User:Sir LeafLeaf/Books/Core Mathematics

Core Topics in Mathematics

 * Introduction
 * Definitions of mathematics
 * Philosophy of mathematics
 * Foundations of mathematics
 * Number theory
 * The Unreasonable Effectiveness of Mathematics in the Natural Sciences


 * Important Mathematicians to Know of
 * Gottlob Frege
 * Kurt Gödel
 * Alfred Tarski
 * L. E. J. Brouwer
 * Arend Heyting
 * David Hilbert


 * Logic
 * Propositional calculus
 * First-order logic
 * Second-order logic
 * Higher-order logic
 * Intuitionistic logic
 * Substructural logic


 * Foundational Approaches
 * Logicism
 * Frege's theorem
 * Hume's principle
 * Intuitionism
 * Formalism (mathematics)
 * Structuralism (philosophy of mathematics)


 * Set Theory and Related Ideas
 * Set theory
 * Type theory
 * Gödel's incompleteness theorems


 * Meaning
 * Semantic theory of truth
 * Formal language
 * Model theory
 * Proof theory


 * Cognitive Science of Mathematics
 * Numerical cognition


 * Algebra
 * Group theory
 * Ring (mathematics)
 * Field (mathematics)
 * Linear algebra
 * Matrix (mathematics)


 * Calculus
 * Calculus
 * Limit of a function
 * Infinitesimal
 * Differential calculus
 * Squeeze theorem
 * Integral
 * Fundamental theorem of calculus


 * Geometry
 * Algebraic geometry


 * Discrete Mathematics
 * Graph theory
 * Seven Bridges of Königsberg
 * Travelling salesman problem
 * Hamiltonian path problem
 * Four color theorem