All HMC Faculty Books

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Some Applications of Geometry Thinking

Bowen Kerins, Darryl Yong, Al Cuoco, and Glenn Stevens

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Some Applications of Geometric Thinking is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Some Applications of Geometric Thinking is to help teachers see that geometric ideas can be used throughout the secondary school curriculum, both as a hub that connects ideas from all parts of secondary school and beyond-algebra, number theory, arithmetic, and data analysis-and as a locus for applications of results and methods from these fields. Some Applications of Geometric Thinking is a volume of the book series IAS/PCMI-The Teacher Program Series' published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
Moving Things Around

Bowen Kerins, Darryl Yong, Al Cuoco, Glenn Stevens, and Mary Pilgrim

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Moving Things Around is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The goal of Moving Things Around is to help participants make what might seem to be surprising connections among seemingly different areas: permutation groups, number theory, and expansions for rational numbers in various bases, all starting from the analysis of card shuffles. Another goal is to use these connections to bring some coherence to several ideas that run throughout school mathematics-rational number arithmetic, different representations for rational numbers, geometric transformations, and combinatorics. The theme of seeking structural similarities is developed slowly, leading, near the end of the course, to an informal treatment of isomorphism. Moving Things Around is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in this series covers the content of one Summer School Teacher Program year and is independent of the rest.
The Magic of Math: Solving for x and Figuring Out Why

Arthur Benjamin

The Magic of Math is the math book you wish you had in school. Using a delightful assortment of examples-from ice-cream scoops and poker hands to measuring mountains and making magic squares-this book revels in key mathematical fields including arithmetic, algebra, geometry, and calculus, plus Fibonacci numbers, infinity, and, of course, mathematical magic tricks. Known throughout the world as the "mathemagician," Arthur Benjamin mixes mathematics and magic to make the subject fun, attractive, and easy to understand for math fan and math-phobic alike.
The Fascinating World of Graph Theory

Arthur Benjamin, Gary Chartrand, and Ping Zhang

Graph theory goes back several centuries and revolves around the study of graphs--mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics--and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.
Applications of Algebra and Geometry to the Work of Teaching

Bowen Kerins, Benjamin Sinwell, Darryl Yong, Al Cuoco, and Glenn Stevens

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Applications of Algebra and Geometry to the Work of Teaching is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. The specific theme developed in Applications of Algebra and Geometry to the Work of Teaching is the use of complex numbers-especially the arithmetic of Gaussian and Eisenstein integers-to investigate some questions that are at the intersection of algebra and geometry, like the classification of Pythagorean triples and the number of representations of an integer as the sum of two squares. Applications of Algebra and Geometry to the Work of Teaching is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.
Famous Functions in Number Theory

Bowen Kerins, Darryl Yong, Al Cuoco, and Glenn Stevens

Designed for precollege teachers by a collaborative of teachers, educators, and mathematicians, Famous Functions in Number Theory is based on a course offered in the Summer School Teacher Program at the Park City Mathematics Institute. But this book isn't a "course" in the traditional sense. It consists of a carefully sequenced collection of problem sets designed to develop several interconnected mathematical themes, and one of the goals of the problem sets is for readers to uncover these themes for themselves. Famous Functions in Number Theory introduces readers to the use of formal algebra in number theory. Through numerical experiments, participants learn how to use polynomial algebra as a bookkeeping mechanism that allows them to count divisors, build multiplicative functions, and compile multiplicative functions in a certain way that produces new ones. One capstone of the investigations is a beautiful result attributed to Fermat that determines the number of ways a positive integer can be written as a sum of two perfect squares. Famous Functions in Number Theory is a volume of the book series IAS/PCMI-The Teacher Program Series published by the American Mathematical Society. Each volume in that series covers the content of one Summer School Teacher Program year and is independent of the rest.
The Art of Mental Calculation: Addiction & Subtraction

Arthur Benjamin and Natalya St. Clair

The Art of Mental Calculation will make math fun and accessible to students of all levels. Whether as an enrichment program for aspiring math geniuses or fun practice as a classroom supplement, this book ail have students excited to practice the joys of mental arithmetic in fun new ways. Following Arthur Benjamin's bestseller Secrets of Mental Math, this new workbook provides over 300 examples and exercises for doing rapid mental addition and subtraction. Through clever writing style, amusing illustrations, and engaging dialogue, the book makes math fun and accessible to everyone. The workbook consists of 20 lessons, 40 reproducible pages, an answer key with full solutions, and a certificate for aspiring mental mathemagicians.
Engineering Design: A Project-Based Introduction

Clive L. Dym, Patrick Little, and Elizabeth J. Orwin

The text focuses particularly on conceptual design, providing a brief, and yet comprehensive introduction to design methodology and project management tools to students early on in their careers.
Solid Mechanics: A Variational Approach, Augmented Edition

Clive L. Dym and Irving H. Shames

Solid Mechanics: A Variational Approach, Augmented Edition presents a lucid and thoroughly developed approach to solid mechanics for students engaged in the study of elastic structures not seen in other texts currently on the market. This work offers a clear and carefully prepared exposition of variational techniques as they are applied to solid mechanics. Unlike other books in this field, Dym and Shames treat all the necessary theory needed for the study of solid mechanics and include extensive applications. Of particular note is the variational approach used in developing consistent structural theories and in obtaining exact and approximate solutions for many problems. Based on both semester and year-long courses taught to undergraduate seniors and graduate students, this text is geared for programs in aeronautical, civil, and mechanical engineering, and in engineering science. The authors’ objective is two-fold: first, to introduce the student to the theory of structures (one- and two-dimensional) as developed from the three-dimensional theory of elasticity; and second, to introduce the student to the strength and utility of variational principles and methods, including briefly making the connection to finite element methods. A complete set of homework problems is included.
Engineering Design: Representation and Reasoning

Clive L. Dym and David C. Brown

This text demonstrates that symbolic representation, and related problem-solving methods, offer significant opportunities to clarify and articulate concepts of design to give a better framework for design research and education. This edition includes recent work on design reasoning, computational design, AI in design, and design cognition, with pointers to the current literature.
Analytical Estimates of Structural Behavior

Clive L. Dym and Harry E. Williams

Explicitly reintroducing the idea of modeling to the analysis of structures, Analytical Estimates of Structural Behavior presents an integrated approach to modeling and estimating the behavior of structures. With the increasing reliance on computer-based approaches in structural analysis, it is becoming even more important for structural engineers to recognize that they are dealing with models of structures, not with the actual structures. As tempting as it is to run innumerable simulations, closed-form estimates can be effectively used to guide and check numerical results, and to confirm physical insights and intuitions.
Comparative Environmental Politics: Theory, Practice, and Prospects

Paul F. Steinberg and Stacy D. VanDeever

How do different societies respond politically to environmental problems around the globe? Answering this question requires systematic, cross-national comparisons of political institutions, regulatory styles, and state-society relations. The field of comparative environmental politics approaches this task by bringing the theoretical tools of comparative politics to bear on the substantive concerns of environmental policy. This book outlines a comparative environmental politics framework and applies it to concrete, real-world problems of politics and environmental management. After a comprehensive review of the literature exploring domestic environmental politics around the world, the book provides a sample of major currents within the field, showing how environmental politics intersects with such topics as the greening of the state, the rise of social movements and green parties, European Union expansion, corporate social responsibility, federalism, political instability, management of local commons, and policymaking under democratic and authoritarian regimes. It offers fresh insights into environmental problems ranging from climate change to water scarcity and the disappearance of tropical forests, and it examines actions by state and nonstate actors at levels from the local to the continental. The book will help scholars and policymakers make sense of how environmental issues and politics are connected around the globe, and is ideal for use in upper-level undergraduate and graduate courses.
Classification of Radial Solutions Arising in the Study of Thermal Structures with Thermal Equilibrium or no Flux at the Boundary

Alfonso Castro and Victor Padrón

We provide a complete classification of the radial solutions to a class of reaction diffusion equations arising in the study of thermal structures such as plasmas with thermal equilibrium or no flux at the boundary. In particular, our study includes rapidly growing nonlinearities, that is, those where an exponent exceeds the critical exponent. We describe the corresponding bifurcation diagrams and determine existence and uniqueness of ground states, which play a central role in characterizing those diagrams. We also provide information on the stability-unstability of the radial steady states.
Theories of Computability

Nicholas Pippenger

Broad in coverage, mathematically sophisticated, and up to date, this book provides an introduction to theories of computability. It treats not only "the" theory of computability (the theory created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages) as theories of computability. These are addressed from the classical perspective of their generation by grammars and from the more modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account, written by one of the leading lights of the subject, will be required reading for graduate students and researchers in theoretical computer science and mathematics.
Engineering Design: A Project-Based Introduction

Clive L. Dym, Patrick Little, Elizabeth J. Orwin, and Erik Spjut

Engineers continue to turn to Engineering Design to learn the tools and techniques of formal design that will be useful in framing the design problems. Insights and tips on team dynamics are provided because design and research is increasingly done in teams. Readers are also introduced to conceptual design tools like objectives trees, morphological charts, and requirement matrices. Case studies are included that show the relevance of these tools to practical settings. The third edition offers a view of the design tools that even the greenest of engineers will have in their toolbox in the coming years.
Biscuits of Number Theory

Arthur T. Benjamin and Ezra B. Brown

An anthology of articles designed to supplement a first course in number theory.
An Introduction to Engineering Mechanics: A Continuum Approach

Jenn Stroud Rossmann and Clive L. Dym

The essence of continuum mechanics — the internal response of materials to external loading — is often obscured by the complex mathematics of its formulation. By building gradually from one-dimensional to two- and three-dimensional formulations, this book provides an accessible introduction to the fundamentals of solid and fluid mechanics, covering stress and strain among other key topics. This undergraduate text presents several real-world case studies, such as the St. Francis Dam, to illustrate the mathematical connections between solid and fluid mechanics, with an emphasis on practical applications of these concepts to mechanical, civil, and electrical engineering structures and design.
Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

Arthur T. Benjamin and Michael B. Shermer

These simple math secrets and tricks will forever change how you look at the world of numbers. Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned "mathemagician" Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun. Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.
Principles of Mathematical Modeling

Clive L. Dym

The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making.
Principles of Mathematical Modeling

Clive L. Dym

The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making.
Proofs that Really Count: The Art of Combinatorial Proof

Arthur T. Benjamin and Jennifer J. Quinn

Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
Engineering Design: A Project-Based Introduction

Clive L. Dym and Patrick Little

Introduces conceptual design methods and project management tools through description, example, and case study. Two design projects are consistently drawn upon to illustrate the design methods and management tools. Also covers important topic of reporting the results of a design project and provides useful insights into team behaviors and dynamics.
* Enhanced coverage of communications and decision-making techniques.
* Introduces conceptual design tools like objectives trees, morphological charts, and requirement matrices.
* Covers project management tools, including work breakdown structures, Gantt charts, and project control tools
Harvey Mudd College : The Third Decade Plus, 1976-1988

D. Kenneth Baker

Kenneth Baker, second president of Harvey Mudd College, describes events at Harvey Mudd College during his tenure from 1976 to 1988.
Stability Theory and Its Applications to Structural Mechanics

Clive L. Dym

Self-contained text focuses on Koiter postbuckling analyses, with mathematical notions of stability of motion. Basing minimum energy principles for static stability upon dynamic concepts of stability of motion, it develops asymptotic buckling and postbuckling analyses from potential energy considerations, with applications to columns, plates, and arches.
Environmental Leadership in Developing Countries: Transnational Relations and Biodiversity Policy in Costa Rica and Bolivia

Paul F. Steinberg

In the absence of world government, effective national policy is essential to the success of international environmental initiatives. Yet research on global environmental cooperation has proceeded without models of policy change in developing countries, where most of the world's people, land, and species are found. In this book Paul Steinberg provides a theoretical framework to explain the domestic responses of developing countries to global environmental concerns. Drawing on extensive field research, he traces the evolution of public policies to protect biological diversity in Costa Rica and Bolivia over the past four decades, to understand how these countries emerged as leaders in tropical conservation and how international institutions might support similar outcomes in other countries.

Environmental Leadership in Developing Countries explodes the myth that developing countries are too preoccupied with short-term economic growth and material survival to devote attention to global environmental concerns. Instead it offers a nuanced account of complex, decades-long efforts to create effective institutions, and analyzes the relative roles of foreign and domestic actors in this process.