|
Michael Spivak
Michael David Spivak (25 May 19401 October 2020)Biographical sketch in Notices of the AMS', Vol. 32, 1985, p. 576. was an American mathematician specializing in differential geometry, an expositor of mathematics, and the founder of Publish-or-Perish Press. Spivak was the author of the five-volume ''A Comprehensive Introduction to Differential Geometry''. Biography Spivak was born in Queens, New York (state), New York. He received an Bachelor of Arts, A.B. from Harvard University in 1960, while in 1964 he received a Doctor of Philosophy, Ph.D. from Princeton University under the supervision of John Milnor, with thesis ''On Spaces Satisfying Poincaré Duality''. In 1985 Spivak received the Leroy P. Steele Prize. Spivak lectured on elementary physics. Spivak's book, ''Physics for Mathematicians: Mechanics I'' (published December 6, 2010), contains the material that these lectures stemmed from and more. Spivak was also the designer of the MathTime Professional 2 fonts (which are wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queens
Queens is a borough of New York City, coextensive with Queens County, in the U.S. state of New York. Located on Long Island, it is the largest New York City borough by area. It is bordered by the borough of Brooklyn at the western tip of Long Island to its west, and Nassau County to its east. Queens also shares water borders with the boroughs of Manhattan, the Bronx, and Staten Island (via the Rockaways). With a population of 2,405,464 as of the 2020 census, Queens is the second most populous county in the State of New York, behind Kings County (Brooklyn), and is therefore also the second most populous of the five New York City boroughs. If Queens became a city, it would rank as the fifth most-populous in the U.S. after New York City, Los Angeles, Chicago, and Houston. Approximately 47% of the residents of Queens are foreign-born. Queens is the most linguistically diverse place on Earth and is one of the most ethnically diverse counties in the United States. Queens was est ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Normal Bundle
In surgery theory, a branch of mathematics, the stable normal bundle of a differentiable manifold is an invariant which encodes the stable normal (dually, tangential) data. There are analogs for generalizations of manifold, notably PL-manifolds and topological manifolds. There is also an analogue in homotopy theory for Poincaré spaces, the Spivak spherical fibration, named after Michael Spivak. Construction via embeddings Given an embedding of a manifold in Euclidean space (provided by the theorem of Hassler Whitney), it has a normal bundle. The embedding is not unique, but for high dimension of the Euclidean space it is unique up to isotopy, thus the (class of the) bundle is unique, and called the ''stable normal bundle''. This construction works for any Poincaré space ''X'': a finite CW-complex admits a stably unique (up to homotopy) embedding in Euclidean space, via general position, and this embedding yields a spherical fibration over ''X''. For more restricted spaces (no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology (journal)
''Topology'' was a peer-reviewed mathematical journal covering topology and geometry. It was established in 1962 and was published by Elsevier. The last issue of ''Topology'' appeared in 2009. Pricing dispute On 10 August 2006, after months of unsuccessful negotiations with Elsevier about the price policy of library subscriptions, the entire editorial board of the journal handed in their resignation, effective 31 December 2006. Subsequently, two more issues appeared in 2007 with papers that had been accepted before the resignation of the editors. In early January the former editors instructed Elsevier to remove their names from the website of the journal, but Elsevier refused to comply, justifying their decision by saying that the editorial board should remain on the journal until all of the papers accepted during its tenure had been published. In 2007 the former editors of ''Topology'' announced the launch of the ''Journal of Topology'', published by Oxford University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gender-neutral Pronouns
A third-person pronoun is a pronoun that refers to an entity other than the speaker or listener. Some languages with gender-specific pronouns have them as part of a grammatical gender system, a system of agreement where most or all nouns have a value for this grammatical category. A few languages with gender-specific pronouns, such as English, Afrikaans, Defaka, Khmu, Malayalam, Tamil, and Yazgulyam, lack grammatical gender; in such languages, gender usually adheres to "natural gender", which is often based on biological gender. Other languages, including most Austronesian languages, lack gender distinctions in personal pronouns entirely, as well as any system of grammatical gender. In languages with pronominal gender, problems of usage may arise in contexts where a person of unspecified or unknown social gender is being referred to but commonly available pronouns are gender-specific. Different solutions to this issue have been proposed and used in various languages. Overview ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Kelly (mathematician)
David C. Kelly is a professor emeritus of mathematics at Hampshire College in Amherst, Massachusetts. He holds an AB from Princeton, an SM from MIT, and an AM from Dartmouth; and has taught at Oberlin College and Talladega College. In 1971 he founded the Hampshire College Summer Studies in Mathematics (HCSSiM), a six-week program for mathematically talented high school students, and directed the program for many years. During his time at Princeton in the early 1960s, Kelly and fellow student Michael Spivak created "Yellow Pig's Day Yellow is the color between green and orange on the spectrum of light. It is evoked by light with a dominant wavelength of roughly 575585 nm. It is a primary color in subtractive color systems, used in painting or color printing. In the ...," an annual celebration of mathematics and the number 17. He continues to be involved in the organization of the holiday each year, commemorating the day with food, songs, a reunion, and mathematics. H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yellow Pig's Day
Yellow is the color between green and orange on the spectrum of light. It is evoked by light with a dominant wavelength of roughly 575585 nm. It is a primary color in subtractive color systems, used in painting or color printing. In the RGB color model, used to create colors on television and computer screens, yellow is a secondary color made by combining red and green at equal intensity. Carotenoids give the characteristic yellow color to autumn leaves, corn, canaries, daffodils, and lemons, as well as egg yolks, buttercups, and bananas. They absorb light energy and protect plants from photo damage in some cases. Sunlight has a slight yellowish hue when the Sun is near the horizon, due to atmospheric scattering of shorter wavelengths (green, blue, and violet). Because it was widely available, yellow ochre pigment was one of the first colors used in art; the Lascaux cave in France has a painting of a yellow horse 17,000 years old. Ochre and orpiment pigments were us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morse Theory
In mathematics, specifically in differential topology, Morse theory enables one to analyze the topology of a manifold by studying differentiable functions on that manifold. According to the basic insights of Marston Morse, a typical differentiable function on a manifold will reflect the topology quite directly. Morse theory allows one to find CW structures and handle decompositions on manifolds and to obtain substantial information about their homology. Before Morse, Arthur Cayley and James Clerk Maxwell had developed some of the ideas of Morse theory in the context of topography. Morse originally applied his theory to geodesics ( critical points of the energy functional on the space of paths). These techniques were used in Raoul Bott's proof of his periodicity theorem. The analogue of Morse theory for complex manifolds is Picard–Lefschetz theory. Basic concepts To illustrate, consider a mountainous landscape surface M (more generally, a manifold). If f is the function M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AMS-TeX
AMS-LaTeX is a collection of LaTeX document classes and packages developed for the American Mathematical Society (AMS). Its additions to LaTeX include the typesetting of multi-line and other mathematical statements, document classes, and fonts containing numerous mathematical symbols. It has largely superseded the plain TeX macro package AMS-TeX. AMS-TeX was originally written by Michael Spivak, and was used by the AMS from 1983 to 1985. MathJax supports AMS-LaTeX through extensions. The following code of the LaTeX2e produces the AMS-LaTeX logo: %%% -- AMS-LaTeX_logo.tex ------- \documentclass \usepackage \begin \AmS-\LaTeX \end The package has a suite of facilities to format multi-line equations. For example, the following code, \begin y &= (x+1)^2 \\ &= x^2+2x+1 \end causes the equals signs in the two lines to be aligned with one another, like this: : \begin y &= (x+1)^2 \\ &= x^2+2x+1 \end AMS-LaTeX also includes many flexible co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lac Operon
The ''lactose'' operon (''lac'' operon) is an operon required for the transport and metabolism of lactose in ''E. coli'' and many other enteric bacteria. Although glucose is the preferred carbon source for most bacteria, the ''lac'' operon allows for the effective digestion of lactose when glucose is not available through the activity of beta-galactosidase. Gene regulation of the ''lac'' operon was the first genetic regulatory mechanism to be understood clearly, so it has become a foremost example of prokaryotic gene regulation. It is often discussed in introductory molecular and cellular biology classes for this reason. This lactose metabolism system was used by François Jacob and Jacques Monod to determine how a biological cell knows which enzyme to synthesize. Their work on the ''lac'' operon won them the Nobel Prize in Physiology in 1965. Bacterial operons are polycistronic transcripts that are able to produce multiple proteins from one mRNA transcript. In this case, when l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus On Manifolds (book)
''Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus'' (1965) by Michael Spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms, and integration on manifolds for advanced undergraduates. Description ''Calculus on Manifolds'' is a brief monograph on the theory of vector-valued functions of several real variables (''f'' : R''n''→R''m'') and differentiable manifolds in Euclidean space. In addition to extending the concepts of differentiation (including the inverse and implicit function theorems) and Riemann integration (including Fubini's theorem) to functions of several variables, the book treats the classical theorems of vector calculus, including those of Cauchy–Green, Ostrogradsky–Gauss (divergence theorem), and Kelvin–Stokes, in the language of differential forms on differentiable manifolds embedded in Euclidean space, and as corollaries of the generalized Stokes theorem on manifolds-with-bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus and integral calculus; the former concerns instantaneous Rate of change (mathematics), rates of change, and the slopes of curves, while the latter concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence (mathematics), convergence of infinite sequences and Series (mathematics), infinite series to a well-defined limit (mathematics), limit. Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Later work, including (ε, δ)-definition of limit, codify ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Gender-neutral Pronouns")
