Book

Math

Discovery

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Math Big Picture

I'm trying to understand how to overview all of math. I'm studying the lists of pages in Wikipedia about mathematics.

I think the most central concept in Math is duality, which is the basis for logic.

I am investigating from the following directions:

  • the ways of figuring things out
  • Duality
  • the areas of math
  • the methods of mathematical proof (natural objects, axioms)
  • the objects in math
  • the ways that variables are used
  • geometries and transformations (for moods)
  • visualizations (sequences, hierarchies, networks)

I want to think about:

  • how mathematical knowledge arises and develops to yield objects, concepts, theorems, endeavors
  • the role of concrete examples and abstraction - generalization

Mathematical concepts

Abstract concepts

  • dualities
  • Definite / deterministic (the) vs. Indefinite / Nondeterministic (a) - P vs. NP - compare with the Axiom of Choice
  • mathematical examples

Objects

  • combinatorial principles
  • mathematical shapes
  • polygons, polyhedra and polytopes
  • regular polytopes - points on a circle or sphere, etc.
  • partition topics
  • factorial and binomial topics
  • convexity topics

Numbers Real, Complex, Quaternion

Functions

  • mathematical functions
  • special functions and eponyms
  • transforms
  • Fourier-related transforms
  • polynomial topics
  • exponential topics
  • logarithm topics

Equations

  • equations
  • inequalities
  • mathematical identities
  • formulae involving pi

Subspaces

  • curves
  • mathematical knots and links
  • surfaces
  • algebraic surfaces
  • manifolds
  • examples in general topology

Operations

  • small groups
  • finite simple groups
  • simple Lie groups
  • Table of Lie groups
  • complex reflection groups
  • permutation topics

Algorithms

  • algorithms
  • complexity classes

Proofs

  • axioms
  • conjectures
  • lemmas
  • mathematical proofs
  • theorems

MathConcepts


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Puslapis paskutinį kartą pakeistas 2018 sausio 21 d., 14:21
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