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What Is Mathematics
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#	Item
451	MATH CIRCLE - ELLIPTIC CURVES WEEKS 1 & 2 SAM LICHTENSTEIN 1. What is a curve? We started by considering the idea of a curve. This is just the set of points in the plane which satisfy a polynomial equation. For example, Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-10-20 22:29:22 Algebraic curves Diophantine equations Analytic number theory Elliptic curve Group theory Rational point Rational number Curve Infinite descent Mathematics Geometry Abstract algebra
452	MP473 Examination, November 2000 Time: 3 hours Answer all questions 1. (a) Explain what is meant by the statements: (i) K is an algebraic number field of degree n, (ii) ω1 , . . . , ωn is an integral basis for K, Add to Reading List Source URL: www.numbertheory.org Language: English - Date: 2000-11-16 18:40:58 Algebraic number theory Constructible universe Ideal class group Euclidean algorithm Field norm Abstract algebra Mathematics Algebra
453	MP473 Examination, November 1998 Time: 3 hours Answer all questions 1. (a) Explain what is meant by the statements: (i) θ is an algebraic integer, (ii) K is an algebraic number field of degree n, (iii) ω1 , . . . , ωn Add to Reading List Source URL: www.numbertheory.org Language: English - Date: 2000-10-30 20:35:30 Ordinal number Constructible universe Ideal class group Connection Fiber bundles Abstract algebra Algebraic number theory Mathematics
454	Almost One Page Informal Description of Manson/Pugh model October 23, 2003, 6:18pm Note: the issue of what it means for an action to occur in more than one execution is elided. hb hb Add to Reading List Source URL: www.cs.umd.edu Language: English - Date: 2003-10-24 05:48:40 Group action Mathematics Concurrency control Lock Constructible universe
455	What is a Good Nearest Neighbors Algorithm for Finding Similar Patches in Images? Neeraj Kumar1⋆ , Li Zhang2 , and Shree Nayar1 1 2 Add to Reading List Source URL: www1.cs.columbia.edu Language: English - Date: 2009-03-22 20:04:19 Search algorithms Binary trees R-tree Phylogenetics K-d tree Nearest neighbor search K-nearest neighbor algorithm Tree Phylogenetic tree Information science Mathematics Computer programming
456	Elliptic curves, their companions, and their statistics Barry Mazur What is the probability that a cubic plane curve with rational coefficients has infinitely many rational points? Questions of this type (more exactly fo Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2011-12-13 10:36:46 Diophantine geometry Elliptic curves Abelian varieties Analytic number theory Group theory Mordell–Weil theorem Rational point Arithmetic of abelian varieties Curve Abstract algebra Mathematics Algebraic geometry
457	From SIAM News, Volume 47, Number 1, January/February[removed]Kadison–Singer Problem Solved By Dana Mackenzie What is the best kind of mathematical problem? Does it resemble a distant mountaintop, beckoning people from f Add to Reading List Source URL: www.siam.org Language: English - Date: 2014-01-23 12:12:41 Graph theory Eigenvalues and eigenvectors Polynomial Richard Kadison Algebra Mathematics Linear algebra
458	WHAT IS THE SURFACE AREA OF A HEDGEHOG? BARRY MAZUR Notes for The Steiner Lecture— St. Johns College, September 30, 2011 Well, I don’t know the answer to the question of the title and no hedgehog will be Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2012-01-10 14:05:53 Curves Euclidean geometry Infinity Archimedes Sphere Area Banach–Tarski paradox Circle Calculus Geometry Mathematics Topology
459	Understanding and misunderstanding the Third International Mathematics and Science Study: what is at stake and why K-12 education studies matter Alan Siegel∗ Abstract. The technical portion of this paper concerns a vid Add to Reading List Source URL: www.cs.nyu.edu Language: English - Date: 2006-10-04 21:42:04 Educational research Education in Singapore Singapore Math Method Trends in International Mathematics and Science Study Standards-based education National Council of Teachers of Mathematics Principles and Standards for School Mathematics New Math Programme for International Student Assessment Education Mathematics education Education reform
460	THE FACES OF EVIDENCE (IN MATHEMATICS) BARRY MAZUR Notes for the presentation and discussion at Museion, February 5, [removed]What is evidence? Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2014-01-16 09:46:11 Fractals Analytic number theory Mandelbrot set Elliptic curve Julia set Philosophy of mathematics Theorem Mathematical proof Representation theory Mathematics Mathematical analysis Complex dynamics

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