LEADER 05152nam 2200493 450 001 996466389803316 005 20231110223927.0 010 $a3-030-75051-5 035 $a(CKB)4940000000613691 035 $a(MiAaPQ)EBC6734187 035 $a(Au-PeEL)EBL6734187 035 $a(OCoLC)1269094774 035 $a(PPN)258052368 035 $a(EXLCZ)994940000000613691 100 $a20220624d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElements of mathematics $ea problem-centered approach to history and foundations /$fGabor Toth 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (534 pages) 225 1 $aUndergraduate Texts in Mathematics 300 $aIncludes index. 311 $a3-030-75050-7 327 $aIntro -- Preface -- Why This Book? -- Audience -- The Historical Context -- In Closing: Gelfand's Teaching Legacy -- Acknowledgment -- Contents -- 0 Preliminaries: Sets, Relations, Maps -- 0.1 Sets -- Exercises -- 0.2 Relations -- Exercise -- 0.3 Maps and Real Functions -- Exercises -- 0.4 Cardinality -- Exercises -- 0.5 The Zermelo-Fraenkel Axiomatic Set Theory* -- Exercise -- 1 Natural, Integral, and Rational Numbers -- 1.1 Natural Numbers -- Exercises -- 1.2 Integers -- Exercises -- 1.3 The Division Algorithm for Integers -- Exercises -- 1.4 Rational Numbers -- Exercises -- 2 Real Numbers -- 2.1 Real Numbers via Dedekind Cuts -- Exercises -- 2.2 Infinite Decimals as Real Numbers -- Exercises -- 2.3 Real Numbers via Cauchy Sequences -- Exercises -- 2.4 Dirichlet Approximation and Equidistribution* -- Exercises -- 3 Rational and Real Exponentiation -- 3.1 Arithmetic Properties of the Limit -- Exercises -- 3.2 Roots, Rational and Real Exponents -- Exercises -- 3.3 Logarithms -- Exercises -- 3.4 The Stolz-Cesàro Theorems -- Exercises -- 4 Limits of Real Functions -- 4.1 Limit Inferior and Limit Superior -- Exercise -- 4.2 Continuity -- Exercise -- 4.3 Differentiability -- Exercises -- 5 Real Analytic Plane Geometry -- 5.1 The Birkhoff Metric Geometry -- Exercise -- 5.2 The Cartesian Model of the Birkhoff Plane -- Exercises -- 5.3 The Cartesian Distance -- Exercise -- 5.4 The Triangle Inequality -- Exercise -- 5.5 Lines and Circles -- Exercises -- 5.6 Arc Length on the Unit Circle -- Exercise -- 5.7 The Birkhoff Angle Measure -- Exercises -- 5.8 The Principle of Shortest Distance* -- Exercises -- 5.9 ? According to Archimedes* -- Exercise -- 6 Polynomial Expressions -- 6.1 Polynomials -- Exercises -- 6.2 Arithmetic Operations on Polynomials -- Exercises -- 6.3 The Binomial Formula -- Exercises -- 6.4 Factoring Polynomials -- Exercises. 327 $a6.5 The Division Algorithm for Polynomials -- Exercises -- 6.6 Symmetric Polynomials -- Exercises -- 6.7 The Cauchy-Schwarz Inequality -- Exercises -- 7 Polynomial Functions -- 7.1 Polynomials as Functions -- Exercises -- 7.2 Roots of Cubic Polynomials -- Exercises -- 7.3 Roots of Quartic and Quintic Polynomials -- Exercise -- 7.4 Polynomials with Rational Coefficients -- Exercises -- 7.5 Factoring Multivariate Polynomials -- Exercises -- 7.6 The Greatest Common Factor -- Exercise -- 8 Conics -- 8.1 The General Conic -- Exercise -- 8.2 Parabolas -- Exercises -- 8.3 Ellipses -- Exercises -- 8.4 Hyperbolas -- Exercises -- 9 Rational and Algebraic Expressions and Functions -- 9.1 Rational Expressions and Rational Functions -- Exercises -- 9.2 The Partial Fraction Decomposition -- Exercises -- 9.3 Asymptotes of Rational Functions -- Exercises -- 9.4 Algebraic Expressions and Functions, Rationalization -- Exercises -- 9.5 Harmonic, Geometric, Arithmetic, Quadratic Means -- Exercises -- 9.6 The Greatest Integer Function -- Exercises -- 10 Exponential and Logarithmic Functions -- 10.1 The Natural Exponential Function According to Newton -- Exercises -- 10.2 The Bernoulli Numbers* -- Exercise -- 10.3 The Natural Logarithm -- Exercises -- 10.4 The General Exponential and Logarithmic Functions -- Exercise -- 10.5 The Natural Exponential Function According to Euler -- Exercises -- 11 Trigonometry -- 11.1 The Unit Circle S vs. the Real Line R -- Exercise -- 11.2 The Sine and Cosine Functions -- Exercises -- 11.3 Principal Identities for Sine and Cosine -- Exercises -- 11.4 Trigonometric Rational Functions -- Exercises -- 11.5 Trigonometric Limits -- Exercises -- 11.6 Cosine and Sine Series According to Newton -- Exercise -- 11.7 The Basel Problem of Euler* -- Exercise -- 11.8 Ptolemy's Theorem -- Exercise -- Further Reading -- Index. 410 0$aUndergraduate Texts in Mathematics 606 $aMathematics$xHistory 606 $aHistòria de la matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematics$xHistory. 615 7$aHistòria de la matemàtica 676 $a510 700 $aTo?th$b Ga?bor$f1964-$01243451 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466389803316 996 $aElements of mathematics$92884162 997 $aUNISA LEADER 06813nam 22007815 450 001 9910143596503321 005 20200706104715.0 010 $a3-540-45535-3 024 7 $a10.1007/3-540-45535-3 035 $a(CKB)1000000000211491 035 $a(SSID)ssj0000324037 035 $a(PQKBManifestationID)11268860 035 $a(PQKBTitleCode)TC0000324037 035 $a(PQKBWorkID)10305013 035 $a(PQKB)11707982 035 $a(DE-He213)978-3-540-45535-6 035 $a(MiAaPQ)EBC3071971 035 $a(PPN)155233882 035 $a(EXLCZ)991000000000211491 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aInteger Programming and Combinatorial Optimization $e8th International IPCO Conference, Utrecht, The Netherlands, June 13-15, 2001. Proceedings /$fedited by Karen Aardal, Bert Gerards 205 $a1st ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (XII, 428 p.) 225 1 $aLecture Notes in Computer Science,$x0302-9743 ;$v2081 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-42225-0 320 $aIncludes bibliographical references at the end of each chapters and index. 327 $aTwo O(log* k)-Approximation Algorithms for the Asymmetric k-Center Problem -- Strongly Polynomial Algorithms for the Unsplittable Flow Problem -- Edge Covers of Setpairs and the Iterative Rounding Method -- The Asymptotic Performance Ratio of an On-Line Algorithm for Uniform Parallel Machine Scheduling with Release Dates -- Approximate k-MSTs and k-Steiner Trees via the Primal-Dual Method and Lagrangean Relaxation -- On the Rank of Mixed 0,1 Polyhedra -- Fast 2-Variable Integer Programming -- Approximating k-Spanner Problems for k > 2 -- A Matroid Generalization of the Stable Matching Polytope -- A 2-Approximation for Minimum Cost {0, 1, 2} Vertex Connectivity -- Combined Connectivity Augmentation and Orientation Problems -- An Extension of a Theorem of Henneberg and Laman -- Bisubmodular Function Minimization -- On the Integrality Gap of a Natural Formulation of the Single-sink Buy-at-Bulk Network Design Problem -- Circuit Mengerian Directed Graphs -- Integral Polyhedra Related to Even Cycle and Even Cut Matroids -- A Unified Framework for Obtaining Improved Approximation Algorithms for Maximum Graph Bisection Problems -- Synthesis of 2-Commodity Flow Networks -- Bounds for Deterministic Periodic Routing sequences -- Cutting Planes for Mixed 0-1 Semidefinite Programs -- Independence Free Graphs and Vertex connectivity Augmentation -- The Throughput of Sequential Testing -- An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs -- Pruning by Isomorphism in Branch-and-Cut -- Facets, Algorithms, and Polyhedral Characterizations for a Multi-item Production Planning Model with Setup Times -- Fences Are Futile: On Relaxations for the Linear Ordering Problem -- Generating Cuts from Multiple-Term Disjunctions -- A (2+?)-Approximation Algorithm for Generalized Preemptive Open Shop Problem with Minsum Objective -- Performance Guarantees of Local Search for Multiprocessor Scheduling -- connected Joins in Graphs -- Two NP-hardness Results for Preemptive Minsum Scheduling of Unrelated Parallel Machines -- Approximation Algorithms for the Minimum Bends Traveling Salesman Problem. 330 $aThis volume contains the papers selected for presentation at IPCO VIII, the Eighth Conference on Integer Programming and Combinatorial Optimization, Utrecht, The Netherlands, 2001. This meeting isa forum for researchers and practitioners working on various aspects of integer programming and combi- torial optimization. The aim is to present recent developments in theory, com- tation, and application of integer programming and combinatorial optimization. Topics include, but are not limited to: approximation algorithms, branch and bound algorithms, computational biology, computational complexity, compu- tional geometry, cutting plane algorithms, diophantine equations, geometry of numbers, graph and network algorithms, integer programming, matroids and submodular functions, on-line algorithms, polyhedral combinatorics, scheduling theory and algorithms, and semide nit e programs. IPCO was established in 1988 when the rs t IPCO program committee was formed. The locations and years of the seven rs t IPCO conferences were: IPCO I, Waterloo (Canada) 1990, IPCO II, Pittsburgh (USA) 1992, IPCO III, - ice (Italy) 1993, IPCO IV, Copenhagen (Denmark) 1995, IPCO V, Vancouver (Canada) 1996, IPCO VI, Houston (USA) 1998, IPCO VII, Graz (Austria) 1999. IPCO is held every year in which no MPS (Mathematical Programming Society) International Symposium takes place. Since the MPS meeting is triennial, IPCO conferences are held twice in every three-year period. Asa rule, IPCO is held somewhere in Northern America in even years, and somewhere in Europe in odd years. 410 0$aLecture Notes in Computer Science,$x0302-9743 ;$v2081 606 $aProbabilities 606 $aAlgorithms 606 $aComputer science?Mathematics 606 $aInformation technology 606 $aBusiness?Data processing 606 $aCombinatorial analysis 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aAlgorithm Analysis and Problem Complexity$3https://scigraph.springernature.com/ontologies/product-market-codes/I16021 606 $aDiscrete Mathematics in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/I17028 606 $aIT in Business$3https://scigraph.springernature.com/ontologies/product-market-codes/522000 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 615 0$aProbabilities. 615 0$aAlgorithms. 615 0$aComputer science?Mathematics. 615 0$aInformation technology. 615 0$aBusiness?Data processing. 615 0$aCombinatorial analysis. 615 14$aProbability Theory and Stochastic Processes. 615 24$aAlgorithm Analysis and Problem Complexity. 615 24$aDiscrete Mathematics in Computer Science. 615 24$aIT in Business. 615 24$aCombinatorics. 676 $a519.77 702 $aAardal$b Karen$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aGerards$b Bert$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910143596503321 996 $aInteger Programming and Combinatorial Optimization$92860150 997 $aUNINA