# Supplementary mathematics

SUPPLEMENTARY MATHEMATICS
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## Definition

   Definition
This book is a guide for those interested in mathematics, which presents an advanced and complementary type of mathematics. In this book, we discuss advanced topics such as calculations, analysis, geometry, etc., and general topics such as the branches of mathematics. This book is different from basic math, basic math teaches basic concepts and teaches math in simple language. The concept of advanced mathematics means to present complex and advanced concepts, it means that extensive concepts are also included with them. This ebook will help you with advanced and extensive and important
concepts of mathematics.

## Introduction

* Introduction

## List of research topics

* Mathematics
* Calculus
* geometry
* Discrete mathematics
* Statistics and Probability
* Mathematics analysis

## Mathematics

* Philosophy of mathematics
* Mathematics awards
* History of mathematics
* Mathematics Olympiad
* Applied mathematics
* pure mathematics
* Computational mathematics
* Engineering Mathematics
* branches of mathematics

## Calculus
### branchs of calculus

* Differential calculus
* Integral calculus

### integrals

* Integral of Fourier
* Linear integral
* Volume integral
* Surface integral
* multiple integral
* Riemann integral
* Riemann-Stiltis integral
* Improper integral
* Gaussian integral
* Integral of logarithmic
* Logarithmic integral function
* Path integral formulation
* integral list of dumb functions
* integral list of exponential functions
* Integral list of inverse hyperbolic functions
* Integration by parts
* Integral list of rational functions
* Integral list of trigonometric functions
* Integral list of inverse trigonometric functions
* List of integrals of hyperbolic functions
* List of integrals of Gaussian functions
* List of integrals of logarithmic functions

### trigonometries

* Trigonometry
* Trigonometric functions
* Spherical Trigonometry
* Exact trigonometric values
* Euler's formula
* Generalized Trigonometry
* Goniometric function
* Harty core
* Greninger diagram
* List of trigonometric identities
* Trigonometric integral
* trigonometric derivative
* trigonometric rules
* trigonometric polynomial
* Formula of half angle of tangent
* Matrix trigonometric functions
* Trigonometric tables
* Unit circle

### series

* Series of math
* Fourier series
* Taylor series
* power series
* Binomial series
* Gregoric series
* Laurent series
* divergent series
* Harmonic series
* Convergent series
* Geometric series
* Ramanujan-Sato series

### derivative

* derivative

### Other:

* Fourier transform
* Laplace's equation
* Laplace transform
* Differential equation
* function (mathematics)
* Logarithm
* Logarithmic function
* Show function
* Linear equation
* Algebra and equation
* Limit of the function
* continuity of the function
* Infinite limit
* finite limit
* Line element
* Volume element
* Inverse trigonometric functions
* Dini criterion
* Etihad Parswal
* Gibbs phenomenon
* Triangular and square wave
* Anti-derivative
* Binomial expansion
* derivative of logarithmic
* Integration of Fourier series
* Derivation of Fourier series

## Geometry
### branches of geometry

* Spatial geometry
* Differential geometry
* Area and volume
* Regular polygon
* Conical section
* Riemannian geometry
* Analytic geometry
* Algebraic geometry
* Euclidean geometry
* Non-Euclidean geometry

### Geometric algorithms

* Internal and external angle
* Cartesian coordinate system
* Three-dimensional space
* Spherical coordinate system
* Cylindrical coordinate system
* Cube
* Cuboid
* Prism
* Cylinder
* Sphere
* Pyramid
* Cone
* Spherical sector
* Rotation
* Parallelepiped
* Polyhedron
* octahedron
* Torus
* Rotation
* Central angle
* Circumferential angle
* Shadow angle
* Spatial angle
* Sector
* radians
* Gradient
* matrix
* Spherical wedge
* Spherical piece
* anti-prism
* Incomplete pyramid
* Thales theorem
* Internal and external multiplication
* Vectors
* Spheroid
* Ellipsoid

## Discrete mathematics

* Theory of sets
* logic (the study of reasoning)
* Number Theory
* Combinations
* Graph Theory
* Digital geometry
* Digital topology
* Algorithmology
* Information theory
* Theory of computability
* Complexity theory
* Fundamental probability theory
* Markov chain theory
* Linear Algebra
* Partially ordered collection
* Possibilities
* proof (mathematics)
* count
* Polynomial long division
* Binary relationship
* Latin square
* Binomial expansion

## Statistics and Probability

* Classification of data
* Law of total probability
* Average
* Diagrams
* Statistics variables
* Inferential statistics
* Descriptive Statistics
* Number of possible modes
* Independent events
* Conditional probability
* Collection and probability
* Sample space
* Society and example
* Complementary event
* Discrete probability distribution
* Mathematical Statistics
* Algebraic statistics
* Bayes law of probability
* statistical model
* Algebraic probability

## Mathematics analysis

* Real analysis
* Mixed analysis
* Functional analysis
* Harmonic analysis
* Complex analysis
* numerical analysis
* Vector analysis
* Analytical analysis
* General analysis
* Analysis of Fourier
* Approximate analysis
* Non-standard analysis

## Mathematical principles

* Addition principle
* Bloch's principle
* Cavalieri's principle
* Clubsuit
* Combinatorial principles
* Contraction principle (large deviations theory)
* Courant minimax principle
* Diamond principle
* Dirichlet's principle
* Duhamel's principle
* Harnack's principle
* Hasse principle
* Hausdorff maximal principle
* Homotopy principle
* Hopf lemma
* Hopf maximum principle
* Hume's principle
* Inclusion–exclusion principle
* Incompressibility method
* Laplace principle (large deviations theory)
* Littlewood's three principles of #real analysis
* Markov's principle
* Maupertuis's principle
* Principle of maximum caliber
* Principle of maximum entropy
* Maximum modulus principle
* Maximum principle
* Method of distinguished element
* Order-extension principle
* Phragmén–Lindelöf principle
* Pigeonhole principle
* Racetrack principle
* Reflection principle
* Rule of product
* Schwarz reflection principle
* Splitting principle
* Square–cube law
* Tilted large deviation principle
* Transfer principle
* Uniform boundedness principle
* Vopěnka's principle
* Well-ordering principle

## References

* References

## Builders
### Builder's joint account

* User:Germany Poul Ah
* User:Mohammad.Hosein.J.Shia
* User:‬FDVDBFNDBSW2552

### other

* user:Kittycataclysm
* user:mathXplore