# Mathematics Decks

Imported and community decks waiting for editorial categorization.

Canonical URL: https://shipslides.com/c/mathematics
Deck count: 22

## Decks

### Algebra
URL: https://shipslides.com/d/mathematics-algebra
LLM text: https://shipslides.com/d/mathematics-algebra/llms.txt
Slides: 31
Tags: mathematics, algebra

Algebra is the mathematics of structure: of operations, of equations, of the symmetries that connect one quantity to another. It begins with the idea that a number you don't yet know can still be reasoned about — that x is a respectable noun. Key sections include: Algeb ra.; Opening What algebra is.; Chapter I Before the symbol.; Chapter II The word itself.; Chapter III Cardano, 1545.; Chapter IV Symbolic notation.; Chapter V Algebraic geometry, version one.; Chapter VI Vectors and matrices.; Chapter VII Solving for many unknowns.; Chapter VIII The single number..

Outline:
1. Algeb ra.
2. Opening What algebra is.
3. Chapter I Before the symbol.
4. Chapter II The word itself.
5. Chapter III Cardano, 1545.
6. Chapter IV Symbolic notation.
7. Chapter V Algebraic geometry, version one.
8. Chapter VI Vectors and matrices.
9. Chapter VII Solving for many unknowns.
10. Chapter VIII The single number.
11. Chapter IX Vectors that don't turn.
12. Chapter X The abstract framework.
13. Chapter XI The unsolvable quintic.
14. Chapter XII The mathematics of symmetry.
15. Chapter XIII The four laws.
16. Chapter XIV Two essential families.
17. Chapter XV Two operations.
18. Chapter XVI Where division works.
19. Chapter XVII The fundamental theorem.
20. Chapter XVIII Linear algebra everywhere.
21. Chapter XIX The ring R[x].
22. Chapter XX Boolean algebra.
23. Chapter XXI Continuous symmetry.
24. Chapter XXII Category theory.
25. Chapter XXIII Algebra in physics.
26. Chapter XXIV Equations as spaces.
27. Chapter XXV The Langlands program.
28. Chapter XXVI Twenty essentials.
29. Chapter XXVII Watch & read.
30. Chapter XXVIII Where to begin.
31. The end of the deck.

### Applied Mathematics
URL: https://shipslides.com/d/mathematics-applied-math
LLM text: https://shipslides.com/d/mathematics-applied-math/llms.txt
Slides: 32
Tags: mathematics, applied, math

Mathematics put to work on the world. Key sections include: Applied math.; Opening What applied math is.; Chapter I Modelling with differential equations.; Chapter II The harmonic oscillator.; Chapter III The wave equation.; Chapter IV The heat equation.; Chapter V The Navier-Stokes equations.; Chapter VI Fourier analysis.; Chapter VII The Fourier transform.; Chapter VIII Signal processing..

Outline:
1. Applied math.
2. Opening What applied math is.
3. Chapter I Modelling with differential equations.
4. Chapter II The harmonic oscillator.
5. Chapter III The wave equation.
6. Chapter IV The heat equation.
7. Chapter V The Navier-Stokes equations.
8. Chapter VI Fourier analysis.
9. Chapter VII The Fourier transform.
10. Chapter VIII Signal processing.
11. Chapter IX Numerical methods.
12. Chapter X Floating-point arithmetic.
13. Chapter XI Newton's method.
14. Chapter XII Runge-Kutta methods.
15. Chapter XIII Finite element method.
16. Chapter XIV Computational fluid dynamics.
17. Chapter XV Optimisation.
18. Chapter XVI Linear programming.
19. Chapter XVII Convex optimisation.
20. Chapter XVIII Calculus of variations.
21. Chapter XIX Optimal control.
22. Chapter XX Mathematical biology.
23. Chapter XXI Mathematical economics.
24. Chapter XXII Mathematical finance.
25. Chapter XXIII The Black-Scholes equation.
26. Chapter XXIV Operations research.
27. Chapter XXV Inverse problems and tomography.
28. Chapter XXVI Numerical linear algebra.
29. Chapter XXVII Eigenproblems and PageRank.
30. Chapter XXVIII Reading list.
31. Chapter XXIX Watch & read.
32. The end of the deck.

### Calculus
URL: https://shipslides.com/d/mathematics-calculus
LLM text: https://shipslides.com/d/mathematics-calculus/llms.txt
Slides: 33
Tags: mathematics, calculus

Calculus is the mathematics of change — of how a quantity behaves as another quantity shifts continuously. It turned the static algebra of equation-solving into a dynamic study of motion, growth, and accumulation. Key sections include: Calcu lus.; Opening What calculus is.; Chapter I Greeks and exhaustion.; Chapter II Kepler's wine barrels.; Chapter III Cavalieri's principle.; Chapter IV Tangent lines.; Chapter V Newton's Principia.; Chapter VI Leibniz and the dx.; Chapter VII The priority dispute.; Chapter VIII Limits made rigorous..

Outline:
1. Calcu lus.
2. Opening What calculus is.
3. Chapter I Greeks and exhaustion.
4. Chapter II Kepler's wine barrels.
5. Chapter III Cavalieri's principle.
6. Chapter IV Tangent lines.
7. Chapter V Newton's Principia.
8. Chapter VI Leibniz and the dx.
9. Chapter VII The priority dispute.
10. Chapter VIII Limits made rigorous.
11. Chapter IX The derivative.
12. Chapter X The integral.
13. Chapter XI The fundamental theorem.
14. Chapter XII Differential equations.
15. Chapter XIII Ordinary DEs.
16. Chapter XIV Partial DEs.
17. Chapter XV Multivariable calculus.
18. Chapter XVI Vector calculus.
19. Chapter XVII Stokes's theorem.
20. Chapter XVIII Green's theorem.
21. Chapter XIX Epsilon-delta.
22. Chapter XX Lebesgue integration.
23. Chapter XXI Measure theory.
24. Chapter XXII Stochastic calculus.
25. Chapter XXIII Calculus of variations.
26. Chapter XXIV Calculus on manifolds.
27. Chapter XXV Complex analysis.
28. Chapter XXVI Numerical methods.
29. Chapter XXVII Calculus in physics.
30. Chapter XXVIII Calculus in economics.
31. Chapter XXIX Twenty essentials.
32. Chapter XXX Watch & read.
33. The end of the deck.

### Cryptography
URL: https://shipslides.com/d/mathematics-cryptography
LLM text: https://shipslides.com/d/mathematics-cryptography/llms.txt
Slides: 32
Tags: mathematics, cryptography

Three thousand years of attempts to make a message readable to its intended recipient and unreadable to anyone else. Until 1976, all of it ran on the same fundamental architecture. Then everything changed. Key sections include: Crypt ography.; // Opening $ what is cryptography; Chapter I $ the shift cipher.; Chapter II $ frequency analysis.; Chapter III $ the polyalphabetic ciphers.; Chapter IV $ the one-time pad.; Chapter V $ the enigma machine.; Chapter VI $ bletchley park.; Chapter VII $ the shannon paper.; Chapter VIII $ the symmetric standards..

Outline:
1. Crypt ography.
2. // Opening $ what is cryptography
3. Chapter I $ the shift cipher.
4. Chapter II $ frequency analysis.
5. Chapter III $ the polyalphabetic ciphers.
6. Chapter IV $ the one-time pad.
7. Chapter V $ the enigma machine.
8. Chapter VI $ bletchley park.
9. Chapter VII $ the shannon paper.
10. Chapter VIII $ the symmetric standards.
11. Chapter IX $ public-key cryptography arrives.
12. Chapter X $ rsa.
13. Chapter XI $ hash functions and digital signatures.
14. Chapter XII $ elliptic-curve cryptography.
15. Chapter XIII $ tls — the internet's plumbing.
16. Chapter XIV $ attacks the algorithm doesn't see.
17. Chapter XV $ what "secure" means.
18. Chapter XVI $ zero-knowledge proofs.
19. Chapter XVII $ compute without revealing.
20. Chapter XVIII $ randomness and the entropy problem.
21. Chapter XIX $ the politics of strong cryptography.
22. Chapter XX $ the quantum threat.
23. Chapter XXI $ post-quantum standardisation.
24. Chapter XXII $ the lattice that is everywhere.
25. Chapter XXIII $ end-to-end messaging.
26. Chapter XXIV $ cryptography in cryptocurrency.
27. Chapter XXV $ twenty-five works.
28. Chapter XXVI $ watch & read.
29. Chapter XXVII $ never roll your own.
30. Chapter XXVIII $ what is not yet known.
31. Chapter XXIX $ the field at present.
32. End of stream.

### Discrete Mathematics
URL: https://shipslides.com/d/mathematics-discrete-math
LLM text: https://shipslides.com/d/mathematics-discrete-math/llms.txt
Slides: 32
Tags: mathematics, discrete, math

The mathematics of objects you can count. Key sections include: Discrete math.; // 01 — Opening What discrete math is.; // 02 — Foundation Sets.; // 03 — Maps Functions.; // 04 — Structure Relations.; // 05 — Combinatorics The art of counting.; // 06 — Permutation & combination Order matters, sometimes.; // 07 — Encoding sequences Generating functions.; // 08 — Self-reference Recurrence relations.; // 09 — Networks Graph theory..

Outline:
1. Discrete math.
2. // 01 — Opening What discrete math is.
3. // 02 — Foundation Sets.
4. // 03 — Maps Functions.
5. // 04 — Structure Relations.
6. // 05 — Combinatorics The art of counting.
7. // 06 — Permutation & combination Order matters, sometimes.
8. // 07 — Encoding sequences Generating functions.
9. // 08 — Self-reference Recurrence relations.
10. // 09 — Networks Graph theory.
11. // 10 — Founding problem Eulerian paths.
12. // 11 — Procedures on graphs Graph algorithms.
13. // 12 — Acyclic graphs Trees.
14. // 13 — On the page Planar graphs.
15. // 14 — A controversy The four-color theorem.
16. // 15 — Number theory Modular arithmetic.
17. // 16 — Chance on finite spaces Discrete probability.
18. // 17 — Combinatorial games Two-player perfect-information.
19. // 18 — Algebra of {0, 1} Boolean algebra.
20. // 19 — Hardware Logic gates.
21. // 20 — Procedures Algorithm design.
22. // 21 — Asymptotic analysis Big-O notation.
23. // 22 — Order n elements Sorting algorithms.
24. // 23 — Discrete secrets Cryptography preview.
25. // 24 — Detecting errors Coding theory.
26. // 25 — A specific code Hamming codes.
27. // 26 — Discrete & combinatorial Discrete optimisation.
28. // 27 — Convex relaxation Linear programming.
29. // 28 — Library Reading list.
30. // 29 — Watch Watch & read.
31. // 30 — Constants The constants.
32. The end of the deck.

### Game Theory · Deep
URL: https://shipslides.com/d/mathematics-game-theory-deep
LLM text: https://shipslides.com/d/mathematics-game-theory-deep/llms.txt
Slides: 30
Tags: mathematics, game, theory, deep

Game theory is what happens when you take rational-choice theory and add other rational choosers. It is the formal mathematics of multi-agent decision — not a metaphor, a proof system. Key sections include: Game Theory Deep.; Opening The mathematics of strategy.; Chapter I Strategic-form games.; Chapter II Mixed strategies.; Chapter III Nash, with proof sketch.; Chapter IV Equilibrium refinements.; Chapter V Incomplete information.; Chapter VI Reverse game theory.; Chapter VII What mechanism design has accomplished.; Chapter VIII The Vickrey-Clarke-Groves mechanism..

Outline:
1. Game Theory Deep.
2. Opening The mathematics of strategy.
3. Chapter I Strategic-form games.
4. Chapter II Mixed strategies.
5. Chapter III Nash, with proof sketch.
6. Chapter IV Equilibrium refinements.
7. Chapter V Incomplete information.
8. Chapter VI Reverse game theory.
9. Chapter VII What mechanism design has accomplished.
10. Chapter VIII The Vickrey-Clarke-Groves mechanism.
11. Chapter IX Auction theory.
12. Chapter X The folk theorem.
13. Chapter XI Bargaining theory.
14. Chapter XII Signalling.
15. Chapter XIII Evolutionary game theory.
16. Chapter XIV Schelling: focal points and credible commitment.
17. Chapter XV Behavioural game theory.
18. Chapter XVI Cooperative game theory.
19. Chapter XVII Matching theory.
20. Chapter XVIII Algorithmic game theory.
21. Chapter XIX Network games.
22. Chapter XX What game theory cannot do.
23. Chapter XXI Game theory and AI alignment.
24. Chapter XXII Open questions.
25. Chapter XXIII Twenty-five works.
26. Chapter XXIV Watch & read.
27. Chapter XXV If you want to learn it.
28. Chapter XXVI Why deep game theory matters.
29. Chapter XXVII The next decade.
30. The end of the deck.

### Geometry
URL: https://shipslides.com/d/mathematics-geometry
LLM text: https://shipslides.com/d/mathematics-geometry/llms.txt
Slides: 32
Tags: mathematics, geometry

Geometry is the mathematics of shape, space, and the relations between them. It is the oldest branch of the discipline that still has a recognisable name. Key sections include: Geome try.; Opening What geometry is.; Chapter I Egypt and Babylon.; Chapter II Thales of Miletus.; Chapter III The Pythagorean theorem.; Chapter IV The Elements.; Chapter V The five postulates.; Chapter VI Compass and straightedge.; Chapter VII Three classical problems.; Chapter VIII Conic sections..

Outline:
1. Geome try.
2. Opening What geometry is.
3. Chapter I Egypt and Babylon.
4. Chapter II Thales of Miletus.
5. Chapter III The Pythagorean theorem.
6. Chapter IV The Elements.
7. Chapter V The five postulates.
8. Chapter VI Compass and straightedge.
9. Chapter VII Three classical problems.
10. Chapter VIII Conic sections.
11. Chapter IX Archimedes of Syracuse.
12. Chapter X Analytic geometry.
13. Chapter XI Projective geometry.
14. Chapter XII The parallel postulate falls.
15. Chapter XIII Hyperbolic geometry.
16. Chapter XIV Spherical geometry.
17. Chapter XV Differential geometry.
18. Chapter XVI Klein's program.
19. Chapter XVII Hilbert's 1900 problems.
20. Chapter XVIII Topology emerges.
21. Chapter XIX Coxeter and 20th-century geometry.
22. Chapter XX Penrose tilings.
23. Chapter XXI An aperiodic monotile.
24. Chapter XXII Computers and geometry.
25. Chapter XXIII Geometry as physics.
26. Chapter XXIV Algebraic geometry.
27. Chapter XXV Tropical geometry.
28. Chapter XXVI Symplectic geometry.
29. Chapter XXVII Twenty essentials.
30. Chapter XXVIII Watch & read.
31. Chapter XXIX Where to begin.
32. The end of the deck.

### A History of Mathematics
URL: https://shipslides.com/d/mathematics-math-history
LLM text: https://shipslides.com/d/mathematics-math-history/llms.txt
Slides: 32
Tags: mathematics, math, history

A condensed history of the longest-running argument in human thought. Key sections include: A history of mathematics.; Opening What this is.; Chapter I The Ishango bone.; Chapter II Babylon and Egypt.; Chapter III Pythagoras and the Greeks.; Chapter IV Euclid.; Chapter V Archimedes.; Chapter VI Diophantus.; Chapter VII Indian mathematics.; Chapter VIII The decimal place-value system..

Outline:
1. A history of mathematics.
2. Opening What this is.
3. Chapter I The Ishango bone.
4. Chapter II Babylon and Egypt.
5. Chapter III Pythagoras and the Greeks.
6. Chapter IV Euclid.
7. Chapter V Archimedes.
8. Chapter VI Diophantus.
9. Chapter VII Indian mathematics.
10. Chapter VIII The decimal place-value system.
11. Chapter IX The Islamic golden age.
12. Chapter X Fibonacci.
13. Chapter XI The cubic equation.
14. Chapter XII Descartes.
15. Chapter XIII Newton vs Leibniz.
16. Chapter XIV Euler.
17. Chapter XV Gauss.
18. Chapter XVI Cauchy.
19. Chapter XVII Riemann.
20. Chapter XVIII Hilbert and the 1900 problems.
21. Chapter XIX Cantor and the transfinite.
22. Chapter XX Noether.
23. Chapter XXI Hardy and Ramanujan.
24. Chapter XXII Bourbaki.
25. Chapter XXIII The first computer proof.
26. Chapter XXIV Wiles and Fermat.
27. Chapter XXV Perelman and Poincaré.
28. Chapter XXVI Tao, Green, and the new style.
29. Chapter XXVII Recent breakthroughs.
30. Chapter XXVIII Reading list.
31. Chapter XXIX Watch & read.
32. The end of the deck.

### Mathematical Logic
URL: https://shipslides.com/d/mathematics-mathematical-logic
LLM text: https://shipslides.com/d/mathematics-mathematical-logic/llms.txt
Slides: 32
Tags: mathematics, mathematical, logic

The mathematical study of mathematical reasoning. Key sections include: Mathematical Logic.; What logic is.; Aristotle's syllogisms.; The algebra of logic.; Begriffsschrift.; Russell's paradox.; Principia Mathematica.; A finitary foundation.; Incompleteness.; The first incompleteness theorem..

Outline:
1. Mathematical Logic.
2. What logic is.
3. Aristotle's syllogisms.
4. The algebra of logic.
5. Begriffsschrift.
6. Russell's paradox.
7. Principia Mathematica.
8. A finitary foundation.
9. Incompleteness.
10. The first incompleteness theorem.
11. The second incompleteness theorem.
12. What Gödel did not prove.
13. Tarski and truth.
14. The Turing machine.
15. The halting problem.
16. Church's lambda calculus.
17. The Church-Turing thesis.
18. Recursion theory.
19. Set theory and the ZFC axioms.
20. The continuum hypothesis.
21. The technique of forcing.
22. Large cardinal axioms.
23. Model theory.
24. Proof theory.
25. Type theory and constructive logic.
26. Modal logic.
27. Coq, Lean, and machine-checked mathematics.
28. Logic in computer science.
29. Reading list.
30. Watch & read.
31. The constants.
32. The end of the deck.

### Number Theory
URL: https://shipslides.com/d/mathematics-number-theory
LLM text: https://shipslides.com/d/mathematics-number-theory/llms.txt
Slides: 31
Tags: mathematics, number, theory

"Mathematics is the queen of the sciences," Gauss wrote, "and number theory is the queen of mathematics." The compliment was not idle. Gauss devoted his greatest energies to it. Key sections include: Number theory.; Opening The queen of mathematics.; Chapter I Euclid on primes.; Chapter II Diophantine equations.; Chapter III Fermat's little theorem.; Chapter IV 1637 conjecture, 1995 proof.; Chapter V Andrew Wiles.; Chapter VI Goldbach's conjecture.; Chapter VII The twin prime conjecture.; Chapter VIII Mersenne primes..

Outline:
1. Number theory.
2. Opening The queen of mathematics.
3. Chapter I Euclid on primes.
4. Chapter II Diophantine equations.
5. Chapter III Fermat's little theorem.
6. Chapter IV 1637 conjecture, 1995 proof.
7. Chapter V Andrew Wiles.
8. Chapter VI Goldbach's conjecture.
9. Chapter VII The twin prime conjecture.
10. Chapter VIII Mersenne primes.
11. Chapter IX Perfect numbers.
12. Chapter X The Riemann hypothesis.
13. Chapter XI The zeta function.
14. Chapter XII The prime number theorem.
15. Chapter XIII Hardy and Ramanujan.
16. Chapter XIV Ramanujan's notebooks.
17. Chapter XV Modular forms.
18. Chapter XVI Elliptic curves.
19. Chapter XVII The modularity theorem.
20. Chapter XVIII Birch and Swinnerton-Dyer.
21. Chapter XIX Algebraic number theory.
22. Chapter XX Class field theory.
23. Chapter XXI L-functions.
24. Chapter XXII Cryptography.
25. Chapter XXIII The quantum threat.
26. Chapter XXIV The Langlands program.
27. Chapter XXV Viazovska, 2016.
28. Chapter XXVI Twenty essentials.
29. Chapter XXVII Watch & read.
30. Chapter XXVIII Where to begin.
31. The end of the deck.

### Probability
URL: https://shipslides.com/d/mathematics-probability
LLM text: https://shipslides.com/d/mathematics-probability/llms.txt
Slides: 34
Tags: mathematics, probability

Probability is the mathematics of uncertainty. It quantifies how often things happen — or, on a different reading, how much we should believe they will. Key sections include: Proba bility.; Opening What probability is.; Chapter I Gambling problems.; Chapter II Cardano's Liber de ludo aleae.; Chapter III The 1654 correspondence.; Chapter IV The first textbook.; Chapter V The law of large numbers.; Chapter VI The normal approximation.; Chapter VII Bayes's theorem.; Chapter VIII Laplace, the consolidator..

Outline:
1. Proba bility.
2. Opening What probability is.
3. Chapter I Gambling problems.
4. Chapter II Cardano's Liber de ludo aleae.
5. Chapter III The 1654 correspondence.
6. Chapter IV The first textbook.
7. Chapter V The law of large numbers.
8. Chapter VI The normal approximation.
9. Chapter VII Bayes's theorem.
10. Chapter VIII Laplace, the consolidator.
11. Chapter IX Random variables.
12. Chapter X The standard distributions.
13. Chapter XI The central limit theorem.
14. Chapter XII Markov chains.
15. Chapter XIII The 1933 axioms.
16. Chapter XIV Measure-theoretic probability.
17. Chapter XV Conditional probability.
18. Chapter XVI Two interpretations.
19. Chapter XVII Stochastic processes.
20. Chapter XVIII Brownian motion.
21. Chapter XIX Ergodic theory.
22. Chapter XX Probability in physics.
23. Chapter XXI Probability in genetics.
24. Chapter XXII Probability in finance.
25. Chapter XXIII Game theory.
26. Chapter XXIV The Monty Hall problem.
27. Chapter XXV The birthday paradox.
28. Chapter XXVI Statistical paradoxes.
29. Chapter XXVII Probability in machine learning.
30. Chapter XXVIII Quantum probability.
31. Chapter XXIX Twenty essentials.
32. Chapter XXX Watch & read.
33. Chapter XXXI Where to begin.
34. The end of the deck.

### Topology
URL: https://shipslides.com/d/mathematics-topology
LLM text: https://shipslides.com/d/mathematics-topology/llms.txt
Slides: 32
Tags: mathematics, topology

Geometry minus distance. The study of properties that survive continuous deformation. Key sections include: Topo logy.; Opening What topology is.; Chapter I Euler's bridges.; Chapter II The Euler characteristic.; Chapter III The Möbius strip.; Chapter IV The Klein bottle.; Chapter V Point-set topology.; Chapter VI Open and closed sets.; Chapter VII Continuous maps.; Chapter VIII Compactness..

Outline:
1. Topo logy.
2. Opening What topology is.
3. Chapter I Euler's bridges.
4. Chapter II The Euler characteristic.
5. Chapter III The Möbius strip.
6. Chapter IV The Klein bottle.
7. Chapter V Point-set topology.
8. Chapter VI Open and closed sets.
9. Chapter VII Continuous maps.
10. Chapter VIII Compactness.
11. Chapter IX Connectedness.
12. Chapter X The algebraic turn.
13. Chapter XI Homotopy.
14. Chapter XII Homology.
15. Chapter XIII The fundamental group.
16. Chapter XIV Knot theory.
17. Chapter XV Reidemeister moves.
18. Chapter XVI Knot invariants.
19. Chapter XVII Three-manifolds.
20. Chapter XVIII The Poincaré conjecture.
21. Chapter XIX Perelman's proof.
22. Chapter XX Differential topology.
23. Chapter XXI Manifolds.
24. Chapter XXII Exotic spheres.
25. Chapter XXIII Topological matter.
26. Chapter XXIV Persistent homology.
27. Chapter XXV Knots in DNA.
28. Chapter XXVI Reading list.
29. Chapter XXVII Watch & read.
30. Chapter XXVIII 2026.
31. Chapter XXIX The constants.
32. The end of the deck.

### Calculus — The Mathematics of Change
URL: https://shipslides.com/d/catalog-math-calculus
LLM text: https://shipslides.com/d/catalog-math-calculus/llms.txt
Slides: 13
Tags: catalog, math, calculus

Newton + Leibniz, ~1665–1684 Key sections include: CALCULUS / The mathematics of change; The Classical Problem; Limits — the Formal Foundation; The Derivative; Geometric Interpretation; The Derivative Rules; The Integral; The Fundamental Theorem; Newton vs. Leibniz; Into Many Dimensions.

Outline:
1. CALCULUS / The mathematics of change
2. The Classical Problem
3. Limits — the Formal Foundation
4. The Derivative
5. Geometric Interpretation
6. The Derivative Rules
7. The Integral
8. The Fundamental Theorem
9. Newton vs. Leibniz
10. Into Many Dimensions
11. Applications
12. Beyond Elementary Calculus
13. Further Study

### Mathematical Cryptography
URL: https://shipslides.com/d/catalog-math-cryptography
LLM text: https://shipslides.com/d/catalog-math-cryptography/llms.txt
Slides: 13
Tags: catalog, math, cryptography

A substitution cipher maps each plaintext letter to a fixed ciphertext letter. Caesar's shift is a special case: c ≡ p + k (mod 26) . Key sections include: MATHEMATICAL CRYPTOGRAPHY; Substitution & the Statistics That Betray It; The One-Time Pad — Unbreakable, Unusable; Modular Arithmetic — Integers, Wrapped; Fermat & Euler — Why RSA Works; RSA (1977) — Factoring as a Trapdoor; Diffie–Hellman — A Secret in Public; Elliptic Curves — Same Idea, Smaller Keys; One-Way: SHA-256 and the Compression Trick; Signing — Authorship Without Disclosure.

Outline:
1. MATHEMATICAL CRYPTOGRAPHY
2. Substitution & the Statistics That Betray It
3. The One-Time Pad — Unbreakable, Unusable
4. Modular Arithmetic — Integers, Wrapped
5. Fermat & Euler — Why RSA Works
6. RSA (1977) — Factoring as a Trapdoor
7. Diffie–Hellman — A Secret in Public
8. Elliptic Curves — Same Idea, Smaller Keys
9. One-Way: SHA-256 and the Compression Trick
10. Signing — Authorship Without Disclosure
11. Zero-Knowledge — Convince Without Revealing
12. Post-Quantum — Past the Reach of Shor
13. Where to Go Next

### Game Theory — Strategy when others strategize too
URL: https://shipslides.com/d/catalog-math-game-theory
LLM text: https://shipslides.com/d/catalog-math-game-theory/llms.txt
Slides: 14
Tags: catalog, math, game, theory

A 13-slide tour of payoffs, equilibria, and the mathematics of mutual anticipation — from von Neumann's chessboard to the FCC spectrum auction. Key sections include: Game Theory /; Strategy when others strategize too.; The Setup; Zero-Sum Games; Non-Zero-Sum Games; Prisoner's Dilemma; Nash Equilibrium; Repeated Games & Tit-for-Tat; The Stag Hunt; Mixed Strategies.

Outline:
1. Game Theory /
2. Strategy when others strategize too.
3. The Setup
4. Zero-Sum Games
5. Non-Zero-Sum Games
6. Prisoner's Dilemma
7. Nash Equilibrium
8. Repeated Games & Tit-for-Tat
9. The Stag Hunt
10. Mixed Strategies
11. Mechanism Design
12. Real Applications
13. Limits of Game Theory
14. Further Reading

### Geometry — A Drafting Table Deck
URL: https://shipslides.com/d/catalog-math-geometry
LLM text: https://shipslides.com/d/catalog-math-geometry/llms.txt
Slides: 14
Tags: catalog, math, geometry

A Drafting Table Deck · XIII Plates Geometry / The science of shape From the surveyor’s rope to the curvature of spacetime — thirty-five centuries of measuring the world. Key sections include: Geometry /; The science of shape; II. Rope-Stretchers & Star-Watchers; III. Pythagoras of Samos; IV. Euclid’s Elements; V. The Five Postulates; VI. The Parallel Problem; VII. The Crack in the Plane; VIII. Riemann’s Manifolds; IX. Gravity is Geometry.

Outline:
1. Geometry /
2. The science of shape
3. II. Rope-Stretchers & Star-Watchers
4. III. Pythagoras of Samos
5. IV. Euclid’s Elements
6. V. The Five Postulates
7. VI. The Parallel Problem
8. VII. The Crack in the Plane
9. VIII. Riemann’s Manifolds
10. IX. Gravity is Geometry
11. X. Topology — Shape Without Size
12. XI. Fractals — The Roughness of Things
13. XII. The Modern Workshop
14. XIII. Plates & Pointers

### Linear Algebra — Vectors, Matrices, Transformations
URL: https://shipslides.com/d/catalog-math-linear-algebra
LLM text: https://shipslides.com/d/catalog-math-linear-algebra/llms.txt
Slides: 13
Tags: catalog, math, linear, algebra

Vectors, matrices, transformations. Key sections include: LINEAR ALGEBRA; 02 Vectors; 03 Vector Spaces; 04 Matrices; 05 Matrix Multiplication; 06 Linear Transformations; 07 Determinant; 08 Eigenvalues & Eigenvectors; 09 Solving Ax = b; 10 Decompositions.

Outline:
1. LINEAR ALGEBRA
2. 02 Vectors
3. 03 Vector Spaces
4. 04 Matrices
5. 05 Matrix Multiplication
6. 06 Linear Transformations
7. 07 Determinant
8. 08 Eigenvalues & Eigenvectors
9. 09 Solving Ax = b
10. 10 Decompositions
11. 11 Applications
12. 12 Modern Frontiers
13. 13 Further Reading

### Mathematicians — Lives behind the theorems
URL: https://shipslides.com/d/catalog-math-mathematicians
LLM text: https://shipslides.com/d/catalog-math-mathematicians/llms.txt
Slides: 13
Tags: catalog, math, mathematicians

Eleven figures, twenty-five centuries. From a Greek cult leader who heard the world as ratios to a wandering Hungarian who slept on his colleagues' couches — the people who invented the language we count, calculate, and reason in. Key sections include: MATHEMATICIANS Lives behind the theorems; Pythagoras; Euclid; Archimedes; Isaac Newton; Leonhard Euler; Carl Friedrich Gauss; Bernhard Riemann; Srinivasa Ramanujan; Emmy Noether.

Outline:
1. MATHEMATICIANS Lives behind the theorems
2. Pythagoras
3. Euclid
4. Archimedes
5. Isaac Newton
6. Leonhard Euler
7. Carl Friedrich Gauss
8. Bernhard Riemann
9. Srinivasa Ramanujan
10. Emmy Noether
11. Alan Turing
12. Paul Erdős
13. Further reading & viewing

### Number Theory — The Queen of Mathematics
URL: https://shipslides.com/d/catalog-math-number-theory
LLM text: https://shipslides.com/d/catalog-math-number-theory/llms.txt
Slides: 13
Tags: catalog, math, number, theory

2 3 “Mathematics is the queen of the sciences, and number theory is the queen of mathematics.” — C. F. Gauss ❦ ❦ Chapter I The Integers §1. The playing field The Integers The integers ℤ = { … , −3, −2, −1, 0, 1, 2, 3, … } form the bedrock of arithmetic — discrete, unbounded, equipped with addition and multiplication. Key sections include: Number Theory; The Integers; The Primes are Infinite; Every Integer is Prime, Uniquely; How to Catch a Prime; The Prime Number Theorem; Modular Arithmetic; Fermat's Little Theorem; Diophantine Equations; Fermat's Last Theorem.

Outline:
1. Number Theory
2. The Integers
3. The Primes are Infinite
4. Every Integer is Prime, Uniquely
5. How to Catch a Prime
6. The Prime Number Theorem
7. Modular Arithmetic
8. Fermat's Little Theorem
9. Diophantine Equations
10. Fermat's Last Theorem
11. Cryptography & Beyond
12. What We Do Not Know
13. Further Reading

### Probability — A Grammar for Uncertainty
URL: https://shipslides.com/d/catalog-math-probability
LLM text: https://shipslides.com/d/catalog-math-probability/llms.txt
Slides: 13
Tags: catalog, math, probability

a grammar for uncertainty Key sections include: PROBABILITY; A gambler's letter sparked a science.; Three rules. The whole edifice.; Probability bends to evidence.; How a rational mind absorbs evidence.; Switch and win two-thirds of the time.; Probability times payoff, summed.; Averages of anything tend to normal.; Some distributions don't tame.; Two answers, both useful..

Outline:
1. PROBABILITY
2. A gambler's letter sparked a science.
3. Three rules. The whole edifice.
4. Probability bends to evidence.
5. How a rational mind absorbs evidence.
6. Switch and win two-thirds of the time.
7. Probability times payoff, summed.
8. Averages of anything tend to normal.
9. Some distributions don't tame.
10. Two answers, both useful.
11. The future depends only on now.
12. A grammar that runs the modern world.
13. Where to go next.

### Topology — Shape without Measurement
URL: https://shipslides.com/d/catalog-math-topology
LLM text: https://shipslides.com/d/catalog-math-topology/llms.txt
Slides: 13
Tags: catalog, math, topology

homeomorphism Same shape, different presentation. The puzzle To a topologist, a coffee cup is a donut. Stretch, bend, twist — but never cut, never glue. Under such deformations the cup with one handle and the torus with one hole are indistinguishable. Both are surfaces of genus one. Key sections include: TOPOLOGY / Shape without measurement; To a topologist, a coffee cup is a donut.; Euler and the seven bridges of Königsberg.; Topology studies properties preserved under continuous deformation.; A topological space is a set with a chosen family of open sets.; Euler characteristic.; The Möbius strip : one side, one edge.; The Klein bottle : a surface with no inside.; Closed loops in space, classified up to ambient isotopy.; Translate shapes into groups..

Outline:
1. TOPOLOGY / Shape without measurement
2. To a topologist, a coffee cup is a donut.
3. Euler and the seven bridges of Königsberg.
4. Topology studies properties preserved under continuous deformation.
5. A topological space is a set with a chosen family of open sets.
6. Euler characteristic.
7. The Möbius strip : one side, one edge.
8. The Klein bottle : a surface with no inside.
9. Closed loops in space, classified up to ambient isotopy.
10. Translate shapes into groups.
11. Poincaré, 1904. Perelman, 2003.
12. From the abstract to the tangible.
13. Continue.

### Unsolved — Open Problems in Mathematics
URL: https://shipslides.com/d/catalog-math-unsolved
LLM text: https://shipslides.com/d/catalog-math-unsolved/llms.txt
Slides: 13
Tags: catalog, math, unsolved

Some questions sit on the board for centuries. They look simple. They aren't. Key sections include: Unsolved; Why open problems matter; The Millennium Prize Problems; P vs NP; The Riemann Hypothesis; Yang–Mills & the Mass Gap; Navier–Stokes Existence & Smoothness; Birch & Swinnerton-Dyer; The Hodge Conjecture; The Twin Prime Conjecture.

Outline:
1. Unsolved
2. Why open problems matter
3. The Millennium Prize Problems
4. P vs NP
5. The Riemann Hypothesis
6. Yang–Mills & the Mass Gap
7. Navier–Stokes Existence & Smoothness
8. Birch & Swinnerton-Dyer
9. The Hodge Conjecture
10. The Twin Prime Conjecture
11. The Collatz Conjecture
12. Goldbach's Conjecture
13. Where to read & watch