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101 0 $aeng
135   $aur|n|||||||||
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 13$aAn elementary transition to abstract mathematics /$fGove Effinger and Gary L. Mullen
205   $a1st ed.
210  1$aBoca Raton :$cCRC Press, Taylor & Francis Group,$d2020.
215   $a1 online resource (x, 282 pages) $cillustrations
225 1 $aTextbooks in mathematics
311 08$a1-03-247517-X 
311 08$a0-367-33693-6 
320   $aIncludes bibliographical references and index.
327   $aA 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 numbers
330   $aAn Elementary Transition to Abstract Mathematics will help students move from introductory courses to those where rigor and proof play a much greater role. The text is organized into five basic parts: the first looks back on selected topics from pre-calculus and calculus, treating them more rigorously, and it covers various proof techniques; the second part covers induction, sets, functions, cardinality, complex numbers, permutations, and matrices; the third part introduces basic number theory including applications to cryptography; the fourth part introduces key objects from abstract algebra; and the final part focuses on polynomials. Features: The material is presented in many short chapters, so that one concept at a time can be absorbed by the student. Two "looking back" chapters at the outset (pre-calculus and calculus) are designed to start the student's transition by working with familiar concepts. Many examples of every concept are given to make the material as concrete as possible and to emphasize the importance of searching for patterns. A conversational writing style is employed throughout in an effort to encourage active learning on the part of the student.
410  0$aTextbooks in mathematics (Boca Raton, Fla.)
606   $aMathematics
606   $aGroup theory
615  0$aMathematics.
615  0$aGroup theory.
676   $a512/.2
700   $aEffinger$b Gove W.$059853
702   $aMullen$b Gary L.
801  0$bOCoLC-P
801  1$bOCoLC-P
906   $aBOOK
912   $a9910972806903321
996   $aAn elementary transition to abstract mathematics$94496721
997   $aUNINA