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Stacks Project
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ... needed to define them". , the book consists of 115 chapters (excluding the license and index chapters) spreading over 7500 pages. The maintainer of the project, who reviews and accepts the changes, is Aise Johan de Jong. See alsoKerodona Stacks project inspired online textbook on categorical homotopy theory maintained by Jacob Lurie References External linksProject website*Latest from the Stacks Project(as of 2013) (Accessed 2020-04-01) Mathematics textbooks {{mathematics-lit-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Open Source
Open source is source code that is made freely available for possible modification and redistribution. Products include permission to use the source code, design documents, or content of the product. The open-source model is a decentralized software development model that encourages open collaboration. A main principle of open-source software development is peer production, with products such as source code, blueprints, and documentation freely available to the public. The open-source movement in software began as a response to the limitations of proprietary code. The model is used for projects such as in open-source appropriate technology, and open-source drug discovery. Open source promotes universal access via an open-source or free license to a product's design or blueprint, and universal redistribution of that design or blueprint. Before the phrase ''open source'' became widely adopted, developers and producers have used a variety of other terms. ''Open source'' ga ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Collaborative Writing
Collaborative writing, or collabwriting is a method of group work that takes place in the workplace and in the classroom. Researchers expand the idea of collaborative writing beyond groups working together to complete a writing task. Collaboration can be defined as individuals communicating, whether orally or in written form, to plan, draft, and revise a document. The success of collaboration in group work is often incumbent upon a group's agreed upon plan of action. At times, success in collaborative writing is hindered by a group's failure to adequately communicate their desired strategies. Definition Collaborative writing refers to a distributed process of labor involving writing, resulting in the co-authorship of a text by more than one writer.Sharples, M., Goodlet, J. S., Beck, E. E., Wood, C. C., Easterbook, S M., & Plowman, L. (1993). Research issues in the study of computer supported collaborative writing. In M. Sharples (ed.) Computer supported collaborative writing. Lond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Stack
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves \mathcal_ and the moduli stack of elliptic curves. Originally, they were introduced by Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. But, through many generalizations the notion of algebraic stacks was finally discovered by Michael Artin. Definition Motivation One of the motivating examples of an algebraic stack is to consider a groupoid scheme (R,U,s,t,m) over a fixed scheme S. For example, if R = \mu_n\times_S\mathbb^n_S (where \mu_n is the group scheme of roots of unity), U = \mathbb^n_S, s = \text_U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations. Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy a given polynomial equation. Basic questions involve the study of the points of special interest like the singular points, the inflection points and the points at infinity. More advanced questions involve the topology ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aise Johan De Jong
Aise Johan de Jong (born 30 January 1966) is a Dutch mathematician born in Belgium. He currently is a professor of mathematics at Columbia University. His research interests include arithmetic geometry and algebraic geometry. Education De Jong attended high school in The Hague, obtained his master's degree at Leiden University and earned his doctorate at the Radboud University Nijmegen in 1992, under supervision of Frans Oort and Joseph H. M. Steenbrink. Career In 1996, de Jong developed his theory of alterations which was used by Fedor Bogomolov and Tony Pantev (1996) and Dan Abramovich and de Jong (1997) to prove resolution of singularities in characteristic 0 and to prove a weaker result for varieties of all dimensions in characteristic ''p'' which is strong enough to act as a substitute for resolution for many purposes. In 2005, de Jong started the Stacks Project, "an open source textbook and reference work on algebraic stacks and the algebraic geometry needed to define ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Lurie
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. Lurie is a 2014 MacArthur Fellow. Life When he was a student in the Science, Mathematics, and Computer Science Magnet Program at Montgomery Blair High School, Lurie took part in the International Mathematical Olympiad, where he won a gold medal with a perfect score in 1994. In 1996 he took first place in the Westinghouse Science Talent Search and was featured in a front-page story in the ''Washington Times''. Lurie earned his bachelor's degree in mathematics from Harvard College in 2000 and was awarded in the same year the Morgan Prize for his undergraduate thesis on Lie algebras. He earned his Ph.D. from the Massachusetts Institute of Technology under supervision of Michael J. Hopkins, in 2004 with a thesis on derived algebraic geometry. In 2007, he became associate professor at MIT, and in 2009 he became professor at Harvard University. In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
