A map that expands the vast field of mathematics "The Map of Mathematics"

Mathematics has been educated in schools since long ago, like "reading and writing abacus". However, the mathematics learned at school is only a part of mathematics field. Those that summarize its broad field in a single figure are released.

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The Map of Mathematics - YouTube


We learn mathematics at school, but it is only a small part of mathematics. The field of mathematics is very diverse.


Mathematics began with "counting things" first. Then it began to measure the length, and in 3000 BC the equation was born in Egypt. After that, inventions such as negative numbers and zero continue.


Current mathematics is divided into two fields "pure mathematics" and "applied mathematics".


However, these two areas are not clearly separated. Research results of pure mathematics may help solve actual problems in 100 years.


I will look at the field of pure mathematics. "Numbers" began with "natural numbers" and "four arithmetic operations" at first. Then it is extended to concepts such as "integer", "rational number", "real number" and "imaginary number". Also, numbers are primes, π, e (Number of Napier), ∞, and so on. There are also numbers that are made up of others, such as cardinal numbers, octant numbers, and quaternions.


In the field of "structure" there are equations, "algebra" that started with research on its solution, and vectors and matrices with multiple dimensions and "linear algebra" defining how to calculate them.


Furthermore, "structure theory" which studies the features of numerals, "combinatorial mathematics" such as trees and graphs, "group theory" which treats mutually related items as a group and "order theory" which defines order are included in the structural field I will.


"Space" starts "geometry" and "trigonometry" ...


"Fractal", "topology", "measure theory", "differential geometry" and so on.


In the field of "change" there are "differential integral theory", and "vector analysis" adapting it to a vector.


And "Dynamical systems" such as hydrodynamics and ecosystems, "chaos theory", "complex analysis" dealing with complex numbers are also fields of change.


From here we will look at the field of applied mathematics.


Mathematics is closely tied to the fields of natural sciences by "mathematical physics", "mathematical chemistry", "mathematical biology" and so on. Of course mathematics is also used in "engineering" fields such as control theory.


There are also "numerical analysis" using approximation etc. "Game theory" which calculates the case where we do our best with each other under rules, game theory is also used in "economics".


And "probability" and "statistics" indispensable for data analysis. These are related to "mathematical finance."


"Mathematical optimization" is the field of choosing the most suitable one among many choices and restrictions. "Computer Science" is closely tied to pure mathematics, and that theory was being studied before the computer appeared. Machine learning consists of various fields such as linear algebra, mathematical optimization, dynamics, probability theory. Furthermore, "cryptographic theory" was created from combinatorial mathematics and number theory.


There is also a field called "fundamental theory of mathematics". He deals with axioms, logic, set theory, categorical theory (Kenro), computational theory, etc. It is a field to study mathematics itself.


The movie says, "The most favorite thing while learning mathematics is the joy when we could understand it by inspiration what seemed complicated.The glimpse of the providence of the universe by understanding a part of mathematics I was feeling like I could feel like it. "

In addition, videos that summarize the fields of chemistry, biology, physics, computer science are also uploaded.

The Map of Chemistry - YouTube


Map of Biology - YouTube


The Map of Physics - YouTube


Map of Computer Science - YouTube