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This treatment covers the mechanics of writing proofs, the area and circumference of circles, and complex numbers and their application to real numbers. 1998 edition.
This book leads readers through a progressive explanation of what mathematical proofs are, why they are important, and how they work, along with a presentation of basic techniques used to construct proofs. The Second Edition presents more examples, more exercises, a more complete treatment of mathematical induction and set theory, and it incorporates suggestions from students and colleagues. Since the mathematical concepts used are relatively elementary, the book can be used as a supplement in any post-calculus course. This title has been successfully class-tested for years. There is an index for easier reference, a more extensive list of definitions and concepts, and an updated bibliography. An extensive collection of exercises with complete answers are provided, enabling students to practice on their own. Additionally, there is a set of problems without solutions to make it easier for instructors to prepare homework assignments. * Successfully class-tested over a number of years * Index for easy reference * Extensive list of definitions and concepts * Updated biblography
A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology
Self-contained and authoritative, this history of mathematics is suited to those with no math background. Its absorbing, entertaining essays focus on the era from 1800 to 2000. Contributors include Henri Poincaré, Judith V. Grabiner, and H. S. M. Coxeter, who discuss topics ranging from logic and infinity to Fermat's Last Theorem.
This unique text is fully based on the NCTM standards. Its many innovative features include the use of an exploratory, problem-solving approach throughout the work (in text discussions, examples, and problems), a theme and narrative that unfold from beginning to end (the search for patterns), a framework that relates math topics to each other, an entertaining writing style, and multicultural coverage. It offers a wide range of traditional and off-beat math topics to choose from and a comprehensive set of pedagogical features and illustrations. The text has been class tested for several years at Central Oregon Community College.
Teaching Secondary Mathematics: Techniques and Enrichment Units,7th edition has been thoroughly revised to nbsp;discuss current methods of teaching mathematics, considering all aspects and responsibilities of the job, beginning with a briefnbsp;overview of the history of mathematics education and how it has evolved over time to include standards for teaching and assessment.nbsp; The authors address how to craft rich and effective daily lesson plans, and how to use a variety of instructional tools and strategies to reach all students in a classroom.nbsp; Problem solving is a key focus from its instructional underpinnings to its recreational and motivational aspects.nbsp; The second part of the book provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum.

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