Passage to Abstract Mathematics

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Addison-Wesley, 2012 - Mathematics - 232 pages

Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses. The text covers logic, proof, numbers, sets, induction, functions, cardinality, and more-material which instructors of upper-level courses often presume their students have already mastered but is generally missing from lower-level courses. This streamlined text can realistically be covered in a semester. The authors resisted the temptation to include topics that are covered in the advanced courses for which this course is a prerequisite.

The text assumes students have taken at least two semesters of calculus. Occasionally, the authors also refer to multivariable calculus and linear algebra, but these are not essential to the understanding of the text.

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About the author (2012)

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Mark E. Watkins is a professor of Mathematics at Syracuse University, having joined its faculty in 1968. He received his BA in mathematics from Amherst College and his MA and PhD from Yale University as a student of Oystein Ore. He has published more than 60 research articles in combinatorics, particularly in algebraic and topological graph theory, and has coauthored (with J.E. Graver) the graduate text Combinatorics with Emphasis on the Theory of Graphs (GTM 54, Springer-Verlag, 1977) and Locally Finite, Planar, Edge-Transitive Graphs (Memoir 601, Amer. Math. Soc. 1997). He has held visiting positions in Canada, France, Austria, and New Zealand, has been twice awarded a DAAD stipend to Germany, and enjoys lecturing in French or German when appropriate. He has taught a full range of undergraduate and graduate mathematics courses and supervised six PhD students. As former Associate Chair for Graduate Studies and a member of the Future Professoriate Program, he has had a special commitment to teaching graduate students how to teach mathematics to undergraduates. His other interests are playing trombone and individual sports.

Jeff Meyer joined the mathematics faculty of Syracuse University in 1997. He earned his BS from the University of Minnesota in mathematics education. His PhD in number theory is from the University of Illinois where he was the tenth PhD student of Bruce C. Berndt. He has published both research and expository papers in analytic number theory, especially Dedekind Sums. Before beginning his graduate studies, he taught junior and senior high school mathematics for five years. He remains active in the professional development of secondary mathematics teachers by giving lectures and conducting workshops for the Syracuse University College of Education and by meeting with in-service teachers through Syracuse University Project Advance. In his spare time he enjoys outdoor activities and traveling with his family.

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