- Make a diagram of concrete mathematical structures that I want to learn about, and related branches of mathematics.
- Survey combinatorics, especially Stanley's book and Wikipedia, for the various kinds of combinatorial constructions.

学习数学

- Map of math How do math's branches, concepts and results unfold?
- Binomial theorem The heart of mathematics. In particular, the reason why there are 4 infinite families of classical Lie groups/algebras.

Challenges in Math to take on

- Understand the ways of figuring things out
- understand the binomial theorem
- explain the four classical Lie groups
- express and apply four geometries (affine, projective, conformal, symplectic) and six transformations (reflection, shear, rotation, dilation, squeeze, translation).
- relate level and metalevel in four ways to provide the basis for logic and geometry
- understand the use of variables

- Understand how math results unfold
- the relationship between the concious and the unconscious, duality, logic
- Langlands program, Poincare/Serre duality

- the association of (conscious) questions and (unconscious) answers
- theorems, and in particular, geometry theorems, Galois theory, the Fundamental Theorem of Algebra, its proofs and its centrality

- the relationship between the concious and the unconscious, duality, logic
- Understand the divisions of everything
- express divisions of everything in terms of finite exact sequences
- understand and interpret Bott periodicity, clock shifts in Clifford algebras
- threesome: Jacobi identity
- foursome: Yates index theorem, Yoneda lemma
- sevensome: Logic
- the criteria: Six operations

- Model how God goes beyond himself
- Make sense of the field with one element
- Finite fields, Riemann hypothesis, modeling infinity with characteristic q

- simplex -1, center and totality, Polytopes

- Make sense of the field with one element
- Understand entropy as the basis for prayer
- Completely characterize an area of math such as plane geometry or chess

Open math challenges to consider

- A theory of what "equivalence" variously means
- The g-conjecture about an h-vectors of a simplicial polytope and the triangulation of a sphere.
- P vs. NP-complete
- a unifying perspective on cohomology (or has Lurie already achieved this?)
- higher order homotopy groups for sphere

Overviews of Math and Its History

- Récoltes et Semailles, Part 1, Alexander Grothendieck. Also, translation into Spanish and other works.
- Notes on the Life and Work of Alexander Grothendieck by Piotr Pragacz

- A View of Mathematics, Alain Connes
- Eugenia Cheng. Mathematics, Morally.
- Thurston. On Proof and Progress.

Math to Learn

- for the ways of figuring things out
- Binomial theorem: Polytopes, Coxeter groups, homology, Gauss-Bonet theorem, Euler's characteristic, Grassmanian
- Geometry: Geometries
- Lie theory, Classical Lie groups, Exceptional Lie groups, Triality
- Tensor, Triviality, Linear algebra
- relation between discrete and continuous projective geometry
- circle folding, origami and what their operations mean geometrically
- Clifford algebra, Geometric algebra, visual complex analysis
- Symplectic geometry, Lagrangian mechanics, Hamiltonian mechanics
- Algebraic geometry, sheaves, how Grothedieck's six operations relate to six representations

- Numbers: Reals, Complexes, Quaternions, Octonions, Cayley-Dickson construction, Associativity, duality-breaking
- Network theory, Set theory axioms.

- for modeling structures
- the eightfold way: homology and cohomology
- for the big picture in mathematics
- Foundations: Set theory, Models, Proof theory, recursive function theory, Automata theory, Mandelbrot set
- Category theory: Voevodsky, Homotopy type theory
- Combinatorics: Symmetric functions, P vs NP
- Functional analysis? Spectral sequence
- Number theory? basics of the Riemann-Zeta function hypothesis.
- Qiaochu Yuan's reading list

- for entropy
- Entropy: Information geometry

- for the properties of life
- for subconscious
- for understanding an area of math

**Math Videos**

General

- Infinite Series
- Numberphile
- Mathologer
- Oxford: The Secrets of Mathematics
- Travels in a Mathematical World

Collections

- Xuan Gottfried Yang
- NPTEL videos
- Clay Mathematics Videos
- Alexander Grothendieck channel
- Graduate Mathematics
- Math Videos

Geometry

- Daniel Chan
- Federico Ardila
- Amritanshu Prasad: Representation Theory: A Combinatorial Viewpoint
- Continuous groups in physics
- DoctorPhys: Theoretical Physics
- Fredric Schuller: Lectures on Geometrical Anatomy of Theoretical Physics
- Curtis McMullen - The Geometry of 3 Manifolds
- Continuous Groups for Physicists
- Video named "17". End of general theory of Lie group and Lie algebra.
- "18" Classification of compact semisimple Lie algebras and Lie groups and their representation theory. Complexification. Direct sum of semisimple and solvable Lie algebras.
- "19" root systems
- "20" simple roots
- "22" orthogonal, symplectic Lie algebras, table of their properties
- "23" unitary Lie algebra An, exceptional algebras
- "24" Representation theory, starting spinors
- "25" Spinors

- Basic Algebraic Geometry: Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity
- Taylor Dupuy Model theory, mathematical logic, Grothendieck, algebraic geometry
- Daniel Murfet: Topos theory
- Nickolas Rollick: Algebraic Geometry
- ML Baker on Elliptic curves and modular forms

Foundations

Web courses

Parsiųstas iš http://www.ms.lt/sodas/Book/StudyMath

Puslapis paskutinį kartą pakeistas 2019 gegužės 21 d., 14:42