03637oam 2200517M 450 991097280690332120251116172554.01-000-70227-81-000-70181-60-429-32481-2(OCoLC)1127538961(CKB)4100000009826840(MiAaPQ)EBC5981975(OCoLC-P)1127538961(FlBoTFG)9780429324819(EXLCZ)99410000000982684020191111d2020 uy 0engur|n|||||||||txtrdacontentcrdamediacrrdacarrierAn elementary transition to abstract mathematics /Gove Effinger and Gary L. Mullen1st ed.Boca Raton :CRC Press, Taylor & Francis Group,2020.1 online resource (x, 282 pages) illustrationsTextbooks in mathematics1-03-247517-X 0-367-33693-6 Includes bibliographical references and index.A look back: precalculus math -- A look back: calculus -- About proofs and proof strategies -- Mathematical induction -- The well-ordering principle -- Sets -- Equivalence relations -- Functions -- Cardinality of sets -- Permutations -- Complex numbers -- Matrices and sets with algebraic structure -- Divisibility in Z and number theory -- Primes and unique factorization -- Congruences and the finite sets Zn -- Solving congruences -- Fermat's theorem -- Diffie-Hellman key exchange -- Euler's formula and Euler's theorem -- RSA cryptographic system -- Groups: definition and examples -- Groups: basic properties -- Groups: subgroups -- Groups: cosets -- Groups: Lagrange's theorem -- Rings -- Subrings and ideals -- Integral domains -- Fields -- Vector spaces -- Vector space properties -- Subspaces of vector spaces -- Polynomials -- Polynomials: unique factorization -- Polynomials over the rational, real and complex numbersAn Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials. Features: The material is presented in many short chapters, so that one concept at a time can be absorbed by the student. Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student's transition by working with familiar concepts. Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns. A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.Textbooks in mathematics (Boca Raton, Fla.)MathematicsGroup theoryMathematics.Group theory.512/.2Effinger Gove W.59853Mullen Gary L.OCoLC-POCoLC-PBOOK9910972806903321An elementary transition to abstract mathematics4496721UNINA