# Mathematics

**What does mathematics mean?****Mathematics**(Greek πάθημα mathematics, “*knowledge, study, learning*“) deals with matters such as quantity, structure, space and change. Mathematicians and philosophers have an opinion on the exact scope and definition of mathematics.

- Mathematicians investigate patterns and use them to form new conjunctures. They try to solve the correctness or the inaccuracy of these conjugates through mathematical proof. When mathematical constructions make good models of real phenomena, mathematical thought can provide us with an estimate of nature and its inner face. Mathematics makes it possible to count, calculate and measure the forms and movements of physical objects using systematic operation using abstraction and logic, and so on. There has been human activity ever since records of practical mathematical writing. The research required to solve mathematical problems may require years, even centuries.

- The first precise recordings are found in Greek mathematics. The tradition of establishing truth in mathematical research has changed since Giuseppe Peano (
*1858-1932*),**David Hilbert**(*1862-1943*), and others have worked on architec- tural systems in the late 19th century (*especially in the book of Euclidean Elements). (It is now deductively meticulously selected from appropriately chosen axioms and definitions.*) Mathematics has been slower than the Renaissance. Then the innovations in mathematics interacted with other new scientific discoveries, providing a rapid increase in mathematical discoveries that still continues today.

**Galileo Galilei**(1564-1642) “The book we call the universe can not be understood unless the language and the letters are written, it is written in the language of mathematics, and the letters are triangles, circles and other geometric forms without which there is no single word of the book. In a dark labyrinth. ”**Carl Friedrich Gauss**(1777-1855) compared mathematics to the queen of sciences.**Benjamin Peirce**(1809-1880) was the science of mathematics for drawing the results of the sciences.**David Hilbert**“We do not speak haphazardly here, it’s not like a game where random rules are stipulated, it’s only a conceptual system with internal necessity, nothing else.”**Albert Einstein**(1879-1955), “Mathematics does not reflect the truth when it is certain, but it is not certain when you reflect the truth.” French mathematician**Claire Voisin**said, “The creative impulse in mathematics is the attempt to express itself everywhere.” He says.

- Mathematics is a fundamental tool in many fields such as natural sciences, engineering, information and finance in the world. Applied mathematics is concerned with the application of mathematical knowledge to other fields. Thanks to its applications, new mathematical disciplines have been born, such as statistics and game theory. In addition, mathematicians struggle to do mathematics without abstract mathematics and without any use in their minds. There is no distinct line separating abstract mathematics and applied mathematics. Discovery in abstract mathematics often becomes the initiator of practical math applications.

**Origin of the Math Words**- The Ancient Greek matesis word is the root of the mathematics word, and I mean knowledge. It was later derived from the word μάθημα (
*máthema*), which comes to meanings such as science, knowledge and learning, respectively. It means to like learning μαθηματικός (*mathematikós*).

**Mathematics Education**- Mathematics is often encountered in everyday life as well as in science. Mathematics is a system based on reasoning, and it gives the person a rational point of view as a means of developing mind. The person creates an environment of free and unbiased thinking. It allows people to think systematically, logically, consistently. That is why mathematics is taught in every field from primary education to higher education programs. Mathematics education is done as preparation for secondary education in primary education and as preparation for higher education in secondary education.

**Modern Uses of Mathematics**- Algebraic geometry and techniques used in robot and computer game models
- Differential equations and numerical analysis techniques are used in aircraft and engine models, in satellite production and more generally in the measurement of dynamic system changes.
- Fractals are used in aeronautical technology to build small volume, large surface area antennas. In addition, fractal geometry is used in living organisms to explain the flow of capillaries and the flow of blood.
- Self-copying machines and symbolic automata are used in the reconstruction of lost parts of digital data sent from Earth stations to Earth.
- Fourier analysis and techniques are used in communications networks to ensure that the data can be sent to very long distances and that the loss is minimal. In addition, Fourier techniques are used to compress pictures, videos and digital music.
- Cellular automata are used to model the reproduction of biological organisms and the spread of disease.
- Applied homology, a subdivision of algebraic topology, is used to determine the mathematical topology of the digital data. The best example of this is the determination of the geography of the planet’s surface from photographs of distant planets.
- Algorithmic techniques are used in programming.
- Abstract logic is used in electrical circuit and computer design.
- The graph theory is used in the topological and combinatorial study of the database. For example, we can determine whether hospitals in a country are ideal for distances to where they are located. Another example is the analysis of the distribution of internet sites.

**Mathematics topics****Numbers**- Natural numbers
- Integers
- Rational numbers
- Irrational numbers
- Real numbers
- Complex numbers
- Quads
- Prime numbers
- Constants
- Hyperbolic numbers
- Double complex numbers
- P-floors
- Consecutive numbers
- The number of love
- Perfect number
- Binary numbers
- Zero

**Space Maths**- Algebraic geometry
- Analytical geometry
- Differential geometry
- Differential topology
- Algebraic topology
- Linear algebra
- Geometry
- Trigonometry
- Differential geometry
- Topology
- Fractal geometry

**Calculus**- Arithmetic
- Analysis
- Derivative
- Fractional calculus
- Functions
- Trigonometric functions
- Calculus
- Vector calculus
- Differential equations
- Dynamic system
- Chaos theory

**Basic mathematical constructions**- Monoid
- Heap (
*mathematics*) - Rings
- Object (
*Algebra*) - Topological Spaces
- Multitudes
- Hilbert axioms
- Sequences

**Basic mathematical concepts**- Algebra
- Clusters
- Numbers
- Connections
- Functions
- Limit
- Continuity
- Derivative and differentiability
- Analytical geometry
- Integralability
- Matrix
- Determinants
- Equivalent
- Homotopy
- Good-ordering principle
- Countability
- Abstractness
- Rate
- Ratio
- Polynomial
- Permutation
- Combination
- Logarithm
- Linear algebra

**Main branches of mathematics**- Abstract algebra
- Numbers theory
- Algebraic geometry
- Group theory
- Analysis
- Topology
- Graph Theory
- General algebra
- Category theory
- Mathematical logic
- Differential equations
- Partial differential equations
- Possibility
- Theory of complex functions

**Finite mathematics**- Combinatorics
- Pure set theory
- Possibility
- Theory of account
- Finite mathematics
- Cryptography
- Graph Theory
- Game theory

**Applied mathematics**- Mechanical
- Numerical analysis
- Optimization
- Possibility
- Statistics
- Financial mathematics

**Famous mathematical theories**- Fermat’s last theorem
- Riemann hypothesis
- Continuity hypothesis
- P = NP
- Goldbach aspiration
- Gödel’s inability theory
- Poincaré
- Cantor’s diagonal method
- Pythagorean theorem
- Central limit theorem
- The basic theorem of the account
- Thought of twins
- The basic theory of algebra
- The basic theory of arithmetic
- Four color theorem
- Zorn pre-order
- Fibonacci sequence

**Possibilities and methods**- Mathematical philosophy
- Intuitive mathematics
- Constructor math
- Foundations of mathematics
- Cluster theory
- Symbolic logic
- Model theory
- Category theory
- Proof of theorem
- Logic
- Conversely, mathematics