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Mathematics for Secondary School Teachers
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.
Calculus Renewal
Calculus Reform. Or, as many would prefer, calculus renewal. These are terms that, for better or worse, have become a part of the vocabulary in mathematics departments across the country. The movement to change the nature of the calculus course at the undergraduate and secondary levels has sparked discussion and controversy in ways as diverse as the actual changes. Such interactions range from "coffee pot conversations" to university curriculum committee agendas to special sessions on calculus renewal at regional and national conferences. But what is the significance of these activities? Where have we been and where are we going with calculus and, more importantly, the entire scope of underg...
Calculus
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Calculus
Calculus: Single Variable, 8th Edition promotes active learning by providing students across multiple majors with a variety of problems with applications from the physical sciences, medicine, economics, engineering, and more. Designed to promote critical thinking to solve mathematical problems while highlighting the practical value of mathematics, the textbook brings calculus to real life with engaging and relevant examples, numerous opportunities to master key mathematical concepts and skills, and a student-friendly approach that reinforces the conceptual understanding necessary to reduce complicated problems to simple procedures. Developed by the Harvard University Calculus Consortium, Calculus focuses on the Rule of Four—viewing problems graphically, numerically, symbolically, and verbally—with particular emphasis placed on introducing a variety of perspectives for students with different learning styles. The eighth edition provides more problem sets, up-to-date examples, and a range of new multi-part graphing questions and visualizations powered by GeoGebra that reinforce the Rule of Four and strengthen students’ comprehension.
The Calculus Collection
The Calculus Collection is a useful resource for everyone who teaches calculus, in high school or in a 2- or 4-year college or university. It consists of 123 articles, selected by a panel of six veteran high school teachers, each of which was originally published in Math Horizons, MAA Focus, The American Mathematical Monthly, The College Mathematics Journal, or Mathematics Magazine. The articles focus on engaging students who are meeting the core ideas of calculus for the first time. The Calculus Collection is filled with insights, alternate explanations of difficult ideas, and suggestions for how to take a standard problem and open it up to the rich mathematical explorations available when you encourage students to dig a little deeper. Some of the articles reflect an enthusiasm for bringing calculators and computers into the classroom, while others consciously address themes from the calculus reform movement. But most of the articles are simply interesting and timeless explorations of the mathematics encountered in a first course in calculus.
Writing in the Teaching and Learning of Mathematics
This book examines the hows and whys of writing in mathematics.
Revolutions in Differential Equations
Discusses the direction in which the field of differential equations, and its teaching, is going.
Undergraduate Mathematics for the Life Sciences
There is a gap between the extensive mathematics background that is beneficial to biologists and the minimal mathematics background biology students acquire in their courses. The result is an undergraduate education in biology with very little quantitative content. New mathematics courses must be devised with the needs of biology students in mind. In this volume, authors from a variety of institutions address some of the problems involved in reforming mathematics curricula for biology students. The problems are sorted into three themes: Models, Processes, and Directions. It is difficult for mathematicians to generate curriculum ideas for the training of biologists so a number of the curriculum models that have been introduced at various institutions comprise the Models section. Processes deals with taking that great course and making sure it is institutionalized in both the biology department (as a requirement) and in the mathematics department (as a course that will live on even if the creator of the course is no longer on the faculty). Directions looks to the future, with each paper laying out a case for pedagogical developments that the authors would like to see.
Proofs Without Words II
Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.
Cryptological Mathematics
This is an introduction to the mathematics involved in the intriguing field of cryptology, the science of writing and reading secret messages which are designed to be read only by their intended recipients. It is written at an elementary level, suitable for beginning undergraduates, with careful explanations of all the concepts used. The basic branches of mathematics required, including number theory, abstract algebra and probability, are used to show how to encipher and decipher messages, and why this works, giving a practical as well as theoretical basis to the subject. Challenging computer programming exercises are also included. The book is written in an engaging style which will appeal to all, and also includes historical background on some of the founders of the subject. It will be of interest both to students wishing to learn cryptology per se, and also to those searching for practical applications of seemingly abstract mathematics.
