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8.1: New Page - Mathematics


8.1: New Page - Mathematics

Does SpringBoard math meet state standards?

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Двухнедельное онлайн-введение в прикладную многопарадигмальную науку о данных. Удаленное общение с нашими экспертами для проведения современного анализа, при желании используя ваш собственный набор данных.

Двухнедельное онлайн-введение в прикладную многопарадигмальную науку о данных. Удаленное общение с нашими экспертами для проведения современного анализа, при желании используя ваш собственный набор данных.

Двухнедельное онлайн-введение в прикладную многопарадигмальную науку о данных.

Динамические изображения с квазикристаллом, интерференцией волн и полутонами Гендерная предвзятость в популярных фильмах: вычислительный подход Анализ и визуализация данных о случаях заболевания холерой во время вспышки 1854 года Конспекты занятий, контрольные работы и оповещения о погодных условиях с помощью системы Mathematica и языка Wolfram Language Использование IPFS, Filecoin и Wolfram Language для создания унифицированного интерфейса децентрализованных сервисов

8.1: New Page - Mathematics

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26 Types of Math

The word mathematics was coined by the Pythagoreans in the 6th century from the Greek word μάθημα (mathema), which means “subject of instruction.” There are many different types of mathematics based on their focus of study. Here are some of them:

1. Algebra

Algebra is a broad division of mathematics. Algebra uses variable (letters) and other mathematical symbols to represent numbers in equations. It is basically completing and balancing the parts on the two sides of the equation.

It can be considered as the unifying type of all the fields in mathematics. Algebra’s concept first appeared in an Arabic book which has a title that roughly translates to ‘the science of restoring of what is missing and equating like with like.’ The word came from Arabic which means completion of missing parts.

2. Geometry

The word geometry comes from the Greek words ‘gē’ meaning ‘Earth’ and ‘metria’ meaning ‘measure’. It is the mathematics concerned with questions of shape, size, positions, and properties of space.

It also studies the relationship and properties of set of points. It involves the lines, angles, shapes, and spaces formed.

3. Trigonometry

Trigonometry comes from the Greek words ‘trigōnon’ which means ‘triangle’ and ‘metria’ which means ‘measure’. As its name suggests, it is the study the sides and angles, and their relationship in triangles.

Some real life applications of trigonometry are navigation, astronomy, oceanography, and architecture.

4. Calculus

Calculus is an advanced branch of mathematics concerned in finding and properties of derivatives and integrals of functions. It is the study of rates of change and deals with finding lengths, areas, and volumes.

Calculus is used by engineers, economists, scientists such as space scientists, etc.

5. Linear Algebra

Linear algebra is a branch of mathematics and a subfield of algebra. It studies lines, planes, and subspaces. It is concerned with vector spaces and linear mappings between those spaces.

This branch of mathematics is used in chemistry, cryptography, geometry, linear programming, sociology, the Fibonacci numbers, etc.

6. Combinatorics

The name combinatorics might sound complicated, but combinatorics is just different methods of counting. The word was derived from the word ‘combination’, therefore in is used to combine objects following rules of arranging those objects.

There are two combinatorics categories: enumeration and graph theory. Permutation, an arrangement where order matters, is often used in both of the categories.

7. Differential Equations

As the name suggest, differential equations are not really a branch of mathematics, rather a type of equation. It is any equation that contains either ordinary derivatives or partial derivatives.

The equations define the relationship between the function, which represents physical quantities, and the derivatives, which represents the rates of change.

8. Real Analysis

Real analysis is also called the theory of functions of a real variable. It is concerned with the axioms dealing with real numbers and real-valued functions of a real-variable.

It is pure mathematics, and is good for people who like plane geometry and proving.

9. Complex Analysis

Complex analysis is also called the theory of functions of a complex variable. It deals with complex numbers and their derivatives, manipulation, and other properties. Complex analysis is applied in electrical engineering, when launching satellite, etc.

10. Abstract Algebra

Sometimes called modern algebra, abstract algebra is an advanced field in algebra concerning the extension of algebraic concepts such as real number systems, complex numbers, matrices, and vector spaces.

One application of abstract algebra is cryptography elliptic curve cryptography involves a lot of algebraic number theory and the likes.

11. Topology

Topology is a type of geometry developed in the 19th century. Its name’s Greek origin, which is ‘topos’, means place. Unlike the other types of geometry, it is not concerned with the exact dimensions, shapes, and sizes of a region.

It studies the physical space a surface unaffected by distortion contiguity, order, and position. Topology is applied in the study of the structure of the universe and in designing robots.

12. Number Theory

Number theory, or higher arithmetic, is the study of positive integers, their relationships, and properties. It is sometimes referred to as “The Queen of Mathematics” because of its foundational function in the subject.

13. Logic

Logic is the discipline in mathematics that studies formal languages, formal reasoning, the nature of mathematical proof, probability of mathematical statements, computability, and other aspects of the foundations of mathematics.

It aims to eliminate any confusion that can be caused by the vagueness of the natural language.

14. Probability

Probability is the branch of mathematics calculating the chances of some things to take place based on the number of the possible cases to the whole number of cases possible. Numbers from 0-1 are used to express the chances of something to occur.

0 means it can never happen and 1 means it will always happen. Real-life applications are in gambling, lottery, sports analysis, games, weather forecasting, etc. Even the chance of an earthquake or a volcano erupting are given a probability.

15. Statistics

Statistics are the collection, analysis, measurement, interpretation, presentation and summarization of data. Statistics is used in many fields such as business analytics, demography, epidemiology, population ecology, etc.

16. Game Theory

Game theory is a branch of mathematics which also involves psychology, economics, contract theory, and sociology. It analyses strategies for dealing with competitive strategies where the outcome also depends on other actions of other partaker in the activity.

It is applied in business, wars, political sciences, biology, philosophy, etc.

17. Functional Analysis

Functional analysis is under the field of mathematical analysis. Its foundation is the study of vector spaces that has limit-related structure such as topology, inner product, norm, etc.

It was developed through the study of functions and the formulation of properties of transformation. Functional analysis is found to be useful for differential and integral equations.

18. Algebraic Geometry

Algebraic geometry is a branch of mathematics that uses algebraic expressions to describe geometric properties of structures.

19. Differential Geometry

Differential geometry is a field in mathematics that utilizes different mathematical techniques (differential calculus, integral calculus, linear algebra, and multilinear algebra) to study geometric problems.

It is used in different studies of electromagnetism, econometrics, geometric modeling, digital signal processing in engineering, study of geological structures.

20. Dynamical Systems (Chaos Theory)

Dynamical Systems (also referred to as chaos theory) is a mathematical concept where the relationship of a point in space to time is described a fixed set of rules. This concept explains the swinging of a clock pendulum, flow of water in a pipe, number of fish in a lake during springtime, etc.

21. Numerical Analysis

Numerical analysis is an area in mathematics which develops, evaluates, and applies algorithms for numerically solving problems that occur throughout the natural sciences, social sciences, medicine, engineering and business.

22. Set Theory

Set theory is a discipline in mathematics that is concerned with the formal properties of a well-defined set of objects as units (regardless of the nature of each element) and using set as a means of expression of other branch of math.

Every object in the set has something similar or follows a rule, and they are called the elements.

23. Category Theory

Category theory is a formalism that is used for representing and manipulating concepts and symbolic representations of domains. Here, the collection of objects and of arrows formalizes mathematical structure.

24. Model Theory

Model theory in mathematics is the study of different structures from a logical standpoint. It involves interpretation of formal and natural languages and the kinds of classifications they can make.

25. Mathematical Physics

Mathematics as mentioned earlier is used in many different other fields. Physics is just one of them. Mathematical physics refers to the mathematical methods applied for different studies and development in physics.

26. Discrete Mathematics

Unlike the many other ones mentioned above, discrete mathematics is not a branch, but a description of the study of mathematical structures that are discrete rather than continuous.

Discrete objects, in simple languages, are the countable objects such as integers. Therefore, discrete mathematics does not include calculus and analysis.

2 thoughts on &ldquo26 Different Types of Mathematics&rdquo

please more about algebra, trigonometry and calculus

I have a question. A teacher of mine discussed a class she took in college converting language into mathematics. She mentioned the name of the class, but I suffer from TBI and forget details. I remember her saying all of language is mathematics and not just the operative words. I would like to read up on that.


  • a composite number, its proper divisors being 1, 2, and 4. It is twice 4 or four times 2.
  • a power of two, being 2 3 (two cubed), and is the first number of the form p 3 , p being an integer greater than 1.
  • the first number which is neither prime nor semiprime.
  • the base of the octal number system, [1] which is mostly used with computers. In octal, one digit represents three bits. In modern computers, a byte is a grouping of eight bits, also called an octet.
  • a Fibonacci number, being 3 plus 5. The next Fibonacci number is 13. 8 is the only positive Fibonacci number, aside from 1, that is a perfect cube. [2]
  • the only nonzero perfect power that is one less than another perfect power, by Mihăilescu's Theorem.
  • the order of the smallest non-abelian group all of whose subgroups are normal.
  • the dimension of the octonions and is the highest possible dimension of a normed division algebra.
  • the first number to be the aliquot sum of two numbers other than itself the discrete biprime 10, and the square number 49.

A number is divisible by 8 if its last three digits, when written in decimal, are also divisible by 8, or its last three digits are 0 when written in binary.

There are a total of eight convex deltahedra. [3]

A polygon with eight sides is an octagon. [4] Figurate numbers representing octagons (including eight) are called octagonal numbers.

A polyhedron with eight faces is an octahedron. [5] A cuboctahedron has as faces six equal squares and eight equal regular triangles. [6]

Sphenic numbers always have exactly eight divisors. [8]

The number 8 is involved with a number of interesting mathematical phenomena related to the notion of Bott periodicity. For example, if O(∞) is the direct limit of the inclusions of real orthogonal groups

Clifford algebras also display a periodicity of 8. [9] For example, the algebra Cl(p + 8,q) is isomorphic to the algebra of 16 by 16 matrices with entries in Cl(p,q). We also see a period of 8 in the K-theory of spheres and in the representation theory of the rotation groups, the latter giving rise to the 8 by 8 spinorial chessboard. All of these properties are closely related to the properties of the octonions.

The spin group Spin(8) is the unique such group that exhibits the phenomenon of triality.

The lowest-dimensional even unimodular lattice is the 8-dimensional E8 lattice. Even positive definite unimodular lattices exist only in dimensions divisible by 8.

A figure 8 is the common name of a geometric shape, often used in the context of sports, such as skating. [10] Figure-eight turns of a rope or cable around a cleat, pin, or bitt are used to belay something. [11]

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8 × x 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8 ÷ x 8 4 2. 6 2 1.6 1. 3 1. 142857 1 0. 8 0.8 0. 72 0. 6 0. 615384 0. 571428 0.5 3
x ÷ 8 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 1.25 1.375 1.5 1.625 1.75 1.875
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
8 x 8 64 512 4096 32768 262144 2097152 16777216 134217728 1073741824 8589934592 68719476736 549755813888
x 8 1 256 6561 65536 390625 1679616 5764801 16777216 43046721 100000000 214358881 429981696 815730721

English eight, from Old English eahta, æhta, Proto-Germanic *ahto is a direct continuation of Proto-Indo-European *oḱtṓ(w)-, and as such cognate with Greek ὀκτώ and Latin octo-, both of which stems are reflected by the English prefix oct(o)-, as in the ordinal adjective octaval or octavary, the distributive adjective is octonary. The adjective octuple (Latin octu-plus) may also be used as a noun, meaning "a set of eight items" the diminutive octuplet is mostly used to refer to eight siblings delivered in one birth.

The Semitic numeral is based on a root *θmn-, whence Akkadian smn-, Arabic ṯmn-, Hebrew šmn- etc. The Chinese numeral, written 八 (Mandarin: Cantonese: baat), is from Old Chinese *priāt-, ultimately from Sino-Tibetan b-r-gyat or b-g-ryat which also yielded Tibetan brgyat.

It has been argued that, as the cardinal number 7 is the highest number of item that can universally be cognitively processed as a single set, the etymology of the numeral eight might be the first to be considered composite, either as "twice four" or as "two short of ten", or similar. The Turkic words for "eight" are from a Proto-Turkic stem *sekiz, which has been suggested as originating as a negation of eki "two", as in "without two fingers" (i.e., "two short of ten two fingers are not being held up") [12] this same principle is found in Finnic *kakte-ksa, which conveys a meaning of "two before (ten)". The Proto-Indo-European reconstruction *oḱtṓ(w)- itself has been argued as representing an old dual, which would correspond to an original meaning of "twice four". Proponents of this "quaternary hypothesis" adduce the numeral 9, which might be built on the stem new-, meaning "new" (indicating the beginning of a "new set of numerals" after having counted to eight). [13]

The modern digit 8, like all modern Arabic numerals other than zero, originates with the Brahmi numerals. The Brahmi digit for eight by the 1st century was written in one stroke as a curve └┐ looking like an uppercase H with the bottom half of the left line and the upper half of the right line removed. However the digit for eight used in India in the early centuries of the Common Era developed considerable graphic variation, and in some cases took the shape of a single wedge, which was adopted into the Perso-Arabic tradition as ٨ (and also gave rise to the later Devanagari form ८) the alternative curved glyph also existed as a variant in Perso-Arabic tradition, where it came to look similar to our digit 5. [ year needed ]

The digits as used in Al-Andalus by the 10th century were a distinctive western variant of the glyphs used in the Arabic-speaking world, known as ghubār numerals (ghubār translating to "sand table"). In these digits, the line of the 5-like glyph used in Indian manuscripts for eight came to be formed in ghubār as a closed loop, which was the 8-shape that became adopted into European use in the 10th century. [14]

Just as in most modern typefaces, in typefaces with text figures the character for the digit 8 usually has an ascender, as, for example, in .

The infinity symbol ∞, described as a "sideways figure eight" is unrelated to the digit 8 in origin it is first used (in the mathematical meaning "infinity") in the 17th century, and it may be derived from the Roman numeral for "one thousand" CIƆ, or alternatively from the final Greek letter, ω.


How to correct formulas

When writing a formula, don't hesitate to use the tools available on the right side of the application. If you made a mistake, you can easily fix it using the Erase tool. Click or tap on it to erase the mistake.

There are situations when Math Input Panel doesn't recognize what you write very well. You can correct the way it interprets your writing by clicking or tapping on "Select and Correct" . Then, select the character you want to correct. A drop-down menu with possible correction options is shown. From that menu select the correct interpretation and resume your writing by clicking or tapping on Write .


More resources

  • The binaries for AMD64 will also work on processors that implement the Intel 64 architecture. (Also known as the "x64" architecture, and formerly known as both "EM64T" and "x86-64".)
  • There are now "web-based" installers for Windows platforms the installer will download the needed software components at installation time.
  • There are redistributable zip files containing the Windows builds, making it easy to redistribute Python as part of another software package. Please see the documentation regarding Embedded Distribution for more information.

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