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The Heart of Calculus
This book contains enrichment material for courses in first and second year calculus, differential equations, modeling, and introductory real analysis. It targets talented students who seek a deeper understanding of calculus and its applications. The book can be used in honors courses, undergraduate seminars, independent study, capstone courses taking a fresh look at calculus, and summer enrichment programs. The book develops topics from novel and/or unifying perspectives. Hence, it is also a valuable resource for graduate teaching assistants developing their academic and pedagogical skills and for seasoned veterans who appreciate fresh perspectives. The explorations, problems, and projects ...
Mathematics and Sports
An accessible compendium of essays on the broad theme of mathematics and sports.
She Does Math!
She Does Math! presents the career histories of 38 professional women and math problems written by them. Each history describes how much math the [Author]; took in high school and college; how she chose her field of study; and how she ended up in her current job. Each of the women present several problems typical of those she had to solve on the job using mathematics. There are many good reasons to buy this book: It contains real-life problems. Any student who asks the question, "Why do I have to learn algebra or trigonometry or geometry?" will find many answers in its pages. Students will welcome seeing solutions from real-world jobs where the math skills they are learning in class are actu...
THE INTELLIGENCE OF MACHINES
In a 1951 lecture Turing, Alan (1951), Turing argued, "It seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers. There would be no question of the machines dying, and they would be able to converse with each other to sharpen their wits. At some stage therefore we should have to expect the machines to take control, in the way that is mentioned in Samuel Butler's Erewhon." Also in a lecture broadcast on the BBC (Turing, Alan 1951). He expressed the opinion: "If a machine can think, it might think more intelligently than we do, and then where should we be? Even if we could keep the machines in a subservient position, for instance ...
Proofs Without Words III
Proofs without words (PWWs) are figures or diagrams that help the reader see why a particular mathematical statement is true, and how one might begin to formally prove it true. PWWs are not new, many date back to classical Greece, ancient China, and medieval Europe and the Middle East. PWWs have been regular features of the MAA journals Mathematics Magazine and The College Mathematics Journal for many years, and the MAA published the collections of PWWs Proofs Without Words: Exercises in Visual Thinking in 1993 and Proofs Without Words II: More Exercises in Visual Thinking in 2000. This book is the third such collection of PWWs.
Recent Advances in Algorithmic Differentiation
The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the ef...
Explorations in Complex Analysis
Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.
The Monty Hall Problem
Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.
Ordinary Differential Equations
For the instructor or student confronting an introductory course in ordinary differential equations there is a need for a brief guide to the key concepts in the subject. Important topics like stability, resonance, existence of periodic solutions, and the essential role of continuation of solutions are often engulfed in a sea of exercises in integration, linear algebra theory, computer programming and an overdose of series expansions. This book is intended as that guide. It is more conceptual than definitive and more light-hearted than pedagogic. It covers key topics and theoretical underpinnings that are necessary for the study of rich topics like nonlinear equations or stability theory. The [Author]; has included a great many illuminating examples and discussions that uncover the conceptual heart of the matter.
Discovering Discrete Dynamical Systems
Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. T...
