Gourt > Science > Math > Geometry > Algebraic Geometry (6)
Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials. When there is more than one variable, geometric considerations enter and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.
Zeros of simultaneous polynomials
In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of polynomials, meaning the set of all points that simultaneously satisfy one or more polynomial equations. For instance, the three-dimensional sphere in three-dimensional Euclidean space could be defined as the set of all points with
- .
"Algebraic Geometry is Algebra with a kick" ~ Solomon Lefschetz. Got my first algebra kick today!
abhishekparab (Abhishek Parab) Thu, 07 Jan 2010 11:38:05 -0000
"Algebraic Geometry is Algebra with a kick" ~ Solomon Lefschetz. Got my first algebra kick today!
Analytical Geometry - Lesson 5: Polar Coordinates - Some algebraic equations or geometric expressions are not best-... http://ow.ly/16hovJ
vsummers61 (Vincent Summers) Wed, 06 Jan 2010 16:34:13 -0000
Analytical Geometry - Lesson 5: Polar Coordinates - Some algebraic equations or geometric expressions are not best-... http://ow.ly/16hovJ
Breakfast of champions @88Orchard: Granola, OJ, coffee with a stack of geometry, pronouns & algebraic equation http://tweetphoto.com/7936834
HumanFolly (Jen Nedeau) Sun, 03 Jan 2010 15:51:42 -0000
Breakfast of champions @88Orchard: Granola, OJ, coffee with a stack of geometry, pronouns & algebraic equation http://tweetphoto.com/7936834
Algebra: Classification: Changed description of algebraic geometry. â Previous revision R.. http://bit.ly/85Cnvm
wikipedialive (wikipedia live) Fri, 01 Jan 2010 17:38:21 -0000
Algebra: Classification: Changed description of algebraic geometry. ← Previous revision R.. http://bit.ly/85Cnvm
Realizing I need to work harder to make the most useful algebraic geometry ideas accessible. !
lawhornsxou (Andrea Alverstofjg) Fri, 01 Jan 2010 15:56:51 -0000
Realizing I need to work harder to make the most useful algebraic geometry ideas accessible. !
AGATHOS - Algebraic Geometry: A Total Hypertext Online System - An online system for learning algebraic geometry.
Algebraic Curves - Lecture Notes from H.W. Lenstra's course Math 274, Berkeley 1995.
Algebraic Curves - An overview.
404
Algebraic Geometry - Links and list of algebraic geometers.
Meta Description: [ Some information about algebraic geometry and
geometers ]
Algebraic Geometry Notebooks for Non-Experts - By Aksel Sogstad. Short introductory sketch of some topics in the algebraic geometry of curves.
Differential Algebraic Geometry - A Scheme-theoretic Approach - Slides in multimedia format from a lecture by Henri Gillet at MSRI.
Introduction to Algebraic Geometry - Illustrated webnotes by Donu Arapura.
Noncommutative Geometry and Algebra - People, groups and publications. Compiled by Paul Smith, University of Washington.
404
Projections of Complex Algebraic Curves to Real 3-space - Graphics.
The Brill-Noether Project - Aims to answer the basic questions this theory B(n,d,k) for vector bundles on algebraic curves. Welcomes contributions.
The Cubic Surface Homepage - Images, software, links. At the University of Mainz, Germany.
The Hodge Conjecture - A description of the conjecture by Deligne (PDF) and details of the prize offered for its resolution.
| MATHEMATICS | |
| Next Video | |
