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Real algebraic geometry
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161	MAKING THE REALS FROM THE RATIONALS, WEEK 2 MATTHEW TAI We started out by asking how to do arithmetic on our sequences. We decided that both addition and multiplication would be pointwise, i.e. that (0, 0, 0, 0, ...) + ( Add to Reading List Source URL: www.themathcircle.org Language: English - Date: 2007-10-20 22:30:42 Field theory Real algebraic geometry Real number Randomness Rational number Fraction Random sequence Multiplication Mathematics Elementary mathematics Elementary arithmetic
162	The Bulletin of Symbolic Logic Volume 18, Number 1, March 2012 THE ABSOLUTE ARITHMETIC CONTINUUM AND THE UNIFICATION OF ALL NUMBERS GREAT AND SMALL Add to Reading List Source URL: www.ohio.edu Language: English - Date: 2012-01-31 12:26:37 Real algebraic geometry Mathematical logic Field theory Real closed field Philip Ehrlich Infinitesimal Surreal number Real number Archimedean property Mathematics Abstract algebra Infinity
163	DISPARITY IN THE STATISTICS FOR QUADRATIC TWIST FAMILIES BARRY MAZUR Very rough notes for a lecture delivered at the MSRI Workshop in Arithmetic Statistics, April 13, 2011. This represents joint work with Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2011-12-13 10:36:48 Linear algebra Analytic number theory Quadratic forms Algebraic number theory Real algebraic geometry Elliptic curve Symbol Symplectic vector space Algebraic number field Algebra Abstract algebra Mathematics
164 $Quadratic forms / Field theory / Algebraic number theory / Linear algebra / Real algebraic geometry / Partial fraction / Euclidean algorithm / Mathematics / Algebra / Abstract algebra$	SUMS OF SQUARES IN Q AND F(T ) KEITH CONRAD 1. Introduction To illustrate the analogies between integers and polynomials, we prove a theorem about sums of squares over Z and then prove an analogous result in F [T ] (wher Add to Reading List Source URL: www.math.uconn.edu Language: English - Date: 2007-12-15 18:52:41 Quadratic forms Field theory Algebraic number theory Linear algebra Real algebraic geometry Partial fraction Euclidean algorithm Mathematics Algebra Abstract algebra
165	Characterizing Algebraic Invariants by Differential Radical Invariants? Khalil Ghorbal and Andr´e Platzer Carnegie Mellon University, Pittsburgh, PA, 15213, USA {kghorbal\|aplatzer}@cs.cmu.edu Add to Reading List Source URL: symbolaris.com Language: English - Date: 2014-04-03 20:43:50 Algebraic geometry Field theory Invariant theory Polynomial Homogeneous polynomial Algebraic function Invariant Field Real algebraic geometry Abstract algebra Mathematics Algebra
166	A SHARPER ESTIMATE ON THE BETTI NUMBERS OF SETS DEFINED BY QUADRATIC INEQUALITIES SAUGATA BASU AND MICHAEL KETTNER Abstract. In this paper we consider the problem of bounding the Betti numbers, bi (S), of a semi-algebrai Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:31:16 Quadratic forms Algebraic topology Betti number Topological graph theory Algebraic geometry Real algebraic geometry Algebraic variety Weil conjectures Algebra Mathematics Abstract algebra
167	BOUNDING THE EQUIVARIANT BETTI NUMBERS AND COMPUTING ´ CHARACTERISTIC OF THE GENERALIZED EULER-POINCARE SYMMETRIC SEMI-ALGEBRAIC SETS SAUGATA BASU AND CORDIAN RIENER Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2014-01-17 21:15:39 Algebraic topology Algebraic geometry Field theory Polynomials Betti number Homogeneous polynomial Algebraic variety Symmetric polynomial Real algebraic geometry Abstract algebra Algebra Mathematics
168	POLYNOMIAL HIERARCHY, BETTI NUMBERS AND A REAL ANALOGUE OF TODA’S THEOREM SAUGATA BASU AND THIERRY ZELL Abstract. Toda [36] proved in 1989 that the (discrete) polynomial time hierarchy, PH, is contained in the class P# Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:44:12 Field theory Real algebraic geometry Algebraic geometry Real closed field Betti number Polynomial Algebraic variety Field Semialgebraic set Abstract algebra Mathematics Algebra
169	REFINED BOUNDS ON THE NUMBER OF CONNECTED COMPONENTS OF SIGN CONDITIONS ON A VARIETY SAL BARONE AND SAUGATA BASU Abstract. Let R be a real closed field, P, Q ⊂ R[X1 , . . . , Xk ] finite subsets of polynomials, with th Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2011-11-06 10:09:22 Algebraic geometry Commutative algebra Field extension Algebraic variety Algebraically closed field Zariski topology Betti number Puiseux series Algebraic closure Abstract algebra Algebra Field theory
170	ON THE BETTI NUMBERS OF SIGN CONDITIONS SAUGATA BASU, RICHARD POLLACK, AND MARIE-FRANC ¸ OISE ROY Abstract. Let R be a real closed field and let Q and P be finite subsets of R[XV1 , . . . , Xk ] such that the set P has Add to Reading List Source URL: www.math.purdue.edu Language: English - Date: 2010-06-16 13:36:45 Orbifold Algebraic geometry Algebraic variety Μ operator

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