An Elementary Transition to Abstract Mathematics (Textbooks in Mathematics)

November 1, 2020
An Elementary Transition to Abstract Mathematics (Textbooks in Mathematics)

An Elementary Transition to Abstract Mathematics will helpstudents move from introductory courses to those where rigor andproof play a much greater role.The text is organized into five basic parts: the first looksback on selected topics from pre-calculus and calculus, treatingthem more rigorously, and it covers various proof techniques; thesecond part covers induction, sets, functions, cardinality, complexnumbers, permutations, and matrices; the third part introducesbasic number theory including applications to cryptography; thefourth part introduces key objects from abstract algebra; and thefinal part focuses on polynomials.Features:The material is presented in many short chapters, so that oneconcept at a time can be absorbed by the student.Two "looking back" chapters at the outset (pre-calculus andcalculus) are designed to start the student’s transition by workingwith familiar concepts.Many examples of every concept are given to make the material asconcrete as possible and to emphasize the importance of searchingfor patterns.A conversational writing style is employed throughout in aneffort to encourage active learning on the part of the student.