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Andrius Kulikauskas
- m a t h 4 w i s d o m - g m a i l
- +370 607 27 665
- My work is in the Public Domain for all to share freely.
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Software
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See: Math videos, Learn math, Study physics
- 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 set theorem.
Overview: Math to learn and use
- Understand the ways of figuring things out
- binomial theorem: Polytopes, Coxeter groups, homology, Gauss-Bonet 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, Cayley-Dickson construction, Associativity, duality-breaking
- 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
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