercises)
19
Representations of algeb…
Ch 20: Semisimple algebras (not started, 0/5 exercises)
20
Semisimple algebras
Ch 21: Characters (not started, 0/5 exercises)
21
Characters
Ch 22: Some applications (not started)
22
Some applications
Ch 23: Quantum states and measurements (not started, 0/2 exercises)
23
Quantum states and measu…
Ch 24: Quantum circuits (not started, 0/4 exercises)
24
Quantum circuits
Ch 25: Shor's algorithm (not started)
25
Shor's algorithm
Ch 26: Limits and series (not started, 0/8 exercises)
26
Limits and series
Ch 27: Bonus: A hint of p-adic numbers (not started, 0/4 exercises)
27
Bonus: A hint of p-adic…
Ch 28: Differentiation (not started, 0/7 exercises)
28
Differentiation
Ch 29: Power series and Taylor series (not started, 0/5 exercises)
29
Power series and Taylor…
Ch 30: Riemann integrals (not started, 0/4 exercises)
30
Riemann integrals
Ch 31: Holomorphic functions (not started, 0/6 exercises)
31
Holomorphic functions
Ch 32: Meromorphic functions (not started, 0/5 exercises)
32
Meromorphic functions
Ch 33: Holomorphic square roots and logarithms (not started, 0/2 exercises)
33
Holomorphic square roots…
Ch 34: Bonus: Topological Abel-Ruffini Theorem (not started, 0/1 exercises)
34
Bonus: Topological Abel-…
Ch 35: Measure spaces (not started, 0/2 exercises)
35
Measure spaces
Ch 36: Constructing the Borel and Lebesgue measure (not started, 0/3 exercises)
36
Constructing the Borel a…
Ch 37: Lebesgue integration (not started, 0/2 exercises)
37
Lebesgue integration
Ch 38: Swapping order with Lebesgue integrals (not started)
38
Swapping order with Lebe…
Ch 39: Bonus: A hint of Pontryagin duality (not started, 0/2 exercises)
39
Bonus: A hint of Pontrya…
Ch 40: Random variables (TO DO) (not started, 0/2 exercises)
40
Random variables (TO DO)
Ch 41: Large number laws (TO DO) (not started, 0/2 exercises)
41
Large number laws (TO DO)
Ch 42: Stopped martingales (TO DO) (not started, 0/6 exercises)
42
Stopped martingales (TO…
Ch 43: Multivariable calculus done correctly (not started, 0/2 exercises)
43
Multivariable calculus d…
Ch 44: Differential forms (not started, 0/2 exercises)
44
Differential forms
Ch 45: Integrating differential forms (not started, 0/7 exercises)
45
Integrating differential…
Ch 46: A bit of manifolds (not started, 0/1 exercises)
46
A bit of manifolds
Ch 47: Basic definitions of Riemann surfaces (not started)
47
Basic definitions of Rie…
Ch 48: Morphisms between Riemann surfaces (not started)
48
Morphisms between Rieman…
Ch 49: Affine and projective plane curves (not started)
49
Affine and projective pl…
Ch 50: Differential forms (not started)
50
Differential forms
Ch 51: The Riemann-Roch theorem (not started)
51
The Riemann-Roch theorem
Ch 52: Line bundles (not started)
52
Line bundles
Ch 53: Algebraic integers (not started, 0/9 exercises)
53
Algebraic integers
Ch 54: The ring of integers (not started, 0/6 exercises)
54
The ring of integers
Ch 55: Unique factorization (finally!) (not started, 0/5 exercises)
55
Unique factorization (fi…
Ch 56: Minkowski bound and class groups (not started, 0/6 exercises)
56
Minkowski bound and clas…
Ch 57: More properties of the discriminant (not started, 0/6 exercises)
57
More properties of the d…
Ch 58: Bonus: Let's solve Pell's equation! (not started, 0/2 exercises)
58
Bonus: Let's solve Pell'…
Ch 59: Things Galois (not started, 0/6 exercises)
59
Things Galois
Ch 60: Finite fields (not started, 0/1 exercises)
60
Finite fields
Ch 61: Ramification theory (not started, 0/1 exercises)
61
Ramification theory
Ch 62: The Frobenius element (not started, 0/5 exercises)
62
The Frobenius element
Ch 63: Bonus: A Bit on Artin Reciprocity (not started, 0/3 exercises)
63
Bonus: A Bit on Artin Re…
Ch 64: Some topological constructions (not started, 0/3 exercises)
64
Some topological constru…
Ch 65: Fundamental groups (not started, 0/4 exercises)
65
Fundamental groups
Ch 66: Covering projections (not started)
66
Covering projections
Ch 67: Objects and morphisms (not started, 0/4 exercises)
67
Objects and morphisms
Ch 68: Functors and natural transformations (not started, 0/3 exercises)
68
Functors and natural tra…
Ch 69: Limits in categories (TO DO) (not started, 0/1 exercises)
69
Limits in categories (TO…
Ch 70: Abelian categories (not started, 0/4 exercises)
70
Abelian categories
Ch 71: Singular homology (not started, 0/2 exercises)
71
Singular homology
Ch 72: The long exact sequence (not started, 0/6 exercises)
72
The long exact sequence
Ch 73: Excision and relative homology (not started, 0/5 exercises)
73
Excision and relative ho…
Ch 74: Bonus: Cellular homology (not started, 0/5 exercises)
74
Bonus: Cellular homology
Ch 75: Singular cohomology (not started, 0/3 exercises)
75
Singular cohomology
Ch 76: Application of cohomology (not started, 0/4 exercises)
76
Application of cohomology
Ch 77: Affine varieties (not started, 0/3 exercises)
77
Affine varieties
Ch 78: Affine varieties as ringed spaces (not started, 0/3 exercises)
78
Affine varieties as ring…
Ch 79: Projective varieties (not started)
79
Projective varieties
Ch 80: Bonus: Bézout's theorem (not started, 0/2 exercises)
80
Bonus: Bézout's theorem
Ch 81: Morphisms of varieties (not started, 0/4 exercises)
81
Morphisms of varieties
Ch 82: Sheaves and ringed spaces (not started, 0/4 exercises)
82
Sheaves and ringed spaces
Ch 83: Localization (not started, 0/4 exercises)
83
Localization
Ch 84: Affine schemes: the Zariski topology (not started, 0/3 exercises)
84
Affine schemes: the Zari…
Ch 85: Affine schemes: the sheaf (not started, 0/5 exercises)
85
Affine schemes: the sheaf
Ch 86: Interlude: eighteen examples of affine schemes (not started, 0/4 exercises)
86
Interlude: eighteen exam…
Ch 87: Morphisms of locally ringed spaces (not started, 0/2 exercises)
87
Morphisms of locally rin…
Ch 88: Interlude: Cauchy's functional equation and Zorn's lemma (not started, 0/3 exercises)
88
Interlude: Cauchy's func…
Ch 89: Zermelo-Fraenkel with choice (not started, 0/5 exercises)
89
Zermelo-Fraenkel with ch…
Ch 90: Ordinals (not started, 0/3 exercises)
90
Ordinals
Ch 91: Cardinals (not started, 0/4 exercises)
91
Cardinals
Ch 92: Inner model theory (not started, 0/4 exercises)
92
Inner model theory
Ch 93: Forcing (not started, 0/2 exercises)
93
Forcing
Ch 94: Breaking the continuum hypothesis (not started, 0/1 exercises)
94
Breaking the continuum h…
App A: Pedagogical comments and references (not started)
A
Pedagogical comments and…
App B: Hints to selected problems (not started)
B
Hints to selected proble…
App C: Sketches of selected solutions (not started)
C
Sketches of selected sol…
App D: Glossary of notations (not started)
D
Glossary of notations
App E: Terminology on sets and functions (not started)
E
Terminology on sets and…
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