Ralph J. Bremigan's Books

Mathematics for Secondary School Teachers

By: Elizabeth G. Bremigan,Ralph J. Bremigan,John D. Lorch

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Mathematics for Secondary School Teachers

By: Elizabeth G. Bremigan,Ralph J. Bremigan,John D. Lorch

Discusses topics of central importance in the secondary school mathematics curriculum, including functions, polynomials, trigonometry, exponential and logarithmic functions, number and operation, and measurement. This volume is primarily intended as the text for a bridge or capstone course for pre-service secondary school mathematics teachers.

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Page Count

444

Publisher

MAA

Published Date

ISBN 10

0883857731

ISBN 13

9780883857731

Calculus for the Life Sciences: A Modeling Approach

By: James L. Cornette,Ralph A. Ackerman

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Calculus for the Life Sciences: A Modeling Approach

By: James L. Cornette,Ralph A. Ackerman

Calculus for the Life Sciences is an entire reimagining of the standard calculus sequence with the needs of life science students as the fundamental organizing principle. Those needs, according to the National Academy of Science, include: the mathematical concepts of change, modeling, equilibria and stability, structure of a system, interactions among components, data and measurement, visualization, and algorithms. This book addresses, in a deep and significant way, every concept on that list. The book begins with a primer on modeling in the biological realm and biological modeling is the theme and frame for the entire book. The authors build models of bacterial growth, light penetration through a column of water, and dynamics of a colony of mold in the first few pages. In each case there is actual data that needs fitting. In the case of the mold colony that data is a set of photographs of the colony growing on a ruled sheet of graph paper and the students need to make their own approximations. Fundamental questions about the nature of mathematical modeling—trying to approximate a real-world phenomenon with an equation—are all laid out for the students to wrestle with. The authors have produced a beautifully written introduction to the uses of mathematics in the life sciences. The exposition is crystalline, the problems are overwhelmingly from biology and interesting and rich, and the emphasis on modeling is pervasive. An instructor's manual for this title is available electronically to those instructors who have adopted the textbook for classroom use. Please send email to textbooks@ams.org for more information. Online question content and interactive step-by-step tutorials are available for this title in WebAssign. WebAssign is a leading provider of online instructional tools for both faculty and students.

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Page Count

736

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470451425

ISBN 13

9781470451424

Bridge to Abstract Mathematics

By: Ralph W. Oberste-Vorth,Aristides Mouzakitis,Bonita A. Lawrence

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Bridge to Abstract Mathematics

By: Ralph W. Oberste-Vorth,Aristides Mouzakitis,Bonita A. Lawrence

A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.

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Page Count

254

Publisher

American Mathematical Society

Published Date

ISBN 10

1470453029

ISBN 13

9781470453022

Book's by Ralph J. Bremigan

Mathematics for Secondary School Teachers

Mathematics for Secondary School Teachers

Calculus for the Life Sciences: A Modeling Approach

Calculus for the Life Sciences: A Modeling Approach

Bridge to Abstract Mathematics

Bridge to Abstract Mathematics

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