LEADER 06730nam 22007575 450 001 9910300147403321 005 20200706185313.0 010 $a1-4614-8939-3 024 7 $a10.1007/978-1-4614-8939-9 035 $a(CKB)3710000000111812 035 $a(EBL)1730860 035 $a(OCoLC)883570867 035 $a(SSID)ssj0001244596 035 $a(PQKBManifestationID)11706917 035 $a(PQKBTitleCode)TC0001244596 035 $a(PQKBWorkID)11319922 035 $a(PQKB)10470199 035 $a(MiAaPQ)EBC1730860 035 $a(DE-He213)978-1-4614-8939-9 035 $a(PPN)178778486 035 $a(EXLCZ)993710000000111812 100 $a20140510d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA Mathematical Odyssey $eJourney from the Real to the Complex /$fby Steven G. Krantz, Harold R. Parks 205 $a1st ed. 2014. 210 1$aNew York, NY :$cSpringer US :$cImprint: Springer,$d2014. 215 $a1 online resource (392 p.) 300 $aDescription based upon print version of record. 311 $a1-4614-8938-5 320 $aIncludes bibliographical references and index. 327 $a""Preface""; ""Contents""; ""1 The Four-Color Problem""; ""1.1 Humble Beginnings""; ""1.2 Kempe, Heawood, and the Chromatic Number""; ""1.3 Heawood's Estimate Confirmed""; ""1.4 Appel, Haken, and a Computer-Aided Proof""; ""A Look Back""; ""References and Further Reading""; ""2 The Mathematics of Finance""; ""2.1 Ancient Mathematics of Finance""; ""2.2 Loans and Charging Interest""; ""2.3 Compound Interest""; ""2.4 Continuously Compounded Interest""; ""2.5 Raising Capital: Stocks and Bonds""; ""2.6 The Standard Model for Stock Prices""; ""2.7 Parameters in the Standard Model"" 327 $a""2.8 Derivatives""""2.9 Pricing a Forward""; ""2.10 Arbitrage""; ""2.11 Call Options""; ""2.12 Value of a Call Option at Expiry""; ""2.13 Pricing a Call Option Using a Replicating Portfolio: A Single Time Step""; ""2.14 Pricing a Call Option Using a Replicating Portfolio: Multiple Time Steps""; ""2.15 Blacka???Scholes Option Pricing""; ""A Look Back""; ""References and Further Reading""; ""3 Ramsey Theory""; ""3.1 Introduction""; ""3.2 The Pigeonhole Principle""; ""3.3 The Happy End Problem""; ""3.4 Relationship Tables and Ramsey's Theorem for Pairs""; ""3.5 Ramsey's Theorem in General"" 327 $a""References and Further Reading""""5 The Plateau Problem""; ""5.1 Paths That Minimize Length""; ""5.2 Surfaces That Minimize Area""; ""5.3 Curvature of a Plane Curve""; ""5.4 Curvature of a Surface""; ""5.5 Curvature of Minimal Surfaces""; ""5.6 Plateau's Observations""; ""5.7 Types of Spanning Surfaces""; ""5.8 The Ennepera???Weierstrass Formula""; ""5.8.1 Costa's Surface""; ""5.9 Solutions by Douglas and RadA?³""; ""5.10 Surfaces Beyond Disc Type""; ""5.11 Currents""; ""5.12 Regularity Theory""; ""5.13 Plateau's Rules""; ""A Look Back""; ""References and Further Reading"" 327 $a""6 Euclidean and Non-Euclidean Geometries""""6.1 The Concept of Euclidean Geometry""; ""6.2 A Review of the Geometry of Triangles""; ""6.3 Some Essential Properties of Euclidean Geometry""; ""6.4 What is Non-Euclidean Geometry?""; ""6.5 Spherical Geometry""; ""6.6 Neutral Geometry""; ""6.7 Hyperbolic Geometry""; ""6.7.1 The Question of Consistency""; ""6.7.2 Models of Hyperbolic Geometry""; ""A Look Back""; ""References and Further Reading""; ""7 Special Relativity""; ""7.1 Introduction""; ""7.2 Principles Underlying Special Relativity""; ""7.3 Some Consequences of Special Relativity"" 327 $a""7.4 Momentum and Energy"" 330 $aMathematics is a poem. It is a lucid, sensual, precise exposition of beautiful ideas directed to specific goals. It is worthwhile to have as broad a cross-section of mankind as possible be conversant with what goes on in mathematics. Just as everyone knows that the Internet is a powerful and important tool for communication, so everyone should know that the Poincaré conjecture gives us important information about the shape of our universe. Just as every responsible citizen realizes that the mass-production automobile was pioneered by Henry Ford, just so everyone should know that the P/NP problem has implications for security and data manipulation that will affect everyone. This book endeavors to tell the story of the modern impact of mathematics, of its trials and triumphs and insights, in language that can be appreciated by a broad audience. It endeavors to show what mathematics means for our lives, how it impacts all of us, and what new thoughts it should cause us to entertain. It introduces new vistas of mathematical ideas and shares the excitement of new ideas freshly minted. It discusses the significance and impact of these ideas, and gives them meaning that will travel well and cause people to reconsider their place in the universe. Mathematics is one of mankind's oldest disciplines. Along with philosophy, it has shaped the very modus of human thought. And it continues to do so. To be unaware of modern mathematics is to be miss out on a large slice of life. It is to be left out of essential modern developments. We want to address this point, and do something about it. This is a book to make mathematics exciting for people of all interests and all walks of life. Mathematics is exhilarating, it is ennobling, it is uplifting, and it is fascinating. We want to show people this part of our world, and to get them to travel new paths. 606 $aMathematics 606 $aHistory 606 $aPopular works 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aPopular Science, general$3https://scigraph.springernature.com/ontologies/product-market-codes/Q00007 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aMathematics. 615 0$aHistory. 615 0$aPopular works. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aHistory of Mathematical Sciences. 615 24$aPopular Science, general. 615 24$aApplications of Mathematics. 676 $a500 676 $a510 676 $a510.9 676 $a519 700 $aKrantz$b Steven G$4aut$4http://id.loc.gov/vocabulary/relators/aut$055961 702 $aParks$b Harold R$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300147403321 996 $aA Mathematical Odyssey$92512357 997 $aUNINA