LEADER 05218nam 22006015 450 001 9910320753703321 005 20200706204731.0 010 $a3-030-00632-8 024 7 $a10.1007/978-3-030-00632-7 035 $a(CKB)4100000007823493 035 $a(DE-He213)978-3-030-00632-7 035 $a(MiAaPQ)EBC6312963 035 $a(PPN)235668966 035 $a(EXLCZ)994100000007823493 100 $a20190402d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Readable Introduction to Real Mathematics /$fby Daniel Rosenthal, David Rosenthal, Peter Rosenthal 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XVIII, 218 p. 63 illus.) 225 1 $aUndergraduate Texts in Mathematics,$x0172-6056 311 $a3-030-00631-X 327 $aPreface to the Second Edition -- Preface for Readers -- Preface for Instructors -- 1. Introduction to the Natural Numbers -- 2. Mathematical Induction -- 3. Modular Arithmetic -- 4. The Fundamental Theorem of Arithmetic -- 5. Fermat's Theorem and Wilson's Theorem -- 6. Sending and Receiving Coded Messages -- 7. The Euclidean Algorithm and Applications -- 8. Rational Numbers and Irrational Numbers -- 9. The Complex Numbers -- 10. Sizes of Infinite Sets -- 11. Fundamentals of Euclidean Plane Geometry -- 12. Constructability -- 13. An Introduction to Infinite Series -- 14. Some Higher Dimensional Spaces -- Index. 330 $aDesigned for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book. From the reviews of the first edition: ?It is carefully written in a precise but readable and engaging style? I thoroughly enjoyed reading this recent addition to the Springer Undergraduate Texts in Mathematics series and commend this clear, well-organised, unfussy text to its target audiences.? (Nick Lord, The Mathematical Gazette, Vol. 100 (547), 2016) ?The book is an introduction to real mathematics and is very readable. ? The book is indeed a joy to read, and would be an excellent text for an ?appreciation of mathematics? course, among other possibilities.? (G.A. Heuer, Mathematical Reviews, February, 2015) ?Many a benighted book misguidedly addresses the need [to teach mathematical thinking] by framing reasoning, or narrowly, proof, not as pervasive modality but somehow as itself an autonomous mathematical subject. Fortunately, the present book gets it right.... [presenting] well-chosen, basic, conceptual mathematics, suitably accessible after a K-12 education, in a detailed, self-conscious way that emphasizes methodology alongside content and crucially leads to an ultimate clear payoff. ? Summing Up: Recommended. Lower-division undergraduates and two-year technical program students; general readers.? (D.V. Feldman, Choice, Vol. 52 (6), February, 2015). 410 0$aUndergraduate Texts in Mathematics,$x0172-6056 606 $aMathematics 606 $aNumber theory 606 $aGeometry 606 $aMathematics, general$3https://scigraph.springernature.com/ontologies/product-market-codes/M00009 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aMathematics. 615 0$aNumber theory. 615 0$aGeometry. 615 14$aMathematics, general. 615 24$aNumber Theory. 615 24$aGeometry. 676 $a510 676 $a510 700 $aRosenthal$b Daniel$4aut$4http://id.loc.gov/vocabulary/relators/aut$0601662 702 $aRosenthal$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRosenthal$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910320753703321 996 $aA Readable Introduction to Real Mathematics$92124848 997 $aUNINA