1.
Specials (Unicode block)
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Specials is a short Unicode block allocated at the very end of the Basic Multilingual Plane, at U+FFF0–FFFF. Of these 16 codepoints, five are assigned as of Unicode 9, U+FFFD � REPLACEMENT CHARACTER used to replace an unknown, unrecognized or unrepresentable character U+FFFE <noncharacter-FFFE> not a character. FFFE and FFFF are not unassigned in the sense. They can be used to guess a texts encoding scheme, since any text containing these is by not a correctly encoded Unicode text. The replacement character � is a found in the Unicode standard at codepoint U+FFFD in the Specials table. It is used to indicate problems when a system is unable to render a stream of data to a correct symbol and it is usually seen when the data is invalid and does not match any character, Consider a text file containing the German word für in the ISO-8859-1 encoding. This file is now opened with an editor that assumes the input is UTF-8. The first and last byte are valid UTF-8 encodings of ASCII, therefore, a text editor could replace this byte with the replacement character symbol to produce a valid string of Unicode code points. The whole string now displays like this, f�r, a poorly implemented text editor might save the replacement in UTF-8 form, the text file data will then look like this, 0x66 0xEF 0xBF 0xBD 0x72, which will be displayed in ISO-8859-1 as f�r. Since the replacement is the same for all errors this makes it impossible to recover the original character, a better design is to preserve the original bytes, including the error, and only convert to the replacement when displaying the text. This will allow the text editor to save the original byte sequence and it has become increasingly common for software to interpret invalid UTF-8 by guessing the bytes are in another byte-based encoding such as ISO-8859-1. This allows correct display of both valid and invalid UTF-8 pasted together, Unicode control characters UTF-8 Mojibake Unicodes Specials table Decodeunicodes entry for the replacement character
2.
Typeface
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In metal typesetting, a font is a particular size, weight and style of a typeface. Each font was a set of type, one piece for each glyph. In modern usage, with the advent of digital typography, font is frequently synonymous with typeface, in particular, the use of vector or outline fonts means that different sizes of a typeface can be dynamically generated from one design. The word font derives from Middle French fonte melted, a casting, the term refers to the process of casting metal type at a type foundry. In a manual printing house the word font would refer to a set of metal type that would be used to typeset an entire page. Unlike a digital typeface it would not include a definition of each character. A font when bought new would often be sold as 12pt 14A 34a, meaning that it would be a size 12-point font containing 14 uppercase As, given the name upper and lowercase because of which case the metal type was located in, otherwise known as majuscule and minuscule. The rest of the characters would be provided in quantities appropriate for the distribution of letters in that language. Some metal type characters required in typesetting, such as dashes, spaces and line-height spacers, were not part of a specific font, line spacing is still often called leading, because the strips used for line spacing were made of lead. In the 1880s–90s, hot lead typesetting was invented, in which type was cast as it was set, either piece by piece or in entire lines of type at one time. In European alphabetic scripts, i. e. Latin, Cyrillic and Greek, the main properties are the stroke width, called weight, the style or angle. The regular or standard font is sometimes labeled roman, both to distinguish it from bold or thin and from italic or oblique. The keyword for the default, regular case is often omitted for variants and never repeated, otherwise it would be Bulmer regular italic, Bulmer bold regular, Roman can also refer to the language coverage of a font, acting as a shorthand for Western European. Different fonts of the same typeface may be used in the work for various degrees of readability and emphasis. The weight of a font is the thickness of the character outlines relative to their height. A typeface may come in fonts of many weights, from ultra-light to extra-bold or black, four to six weights are not unusual, many typefaces for office, web and non-professional use come with just a normal and a bold weight which are linked together. If no bold weight is provided, many renderers support faking a bolder font by rendering the outline a second time at an offset, the base weight differs among typefaces, that means one normal font may appear bolder than some other normal font. For example, fonts intended to be used in posters are often quite bold by default while fonts for long runs of text are rather light, therefore, weight designations in font names may differ in regard to the actual absolute stroke weight or density of glyphs in the font
3.
Mathematics
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Mathematics is the study of topics such as quantity, structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope, Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof, when mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry, rigorous arguments first appeared in Greek mathematics, most notably in Euclids Elements. Galileo Galilei said, The universe cannot be read until we have learned the language and it is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth, carl Friedrich Gauss referred to mathematics as the Queen of the Sciences. Benjamin Peirce called mathematics the science that draws necessary conclusions, David Hilbert said of mathematics, We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules, rather, it is a conceptual system possessing internal necessity that can only be so and by no means otherwise. Albert Einstein stated that as far as the laws of mathematics refer to reality, they are not certain, Mathematics is essential in many fields, including natural science, engineering, medicine, finance and the social sciences. Applied mathematics has led to entirely new mathematical disciplines, such as statistics, Mathematicians also engage in pure mathematics, or mathematics for its own sake, without having any application in mind. There is no clear line separating pure and applied mathematics, the history of mathematics can be seen as an ever-increasing series of abstractions. The earliest uses of mathematics were in trading, land measurement, painting and weaving patterns, in Babylonian mathematics elementary arithmetic first appears in the archaeological record. Numeracy pre-dated writing and numeral systems have many and diverse. Between 600 and 300 BC the Ancient Greeks began a study of mathematics in its own right with Greek mathematics. Mathematics has since been extended, and there has been a fruitful interaction between mathematics and science, to the benefit of both. Mathematical discoveries continue to be made today, the overwhelming majority of works in this ocean contain new mathematical theorems and their proofs. The word máthēma is derived from μανθάνω, while the modern Greek equivalent is μαθαίνω, in Greece, the word for mathematics came to have the narrower and more technical meaning mathematical study even in Classical times
4.
Set (mathematics)
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In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right. For example, the numbers 2,4, and 6 are distinct objects when considered separately, Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a part of mathematics. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, the German word Menge, rendered as set in English, was coined by Bernard Bolzano in his work The Paradoxes of the Infinite. A set is a collection of distinct objects. The objects that make up a set can be anything, numbers, people, letters of the alphabet, other sets, Sets are conventionally denoted with capital letters. Sets A and B are equal if and only if they have precisely the same elements. Cantors definition turned out to be inadequate, instead, the notion of a set is taken as a notion in axiomatic set theory. There are two ways of describing, or specifying the members of, a set, one way is by intensional definition, using a rule or semantic description, A is the set whose members are the first four positive integers. B is the set of colors of the French flag, the second way is by extension – that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets, one often has the choice of specifying a set either intensionally or extensionally. In the examples above, for instance, A = C and B = D, there are two important points to note about sets. First, in a definition, a set member can be listed two or more times, for example. However, per extensionality, two definitions of sets which differ only in one of the definitions lists set members multiple times, define, in fact. Hence, the set is identical to the set. The second important point is that the order in which the elements of a set are listed is irrelevant and we can illustrate these two important points with an example, = =. For sets with many elements, the enumeration of members can be abbreviated, for instance, the set of the first thousand positive integers may be specified extensionally as, where the ellipsis indicates that the list continues in the obvious way. Ellipses may also be used where sets have infinitely many members, thus the set of positive even numbers can be written as
5.
Typewriter
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A typewriter is a mechanical or electromechanical machine for writing characters similar to those produced by printers movable type. A typewriter operates by means of keys that strike a ribbon to transmit ink or carbon impressions onto paper, typically, a single character is printed on each key press. The machine prints characters by making ink impressions of type elements similar to the used in movable type letterpress printing. At the end of the century, the term typewriter was also applied to a person who used a typing machine. After its invention in the 1860s, the quickly became an indispensable tool for practically all writing other than personal handwritten correspondence. It was widely used by writers, in offices. As with the automobile, telephone, and telegraph, a number of people contributed insights, historians have estimated that some form of typewriter was invented 52 times as thinkers tried to come up with a workable design. Some of the early typing instruments, In 1575 an Italian printmaker, Francesco Rampazzetto, invented the scrittura tattile, in 1714, Henry Mill obtained a patent in Britain for a machine that, from the patent, appears to have been similar to a typewriter. In 1802 Italian Agostino Fantoni developed a particular typewriter to enable his blind sister to write, in 1808 Italian Pellegrino Turri invented a typewriter. He also invented carbon paper to provide the ink for his machine, in 1823 Italian Pietro Conti di Cilavegna invented a new model of typewriter, the tachigrafo, also known as tachitipo. In 1829, William Austin Burt patented a machine called the Typographer which, the Science Museum describes it merely as the first writing mechanism whose invention was documented, but even that claim may be excessive, since Turris invention pre-dates it. Even in the hands of its inventor, this machine was slower than handwriting, Burt and his promoter John D. Sheldon never found a buyer for the patent, so the invention was never commercially produced, because the typographer used a dial, rather than keys, to select each character, it was called an index typewriter rather than a keyboard typewriter. Index typewriters of that era resemble the squeeze-style embosser from the 1960s more than they resemble the modern keyboard typewriter, by the mid-19th century, the increasing pace of business communication had created a need for mechanization of the writing process. Stenographers and telegraphers could take down information at rates up to 130 words per minute, from 1829 to 1870, many printing or typing machines were patented by inventors in Europe and America, but none went into commercial production. Charles Thurber developed multiple patents, of which his first in 1843 was developed as an aid to the blind, in 1855, the Italian Giuseppe Ravizza created a prototype typewriter called Cembalo scrivano o macchina da scrivere a tasti. It was a machine that let the user see the writing as it was typed. In 1861, Father Francisco João de Azevedo, a Brazilian priest, made his own typewriter with basic materials and tools, such as wood, in that same year the Brazilian emperor D
6.
Bold type
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In typography, emphasis is the exaggeration of words in a text with a font in a different style from the rest of the text—to emphasize them. It is the equivalent of prosodic stress in speech, the most common methods in Bold fall under the general technique of emphasis through a change or modification of font, italics, boldface and small caps. Other methods include the alteration of letter case and spacing as well as color, the human eye is very receptive to differences in brightness within a text body. Therefore, one can differentiate types of emphasis according to whether the emphasis changes the “blackness” of text. With one or the other of these techniques, words can be highlighted without making them out much from the rest of the text. This was used for marking passages that have a different context, such as words from languages, book titles. By contrast, a bold font weight makes text darker than the surrounding text, for example, printed dictionaries often use boldface for their keywords, and the names of entries can conventionally be marked in bold. Small capitals are used for emphasis, especially for the first line of a section, sometimes accompanied by or instead of a drop cap. If the text body is typeset in a typeface, it is also possible to highlight words by setting them in a sans serif face. It is still using some font superfamilies, which come with matching serif and sans-serif variants. In Japanese typography, due to the legibility of heavier Minchō type. Of these methods, italics, small capitals and capitalisation are oldest, with bold type, the house styles of many publishers in the United States use all caps text for, chapter and section headings, newspaper headlines, publication titles, warning messages, word of important meaning. Capitalization is used less commonly today by British publishers. All-uppercase letters are a form of emphasis where the medium lacks support for boldface, such as old typewriters, plain-text email, SMS. Culturally all-caps text has become an indication of shouting, for example when quoting speech and it was also once often used by American lawyers to indicate important points in a legal text. Another means of emphasis is to increase the spacing between the letters, rather than making them darker, but still achieving a distinction in blackness and this results in an effect reverse to boldface, the emphasized text becomes lighter than its environment. This is often used in typesetting and typewriter manuscripts. On typewriters a full space was used between the letters of a word and also one before and one after the word
7.
Blackboard
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A blackboard is a reusable writing surface on which text or drawings are made with sticks of calcium sulfate or calcium carbonate, known, when used for this purpose, as chalk. Blackboards were originally made of smooth, thin sheets of black or dark grey slate stone, a blackboard can simply be a piece of board painted with matte dark paint. Black plastic sign material, using the trade name sintra is also used to create custom chalkboard art, a more modern variation consists of a coiled sheet of plastic drawn across two parallel rollers, which can be scrolled to create additional writing space while saving what has been written. The highest grade blackboards are made of a rougher version porcelain enamelled steel, porcelain is very hard wearing and blackboards made of porcelain usually last 10–20 years in intensive use. Manufacturing of slate blackboards began by the 1840s, green chalkboards, generally made of porcelain enamel on a steel base, first appeared in the 1960s. Lecture theatres may contain a number of blackboards in a grid arrangement, the lecturer then moves boards into reach for writing and then moves them out of reach, allowing a large amount of material to be shown simultaneously. The chalk marks can be wiped off with a damp cloth. However, chalk marks made on some types of wet blackboard can be difficult to remove, sticks of processed chalk are produced especially for use with blackboards in white and also in various colours. These are often not from chalk rock but from calcium sulfate in its dihydrate form. Chalk sticks containing calcium carbonate typically contain 40-60% of CaCO3, as compared to whiteboards, blackboards have a variety of advantages, Chalk requires no special care, whiteboard markers must be capped or else they dry out. Chalk is an order of magnitude cheaper than whiteboard markers for a amount of writing. It is easier to draw lines of different weights and thicknesses with chalk than with whiteboard markers, dashed lines can be drawn very quickly using a technique involving the friction of the chalk and blackboard. Chalk has a smell, whereas whiteboard markers often have a pungent odor. Chalk writing often provides better contrast than whiteboard markers, Chalk can be easily erased, writing which has been left on a whiteboard for a prolonged period may require a solvent to remove. Chalk can be removed from most clothing, whiteboard markers often permanently stain fabric. On the other hand, chalk produces dust, the amount depending on the quality of chalk used, the dust also precludes the use of chalk in areas shared with dust-sensitive equipment such as computers. The writing on chalkboards is difficult to read in the dark, Chalk sticks are notorious for shrinking through use, and breaking in half unless inserted in a writing utensil designed to store chalk. According to a run by Michael Oehler, a professor at the University of Media and Communication in Cologne, Germany
8.
Robert C. Gunning
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Robert Clifford Gunning is a professor of mathematics at Princeton University specializing in complex analysis, who introduced indigenous bundles. He then taught at the University of Chicago and in 1956 as Higgins-Lecturer at Princeton University, at Princeton, Gunning became in 1957 assistant professor, in 1962 associate professor, and in 1966 professor. He was a professor in São Paulo in 1958, Cambridge in 1959/60, Munich in 1967, Oxford in 1968, Boulder in 1970. Gunning is known as the author of important books on functions of complex variables. From 1958 to 1961 he was a Sloan Fellow and he served as Princeton Universitys dean of the faculty from 1989 to 1995. In 2003 he received Princeton Universitys prize for outstanding teaching, for a number of years he was an editor for Princeton University Press and for the Annals of Mathematical Studies. He was also the editor of the works of Salomon Bochner. In 1970 he was a speaker at the International Mathematical Congress in Nice. Among his doctoral students are Sheldon Katz, Henry Laufer, Richard S. Hamilton, in 2012 he became a fellow of the American Mathematical Society. Analytic functions of complex variables. Lectures on Vector Bundles over Riemann Surfaces, Riemann Surfaces and generalized Theta Functions. Springer, Ergebnisse der Mathematik und ihrer Grenzgebiete,1976, on uniformization of complex manifolds, The role of connections, Princeton University Press 1978 Introduction to holomorphic functions of several variables. Robert Gunning at the Mathematics Genealogy Project Robert Gunnings homepage
9.
Jean-Pierre Serre
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Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000, born in Bages, Pyrénées-Orientales, France, to pharmacist parents, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the École Normale Supérieure in Paris. He was awarded his doctorate from the Sorbonne in 1951, from 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France and his wife, Professor Josiane Heulot-Serre, was a chemist, she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil, the French mathematician Denis Serre is his nephew. Serres thesis concerned the Leray–Serre spectral sequence associated to a fibration, together with Cartan, Serre established the technique of using Eilenberg–MacLane spaces for computing homotopy groups of spheres, which at that time was one of the major problems in topology. In his speech at the Fields Medal award ceremony in 1954, Hermann Weyl gave high praise to Serre, Serre subsequently changed his research focus. However, Weyls perception that the place of classical analysis had been challenged has subsequently been justified. In the 1950s and 1960s, a collaboration between Serre and the two-years-younger Alexander Grothendieck led to important foundational work, much of it motivated by the Weil conjectures. Two major foundational papers by Serre were Faisceaux Algébriques Cohérents, on coherent cohomology, even at an early stage in his work Serre had perceived a need to construct more general and refined cohomology theories to tackle the Weil conjectures. The problem was that the cohomology of a coherent sheaf over a finite field couldnt capture as much topology as singular cohomology with integer coefficients, amongst Serres early candidate theories of 1954–55 was one based on Witt vector coefficients. Around 1958 Serre suggested that isotrivial principal bundles on algebraic varieties — those that become trivial after pullback by a finite étale map — are important and this acted as one important source of inspiration for Grothendieck to develop étale topology and the corresponding theory of étale cohomology. These tools, developed in full by Grothendieck and collaborators in Séminaire de géométrie algébrique 4 and SGA5, from 1959 onward Serres interests turned towards group theory, number theory, in particular Galois representations and modular forms. In his paper FAC, Serre asked whether a finitely generated module over a polynomial ring is free. This question led to a deal of activity in commutative algebra. This result is now known as the Quillen-Suslin theorem, Serre, at twenty-seven in 1954, is the youngest ever to be awarded the Fields Medal. He went on to win the Balzan Prize in 1985, the Steele Prize in 1995, the Wolf Prize in Mathematics in 2000 and he has been awarded other prizes, such as the Gold Medal of the French National Scientific Research Centre. He is a member of several scientific Academies and has received many honorary degrees
