
	Where results make sense

Topic: List of algebraic geometry topics

Related Topics

List of geometers

Projective line

List of geometry topics

Plane geometry

Complementary angles

In the News (Tue 8 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Algebraic geometry Summary
		Algebraic geometry is the area of mathematics that studies the properties of sets (or loci) defined as the set of common zeros of a collection of polynomial equations on the coordinates of the points of some Cartesian coordinate system.
		Algebraic geometry was largely developed by Islamic mathematicians, particularly the Persian mathematician/poet Omar Khayyám (born 1048).
		Algebraic geometry was further developed by the Italian geometers in the early part of the 20th century.
	www.bookrags.com /Algebraic_geometry (2571 words)

	Encyclopedia: Algebraic geometry
		Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry.
		Algebraic geometry was developed largely by the Italian geometers in the early part of the 20th century.
		Topics in mathematics related to space Abstract algebra is the field of mathematics concerned with the study of algebraic structures such as groups, rings and fields.
	www.nationmaster.com /encyclopedia/Algebraic-geometry (4572 words)

	Geometry
		The phrase "discrete geometry," which at one time stood mainly for the areas of packing, covering, and tiling, has gradually grown to include in addition such areas as combinatorial geometry, convex polytopes, and arrangements of points, lines, planes, circles, and other geometric objects in the plane and in higher dimensions.
		Similarly, "computational geometry," which referred not long ago to simply the design and analysis of geometric algorithms, has in recent years broadened its scope, and now means the study of geometric problems from a computational point of view, including also computational convexity, computational topology, and questions involving the combinatorial complexity of arrangements and polyhedra.
		In Chapter 16 we use this algebra for proving that the three classical problems are insoluble: Trisecting an angle with legal use of straightedge and compass, doubling the cube using straightedge and compass, and finally we see how the transcendency of the number 7r precludes the squaring of the circle using straightedge and compass.
	www.wordtrade.com /science/mathematics/geometry.htm (6586 words)

	Glossary of scheme theory - Wikipedia, the free encyclopedia
		For an introduction to the theory of schemes in algebraic geometry, see affine scheme, projective space, sheaf and scheme.
		Historically there was a process by which projective geometry added more and points (complex points, line at infinity) to simplify the geometry by refining the basic objects.
		Much of algebraic geometry is concerned only about noetherian (or, at any rate, locally noetherian) schemes, but non-noetherian and even non-locally noetherian schemes do turn up.
	en.wikipedia.org /wiki/Glossary_of_scheme_theory (844 words)

	Algebraic variety -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-31)
		In classical (Click link for more info and facts about algebraic geometry) algebraic geometry (and to some extent also in modern algebraic geometry), the main objects of study are algebraic varieties.
		An affine algebraic variety is defined to be an irreducible algebraic set in some (Click link for more info and facts about affine space) affine space, over an (Click link for more info and facts about algebraically closed field) algebraically closed field K.
		An abstract algebraic variety is a particular kind of (An elaborate and systematic plan of action) scheme.
	www.absoluteastronomy.com /encyclopedia/A/Al/Algebraic_variety.htm (851 words)

	Kingwood College Mathematics Department
		Topics for all formats include basic arithmetical operations on integers and rational numbers, order of operations, introduction to basic geometric concepts, simplification of algebraic expressions and techniques of solving simple linear equations.
		Topics may include, but are not limited to, sets, logic, number theory, measurement, geometric concepts, and an introduction to probability and statistics.
		Topics include concepts of geometry, probability, and statistics, as well as applications of the algebraic properties of real numbers to concepts of measurement with an emphasis on problem solving and critical thinking.
	kcweb.nhmccd.edu /programs/math/classes.htm (700 words)

	William Kingdon Clifford - Wikipedia, the free encyclopedia
		Along with Hermann Grassmann he discovered what is now often called geometric algebra, which is a special case of the Clifford algebras named in his honor.
		In his theory of graphs, or geometrical representations of algebraic functions, there are valuable suggestions which have been worked out by others.
		He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers "Preliminary Sketch of Biquaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics.
	www.wikipedia.org /wiki/William_Kingdon_Clifford (699 words)

	Mathematics 261: Algebraic Topology I (Site not responding. Last check: 2007-10-31)
		This course is an introduction to algebraic topology.
		The principal algebraic invariants considered in this course are the fundamental group (also known as the first homotopy group) and the homology groups.
		It is fundamental for students interested in research in Algebraic Geometry, Differential Geometry, Mathematical Physics, and Topology; it is also important for students in Algebra and in Number Theory.
	www.math.duke.edu /graduate/courses/spring04/math261.html (215 words)

	Differential geometry and topology Summary
		Initially and up to the middle of the nineteenth century, differential geometry was studied from the extrinsic point of view: curves and surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions).
		The apparatus of differential geometry is that of calculus on manifolds: this includes the study of manifolds, tangent bundles, cotangent bundles, differential forms, exterior derivatives, integrals of p-forms over p-dimensional submanifolds and Stokes' theorem, wedge products, and Lie derivatives.
		Contact geometry is an analog of symplectic geometry which works for certain manifolds of odd dimension.
	www.bookrags.com /Differential_geometry_and_topology (2906 words)

	Basic Library List-Geometry
		Geometry, Relativity, and the Fourth Dimension Mineola, NY: Dover, 1977.
		Geometry: A Comprehensive Course Mineola, NY: Dover, 1988.
		Combinatorial Geometry in the Plane New York, NY: Holt, Rinehart and Winston, 1964.
	www.maa.org /BLL/geometry.htm (2473 words)

	Algebraic Areas of Mathematics
		We have included here the combinatorial topics and number theory; each is arguably a distinctive area of mathematics but (as the MathMap suggests) these parts of mathematics, shown in shades of red, share definite affinities.
		For example, Klein's vision of geometry was essentially to reduce it to a study of the underlying group of invariants; Lie groups first arose from Lie's investigations of differential equations.
		Of particular interest are several classes of rings of interest in number theory, field theory, algebraic geometry, and related areas; however, other classes of rings arise, and a rich structure theory arises to analyze commutative rings in general, using the concepts of ideals, localizations, and homological algebra.
	www.math.niu.edu /~rusin/known-math/index/tour_alg.html (1113 words)

	PCTM Position Paper: Geometry for All
		Geometry is a vehicle for representing phenomena whose origin is not visual or physical.
		In most school geometry programs, the van Hiele model is contradicted by the traditional reality in that geometry is viewed as a high school course where most students are exposed to a formal, abstract level with little to no regard for their appropriate conceptual readiness.
		Geometry is increasingly used to model and solve real-world problems, often connecting to algebraic representations through a coordinate system.
	www.pctm.org /GeometryForAll.html (3228 words)

	Mathematics
		The theory of algebraic curves is a central branch of mathematics, having relations to fields as diverse as complex analysis, number theory, combinatorics, codes, topology, representation theory, and physics.
		Topics will be chosen from the following: general cohomology theories (étale cohomology, flat cohomology, motivic cohomology, or p-adic Hodge theory), curves and Abelian varieties over arithmetic schemes, moduli spaces, Diophantine geometry, algebraic cycles.
		Part b: basic topics may vary from year to year and may include elements of Morse theory and the calculus of variations, locally symmetric spaces, special geometry, comparison theorems, relation between curvature and topology, metric functionals and flows, geometry in low dimensions.
	pr.caltech.edu /catalog/courses/listing/ma.html (2506 words)

	Graduate Programs in Mathematics
		Below is a partial list of current research areas and some of the studies being undertaken, a list that constitutes a rich cross section of the whole of mathematics.
		Concentrates on the techniques of algebraic geometry arising from commutative and homological algebra, beginning with a discussion of the basic results for general algebraic varieties and developing the necessary commutative algebra as needed.
		Topics will be chosen from: computational group theory, computational number theory, algorithms for computing with finite fields, the discrete Fourier Transform and its applications, the Knuth-Bendix algorithm for finitely presented algebras, polynomial factorization and related topics in computer algebra.
	www.math.neu.edu /WWW_math/Grad/grad_program.html (6075 words)

	Geometry Algorithm Monographs
		This is an advanced book about computing in differential geometry involving linear spaces, projective spaces, algebraic geometry, ruled and developable surfaces.
		Some topics it covers are: communication complexity, pseudo-randomness, Markov chains, derandomization, convex hulls and Voronoi diagrams, linear programming, geometric sampling, minimum spanning trees, circuit complexity, and multidimensional searching.
		There is a historical introduction, a refresher of vector geometry, and two excellent chapters on differential geometry, I and II, well-placed in the middle of the book.
	www.geometryalgorithms.com /books_monographs.shtml (878 words)

	Open Directory - Science: Math: Geometry (Site not responding. Last check: 2007-10-31)
		Geometry and the Imagination in Minneapolis - Geometry exercises for a two-week summer workshop led by John Conway, Peter Doyle, Jane Gilman and Bill Thurston at the Geometry Center in Minneapolis, June 1991.
		Geometry Formulas and Facts - Excerpts from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (1995), namely, the geometry section minus differential geometry.
		Geometry from the Land of the Incas - Presents problems involving circles and triangles, with proofs, SAT practice quizzes and famous quotes.
	dmoz.org /Science/Math/Geometry (961 words)

	Differential geometry and topology - Gurupedia (Site not responding. Last check: 2007-10-31)
		Differential geometry is the study of geometry using calculus.
		This is an analog of symplectic geometry which works for manifolds of odd dimension.
		Finsler geometry has the Finsler manifold as the main object of study — this is a differential manifold with a Finsler metric, i.e.
	www.gurupedia.com /d/di/differential_geometry.htm (938 words)

	Amazon.com: Algebraic Geometry (Graduate Texts in Mathematics): Books: Robin Hartshorne (Site not responding. Last check: 2007-10-31)
		Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris.
		That algebraic geometry has so many applications is quite amazing, since it was not too long ago that it was thought of as a highly abstract, esoteric topic.
		It was the study of algebraic functions of one variable that led to the introduction of Riemann surfaces, and the later to a consideration of algebraic functions of two variables.
	www.amazon.com /Algebraic-Geometry-Graduate-Texts-Mathematics/dp/0387902449 (2118 words)

	LIST OF ARTICLES BY CATEGORY
		None of these are yet comprehensive or up-to-date, but filling in or creating these lists will create an easy way to track articles by their categories, as well as creating an implicit to-do list of topics for which articles have not yet been written.
		List of astronomical topics, expanded list of topics from N-Z
		List of anomalous phenomenon (paranormal) and parapsychology topics
	www.websters-online-dictionary.org /definition/LIST+OF+ARTICLES+BY+CATEGORY (307 words)

	Proper map - Wikipedia, the free encyclopedia
		In mathematics, a continuous function between topological spaces is called proper if inverse images of compact subsets are compact.
		In algebraic geometry, a related concept is used.
		of algebraic varieties or is called proper if it is separated and universally closed.
	www.wikipedia.org /wiki/Proper_morphism (468 words)

	Spectral Geometry (L24) (Site not responding. Last check: 2007-10-31)
		However results that are needed from analysis and algebra will be stated mostly without proof, so the level of knowledge required will be that which is sufficient to understand and apply the statements of the theorems rather than knowing or understanding their proofs.
		The book `Eigenvalues in Riemannian Geometry' by Isaac Chavel is introductory in the sense of showing the historic basis (c.1980) from which the more recent results have flowed.
		I of the Handbook of Differential Geometry (published by Elsevier Science in 2000) gives an excellent overview of the subject and the place within it of the topics chosen for the course.
	www.maths.cam.ac.uk /CASM/courses/descriptions/node28.html (317 words)

	Directory - Science: Math: Geometry: Algebraic Geometry (Site not responding. Last check: 2007-10-31)
		Algebraic Geometry · cached · Links and list of algebraic geometers.
		Differential Algebraic Geometry - A Scheme-theoretic Approach · cached · Slides in multimedia format from a lecture by Henri Gillet at MSRI.
		Introduction to Algebraic Geometry · cached · Illustrated webnotes by Donu Arapura.
	www.incywincy.com /default?p=904279 (150 words)

	Commutative Algebra : with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) (Site not responding. Last check: 2007-10-31)
		Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry.
		The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics.
		Anyway, algebraic geometry is the course that you have to have a good professor to help you, otherwise stop study this field.
	494062.onlinesportdiscount.com /3439343036322d312d30333837393432363936.html (1035 words)

	Algebraic Geometry Codes (Site not responding. Last check: 2007-10-31)
		What I have here is a collection of notes I managed to put down when learning the basic theory behind algebraic geometry codes.
		A part of this work is to be presented in the course, "seminar topics in communications engineering", during my MS program in TUM.
		Algebraic Geometry Codes -- only very simple codes from Klein quartic is considered.
	www.lrz-muenchen.de /~prasanna/algeom.htm (157 words)

	ALGEBRAIC GEOMETRY (Site not responding. Last check: 2007-10-31)
		This is a graduate-level text on algebraic geometry that provides a quick and fully self-contained development of the fundamentals, including all commutative algebra which is used.
		A taste of the deeper theory is given: some topics, such as local algebra and ramification theory, are treated in depth.
		The book culminates with a selection of topics from the theory of algebraic curves, including the Riemann—Roch theorem, elliptic curves, the zeta function of a curve over a finite field, and the Riemann hypothesis for elliptic curves.
	www.worldscibooks.com /mathematics/3873.html (159 words)

	[No title]
		Basically, topology is the modern version of geometry, the study of all different sorts of spaces.
		The thing that distinguishes different kinds of geometry from each other (including topology here as a kind of geometry) is in the kinds of transformations that are allowed before you really consider something changed.
		The title itself indicates that Euler was aware that he was dealing with a different type of geometry where distance was not relevant.
	www.lycos.com /info/topology--geometry.html (283 words)

	Amazon.com: Algebraic Geometry: A First Course (Graduate Texts in Mathematics): Books: Joe Harris (Site not responding. Last check: 2007-10-31)
		It is rare to find a book on algebraic geometry that attempts to make the subject concrete and understandable, and yet points the way to more modern "scheme-theoretic" formulations.
		He also discusses the origins of schemes in algebraic geometry, giving the reader a better appreciation of just where these objects arise, namely the association to an arbitrary ideal, instead of merely a radical ideal.
		In addition, algebraic groups on varieties are discussed in lecture 10, allowing one to discuss a kind of glueing operation on varieties, just as in geometric topology, namely by taking the quotient of varieties via finite groups.
	www.amazon.com /Algebraic-Geometry-Course-Graduate-Mathematics/dp/0387977163 (2148 words)

Try your search on: Qwika (all wikis)