What are the Different Branches of Mathematics?

[EngWiPy]

Hello,

I am just curious, what are the branches of Mathematics, and what does each branch concern of?

Regards

 

[HallsofIvy]

You could get as many answers to that as there are mathematicians!
Here is a pretty good list:
http://en.wikipedia.org/wiki/Lists_of_mathematics_topics

 

[g_edgar]

There is also this
http://www.math.niu.edu/~rusin/known-math/welcome.html

 

[kstahmer]

Interesting question, asked the same question. Did a Google search and got a multitude of answers.

When I first studied mathematics decades ago, was taught the major branches of mathematics were:

• Analysis (e.g. functions, sequences, series, limits, derivatives, integrals, real analysis, complex analysis, complex number theory, functional analysis, measure theory)
  
• Algebra (e.g. linear algebra, group theory, ring theory, Galois Theory, number theory, algebraic number theory, combinatorics)
  
• Topology (e.g. point set topology, combinatorial topology, algebraic topology)
  
• Logic and Set Theory (e.g. propositional calculus, predicate calculus, metamathematics, recursion theory, category theory, von Neumann-Bernays-Gödel (NBG) set theory, Zermelo-Fraenkel (ZF) set theory, model theory, fuzzy logic)
  
• Applied Mathematics (e.g. ordinary differential equations (ODE), partial differential equations (PDE), Fourier series, Fourier transforms, game theory)

Yet my anachronistic list isn't the end-all and be-all of lists. Some colleges and universities include statistics and numerical analysis as separate branches of mathematics. Some include geometry as a separate branch. There many other variations as well.

There also variations within the branches. Is algebraic topology, algebra or topology? Is complex number theory, analysis or algebra? Opinions vary.

 

[CellCoree]

,

I am happy to answer your question about the branches of Mathematics. Mathematics is a vast and diverse field that is essential in understanding and describing the world around us. There are several branches of Mathematics, each with its own focus and applications. Some of the important branches include:

1. Arithmetic: This branch deals with the basic operations of numbers such as addition, subtraction, multiplication, and division.

2. Algebra: Algebra uses symbols and equations to represent relationships between numbers and solve problems.

3. Geometry: This branch deals with the study of shapes, sizes, and their properties.

4. Trigonometry: Trigonometry is the study of triangles and their relationships, often used in navigation and engineering.

5. Calculus: Calculus deals with the study of change and is used to solve problems involving rates of change, such as in physics and engineering.

6. Statistics: This branch deals with the collection, analysis, interpretation, and presentation of data.

7. Probability: Probability is the study of chance and uncertainty, and it is used in fields such as finance, insurance, and gaming.

These are just a few of the many branches of Mathematics. Other important branches include number theory, topology, and differential equations. Each branch has its own unique applications and plays a crucial role in various fields such as science, engineering, finance, and economics. I hope this helps to give you a better understanding of the different branches of Mathematics and their importance in the world of science and beyond.