概论
数学
发现
Andrius Kulikauskas
 ms@ms.lt
 +370 607 27 665
 My work is in the Public Domain for all to share freely.
用中文
Software

See: Math videos, Learn math
 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
Math Notebook: Investigations
Priorities: What to learn
 What are the fundamental math principles?
 Study the theorems of plane geometry, universal hyperbolic geometry, etc.
 Organize the most important math theorems and analyze their content in terms of more basic ideas.
 What are the elementary math concepts?
 Study how important math concepts relate more basic concepts.
 Relate basic concepts and more advanced concepts to duality.
 What is a perspective?
 Short and long exact sequences.
 Fiber bundles, vector bundles.
 Homology and cohomology.
 Tensors.
 Sheaves.
 What is a geometry?
 SL(2,C) and Mobius transformations.
 Differences between affine, projective, conformal, symplectic geometry.
 Classical Lie groups.
 What is going beyond oneself?
 Study finite fields and interpret {$F^{1^n}$}.
 Study points at infinity and how they relate to coordinate systems.
 What is the foursome?
 Yoneda lemma.
 Yates index theorem.
Overview: Math to learn and use
 Understand the ways of figuring things out
 binomial theorem: Polytopes, Coxeter groups, homology, GaussBonet theorem, Euler's characteristic, Grassmanian
 four classical Lie groups, Lie theory, Exceptional Lie groups, Triality
 four geometries (affine, projective, conformal, symplectic) and how, in logic, they relate level and metalevel. Geometry
 relation between discrete and continuous projective geometry
 Symplectic geometry, Lagrangian mechanics, Hamiltonian mechanics
 Numbers: Reals, Complexes, Quaternions, Octonions, CayleyDickson construction, Associativity, dualitybreaking
 SL(2,C) and Möbius transformations as the basis for six transformations (reflection, shear, rotation, dilation, squeeze, translation). Visual complex analysis.
 Network theory, Set theory axioms.
 Understand how math results unfold
 math answers
 A theory of what "equivalence" variously means
 Foundations: Set theory, Models, Proof theory, Automata theory
 duality and logic as the relationship between the concious and the unconscious
 theorems
 Understand perspectives
 Understand the divisions of everything
 Understand representations
 Understand topologies
 Understand the eightfold way
 Snake lemma, homology and cohomology
 a unifying perspective on cohomology (or has Lurie already achieved this?)
 Model how God goes beyond himself
 entropy as the basis for prayer: Information geometry
 Completely characterize an area of math such as plane geometry or chess
Overviews of Math and Its History
General resources for studying math
