Abstract Mathematics

Overview

• Algebra is the field of mathematics that studies mathematical sets with a collection of operations (typically binary) on those sets.
  • Number Theory
  • Algebra
    • Group Theory
    • Linear Algebra
    • Category Theory
  • Logic
    • Computer Science
• Geometry is the field that deals with spatial relationships. It is maybe the first area to be formalized with Euclid's Elements.
  • Geometry
  • Trigonometry
  • Topology
    
    • Algebraic Topology
• Analysis is usually synonomous with the calculus. It is build upon and draws heavily from the other branches of mathematics.
  • Real Analysis
  • Complex Analysis
  • Differential Equations
  • Functional Analysis

Philosophy

The philosophy of mathematics is an interesting field in its right, and often is useful for building an intuition, especially for some of the more abstract applications of math.

• Philosophy -