OMS (aka TeX math symbol) is a 7-bit TeX encoding developed by Donald E. Knuth. [1] It encodes mathematical symbols with variable sizes like for capital Pi notation, brackets, braces and radicals.
OMS [2] | ||||||||||||||||
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | A | B | C | D | E | F | |
0x | − | ⋅ | × | ∗ | ÷ | ⋄ | ± | ∓ | ⊕ | ⊖ | ⊗ | ⊘ | ⊙ | ○ | ∘ | ∙ |
1x | ≍ | ≡ | ⊆ | ⊇ | ≤ | ≥ | ≼ | ≽ | ∼ | ≈ | ⊂ | ⊃ | ≪ | ≫ | ≺ | ≻ |
2x | ← | → | ↑ | ↓ | ↔ | ↗ | ↘ | ≃ | ⇐ | ⇒ | ⇑ | ⇓ | ⇔ | ↖ | ↙ | ∝ |
3x | ′ | ∞ | ∈ | ∋ | △ | ▽ | ◌̸ | ◌̍ | ∀ | ∃ | ¬ | ∅ | ℜ | ℑ | ⊤ | ⊥ |
4x | ℵ | 𝒜 | ℬ | 𝒞 | 𝒟 | ℰ | ℱ | 𝒢 | ℋ | ℐ | 𝒥 | 𝒦 | ℒ | ℳ | 𝒩 | 𝒪 |
5x | 𝒫 | 𝒬 | ℛ | 𝒮 | 𝒯 | 𝒰 | 𝒱 | 𝒲 | 𝒳 | 𝒴 | 𝒵 | ∪ | ∩ | ⊎ | ∧ | ∨ |
6x | ⊢ | ⊣ | ⌊ | ⌋ | ⌈ | ⌉ | { | } | ⟨ | ⟩ | ∣ | ∥ | ↕ | ⇕ | ∖ | ≀ |
7x | √ | ∐ | ∇ | ∫ | ⊔ | ⊓ | ⊑ | ⊒ | § | † | ‡ | ¶ | ♣ | ♢ | ♡ | ♠ |
Donald Ervin Knuth is an American computer scientist and mathematician. He is a professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms".
In mathematics and computing, the hexadecimal numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbols, hexadecimal uses sixteen distinct symbols, most often the symbols "0"–"9" to represent values 0 to 9, and "A"–"F" to represent values from ten to fifteen.
Literate programming is a programming paradigm introduced in 1984 by Donald Knuth in which a computer program is given as an explanation of how it works in a natural language, such as English, interspersed (embedded) with snippets of macros and traditional source code, from which compilable source code can be generated. The approach is used in scientific computing and in data science routinely for reproducible research and open access purposes. Literate programming tools are used by millions of programmers today.
LaTeX is a software system for typesetting documents. LaTeX markup describes the content and layout of the document, as opposed to the formatted text found in WYSIWYG word processors like Microsoft Word, LibreOffice Writer and Apple Pages. The writer uses markup tagging conventions to define the general structure of a document, to stylise text throughout a document, and to add citations and cross-references. A TeX distribution such as TeX Live or MiKTeX is used to produce an output file suitable for printing or digital distribution.
TeX, stylized within the system as TeX, is a typesetting system which was designed and written by computer scientist and Stanford University professor Donald Knuth and first released in 1978. TeX is a popular means of typesetting complex mathematical formulae; it has been noted as one of the most sophisticated digital typographical systems.
Blackboard bold is a style of writing bold symbols on a blackboard by doubling certain strokes, commonly used in mathematical lectures, and the derived style of typeface used in printed mathematical texts. The style is most commonly used to represent the number sets , (integers), , , and .
Metafont is a description language used to define raster fonts. It is also the name of the interpreter that executes Metafont code, generating the bitmap fonts that can be embedded into e.g. PostScript. Metafont was devised by Donald Knuth as a companion to his TeX typesetting system.
Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by German mathematicians Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for Ordnung, meaning the order of approximation.
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible. He suggested that we may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q 1: q 2. .... qI; which will be called "m-configurations". He then described the operation of such machine, as described below, and argued:
It is my contention that these operations include all those which are used in the computation of a number.
Web is a computer programming system created by Donald E. Knuth as the first implementation of what he called "literate programming": the idea that one could create software as works of literature, by embedding source code inside descriptive text, rather than the reverse, in an order that is convenient for exposition to human readers, rather than in the order demanded by the compiler.
The device independent file format (DVI) is the output file format of the TeX typesetting program, designed by David R. Fuchs and implemented by Donald E. Knuth in 1982. Unlike the TeX markup files used to generate them, DVI files are not intended to be human-readable; they consist of binary data describing the visual layout of a document in a manner not reliant on any specific image format, display hardware or printer. DVI files are typically used as input to a second program which translates DVI files to graphical data. For example, most TeX software packages include a program for previewing DVI files on a user's computer display; this program is a driver. Drivers are also used to convert from DVI to popular page description languages and for printing.
Computers and Typesetting is a 5-volume set of books by Donald Knuth published in 1986 describing the TeX and Metafont systems for digital typography. Knuth's computers and typesetting project was the result of his frustration with the lack of decent software for the typesetting of mathematical and technical documents. The results of this project include TeX for typesetting, Metafont for font construction and the Computer Modern typefaces that are the default fonts used by TeX. In the series of five books Knuth not only describes the TeX and Metafont languages, he also describes and documents the source code of the TeX and Metafont interpreters, and the source code for the Computer Modern fonts used by TeX. The book set stands as a tour de force demonstration of literate programming.
Computer Modern is the original family of typefaces used by the typesetting program TeX. It was created by Donald Knuth with his Metafont program, and was most recently updated in 1992. Computer Modern, or variants of it, remains very widely used in scientific publishing, especially in disciplines that make frequent use of mathematical notation.
AMS Euler is an upright cursive typeface, commissioned by the American Mathematical Society (AMS) and designed and created by Hermann Zapf with the assistance of Donald Knuth and his Stanford graduate students. It tries to emulate a mathematician's style of handwriting mathematical entities on a blackboard, which is upright rather than italic. It blends very well with other typefaces made by Hermann Zapf, such as Palatino, Aldus and Melior, but very badly with the default TeX font Computer Modern. All the alphabets were implemented with the computer-assisted design system Metafont developed by Knuth. Zapf designed and drew the Euler alphabets in 1980–81 and provided critique and advice of digital proofs in 1983 and later. The typeface family is copyright by American Mathematical Society, 1983. Euler Metafont development was done by Stanford computer science and/or digital typography students; first Scott Kim, then Carol Twombly and Daniel Mills, and finally David Siegel, all assisted by John Hobby. Siegel finished the Metafont Euler digitization project as his M.S. thesis in 1985.
Knuth reward checks are checks or check-like certificates awarded by computer scientist Donald Knuth for finding technical, typographical, or historical errors, or making substantial suggestions for his publications. The MIT Technology Review describes the checks as "among computerdom's most prized trophies".
The dangerous bend or caution symbol ☡ was created by the Nicolas Bourbaki group of mathematicians and appears in the margins of mathematics books written by the group. It resembles a road sign that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.
In typography, a thin space is a space character whose width is usually 1⁄5 or 1⁄6 of an em. It is used to add a narrow space, such as between nested quotation marks or to separate glyphs that interfere with one another. It is not as narrow as the hair space. It is also used in the International System of Units and in many countries as a thousands separator when writing numbers in groups of three digits, in order to facilitate reading.
OML is a 7-bit TeX encoding developed by Donald E. Knuth. It encodes italic Latin and Greek letters for mathematical formulas and various symbols.
OT1 is a 7-bit TeX encoding developed by Donald E. Knuth.
Stanford/ITS character set is an extended ASCII character set based on SEASCII with modifications allowing compatibility with 1968 ASCII.