Answering Fundamental Questions: An Introduction to Mathematics

Hardcover | July 26, 2009

byWilliam Johnston, Alex McAllister

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A Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-levelmathematics courses (where they will have to prove theorems and grapple with mathematical abstractions). The text simultaneously promotes the goals of a ``survey' course, describing the intriguing questions and insights fundamental to many diverse areas of mathematics, including Logic, AbstractAlgebra, Number Theory, Real Analysis, Statistics, Graph Theory, and Complex Analysis. The main objective is "to bring about a deep change in the mathematical character of students -- how they think and their fundamental perspectives on the world of mathematics." This text promotes three major mathematical traits in a meaningful, transformative way: to develop an ability tocommunicate with precise language, to use mathematically sound reasoning, and to ask probing questions about mathematics. In short, we hope that working through A Transition to Advanced Mathematics encourages students to become mathematicians in the fullest sense of the word. A Transition to Advanced Mathematics has a number of distinctive features that enable this transformational experience. Embedded Questions and Reading Questions illustrate and explain fundamental concepts, allowing students to test their understanding of ideas independent of the exercise sets. Thetext has extensive, diverse Exercises Sets; with an average of 70 exercises at the end of section, as well as almost 3,000 distinct exercises. In addition, every chapter includes a section that explores an application of the theoretical ideas being studied. We have also interwoven embeddedreflections on the history, culture, and philosophy of mathematics throughout the text.

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A Transition to Advanced Mathematics: A Survey Course promotes the goals of a ``bridge'' course in mathematics, helping to lead students from courses in the calculus sequence (and other courses where they solve problems that involve mathematical calculations) to theoretical upper-levelmathematics courses (where they will have to prove ...

William Johnston is an Associate Dean of the College and Stodghill and Professor of Mathematics. Alex McAllister is an Associate Professor of Mathematics. Both are at Centre College.

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Format:HardcoverDimensions:560 pages, 10 × 7 × 0.98 inPublished:July 26, 2009Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195310764

ISBN - 13:9780195310764

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