What are the main topics of Math:Edit

Their are three major "topics" in math.  These three topics are as follows; Applied math, (The practiacal applications of math and using it in the real world EX: Mathematical Biology, Engineering etc...) Pure math, (The depths of math with abstract complicated topics such as; Numbers, Topology, Equations, Matrices, Vectores etc...) and Foundations of math (Axioms, asking the question; Is math just a silly idea made up in our heads?).

​Pure Maths:Edit

Math starts with a basis.  A foundation or building block that everything else is expanded upon.  Math's building block starts with Pure Mathematics .  Pure mathematics explores the complicated abstract and out their topics that are not usually used in everyday life.  These are topics rarely seen by the lay person and have an unseen beauty that many do not discover in school.  Some examples of these applied mathematics are; Algebra, Ring Theory, Number Systems, Quaternion Numbers, Prime Numbers, Exponential Numbers, Infinities, Matrices, Number Theory, Combinatorics, Partation Thory and many others.  These topics are mostly viewed by the stereotyped mathematician, and most do not see how fun and intricate these gems are.

​Applied Math:Edit

Applied math is the expansion and applications of math in mostly practical and real world ways. These topics where math is used or applied to solve a problem range from Theoretical Physics to Mathematical Biology. These are the most common uses and applications of math and are the most well known scenarios where math is used or applied. Most of these topics involve Sciences Finances even Economics

Foundation of Math:​ Edit

The Foundation of Math deals with the philosophy of math and its axioms. It asks the big questions such as; Is math just a fantasy humans created that really describes nothing at all?. It deals with the big picture and the fabric of our reality.

​Sub Categories:Edit

Most of these topics of math that I will discuss will either be part of; Foundations, Pure math or Applied math.  These topics or fields will be broken down and will be refrences for further research.  These refrences will not be every topic in math because in the future new topics may be discovered and their are many more sub topics in the sub categories.

​Pure mathematics:Edit

​Number systems:Edit

  • Natural Numbers
  • Intigers
  • Rational Numbers
  • Real Numbers
  • Complex Numbers
  • Quaternion
  • Octonion
  • Cardinal Numbers
  • Prime Numbers
  • Infinities
  • Exponentioal Numbers


  • ​Equations
  • Algebra
  • Algebraic Geometry
  • Matrices
  • Vectores
  • Number Theory
  • Combinatorics
  • Group Theory
  • Order Theory


  • ​Trigonometry
  • Geometry
  • Fractal Geometry
  • Topology
  • Measure Theory
  • Differential Geometry


  • Calculas
  • Vector Calculas
  • Dynamical Systems
  • Chaos Theory
  • Complex Analysis

​Applied Mathematics:Edit

  • Mathematical Physics
  • Theoretical Physics
  • Mathematical Chemistry
  • Biomath
  • Engineering
  • Numerical Analysis
  • Game Theory
  • Probability
  • Statistics
  • Mathematical Finance
  • Optimization
  • Computer Science
  • Machine Learning
  • Cryptography


  • Fundamental Rules
  • Mathematical Logic
  • Set Theory
  • Category Theory
  • Theory of Computation
  • Complexity Theory


​As you can see if you dove deeper into these topic you would see the many hidden beautys and gems of mathematics.  I myself love mathematics so deeply and i believe everyone should be exposed to its beauty.  Their are many more topics not shown here so feel free to add more.

Note: Please do not add any false Info.