04345nam 22006975 450 991029997880332120200703070511.03-319-05654-910.1007/978-3-319-05654-8(CKB)3710000000212208(SSID)ssj0001298251(PQKBManifestationID)11822244(PQKBTitleCode)TC0001298251(PQKBWorkID)11241204(PQKB)11461912(DE-He213)978-3-319-05654-8(MiAaPQ)EBC6312043(MiAaPQ)EBC5587769(Au-PeEL)EBL5587769(OCoLC)883733706(PPN)179926705(EXLCZ)99371000000021220820140703d2014 u| 0engurnn|008mamaatxtccrA Readable Introduction to Real Mathematics /by Daniel Rosenthal, David Rosenthal, Peter Rosenthal1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XII, 161 p. 50 illus.) Undergraduate Texts in Mathematics,0172-6056Bibliographic Level Mode of Issuance: Monograph3-319-05653-0 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.Designed 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 engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. 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 * constructability (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass) This textbook is suitable for a wide variety of courses and for a broad range of students in the fields of education, liberal arts, physical sciences and mathematics. Students at the senior high school level who like mathematics will also be able to further their understanding of mathematical thinking by reading this book.Undergraduate Texts in Mathematics,0172-6056MathematicsNumber theoryGeometryMathematics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/M00009Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M21006Mathematics.Number theory.Geometry.Mathematics, general.Number Theory.Geometry.510Rosenthal Danielauthttp://id.loc.gov/vocabulary/relators/aut601662Rosenthal Davidauthttp://id.loc.gov/vocabulary/relators/autRosenthal Peterauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299978803321A Readable Introduction to Real Mathematics2124848UNINA