All HMC Faculty BooksCopyright (c) 2023 Claremont Colleges All rights reserved.
https://scholarship.claremont.edu/hmc_facbooks
Recent documents in All HMC Faculty Booksen-usMon, 14 Aug 2023 16:30:38 PDT3600Moving Things Around
https://scholarship.claremont.edu/hmc_facbooks/42
https://scholarship.claremont.edu/hmc_facbooks/42Tue, 21 Mar 2017 14:57:27 PDT
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.
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Bowen Kerins et al.Some Applications of Geometry Thinking
https://scholarship.claremont.edu/hmc_facbooks/41
https://scholarship.claremont.edu/hmc_facbooks/41Tue, 21 Mar 2017 14:50:27 PDT
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.
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Bowen Kerins et al.Famous Functions in Number Theory
https://scholarship.claremont.edu/hmc_facbooks/40
https://scholarship.claremont.edu/hmc_facbooks/40Tue, 21 Mar 2017 14:40:28 PDT
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.
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Bowen Kerins et al.Applications of Algebra and Geometry to the Work of Teaching
https://scholarship.claremont.edu/hmc_facbooks/39
https://scholarship.claremont.edu/hmc_facbooks/39Tue, 21 Mar 2017 14:00:37 PDT
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.
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Bowen Kerins et al.The Magic of Math: Solving for x and Figuring Out Why
https://scholarship.claremont.edu/hmc_facbooks/38
https://scholarship.claremont.edu/hmc_facbooks/38Tue, 28 Feb 2017 15:08:14 PSTThe 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.
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Arthur BenjaminThe Fascinating World of Graph Theory
https://scholarship.claremont.edu/hmc_facbooks/37
https://scholarship.claremont.edu/hmc_facbooks/37Tue, 28 Feb 2017 14:43:41 PST
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.
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Arthur Benjamin et al.The Art of Mental Calculation: Addiction & Subtraction
https://scholarship.claremont.edu/hmc_facbooks/36
https://scholarship.claremont.edu/hmc_facbooks/36Tue, 28 Feb 2017 14:10:33 PST
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.
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Arthur Benjamin et al.Solid Mechanics: A Variational Approach, Augmented Edition
https://scholarship.claremont.edu/hmc_facbooks/31
https://scholarship.claremont.edu/hmc_facbooks/31Mon, 03 Feb 2014 11:35:48 PSTSolid 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.
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Clive L. Dym et al.Analytical Estimates of Structural Behavior
https://scholarship.claremont.edu/hmc_facbooks/30
https://scholarship.claremont.edu/hmc_facbooks/30Mon, 03 Feb 2014 11:35:47 PST
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.
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Clive L. Dym et al.An Introduction to Engineering Mechanics: A Continuum Approach
https://scholarship.claremont.edu/hmc_facbooks/29
https://scholarship.claremont.edu/hmc_facbooks/29Mon, 03 Feb 2014 11:35:44 PST
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.
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Jenn Stroud Rossmann et al.Principles of Mathematical Modeling
https://scholarship.claremont.edu/hmc_facbooks/28
https://scholarship.claremont.edu/hmc_facbooks/28Mon, 03 Feb 2014 11:35:41 PST
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.
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Clive L. DymEngineering Design: A Project-Based Introduction
https://scholarship.claremont.edu/hmc_facbooks/27
https://scholarship.claremont.edu/hmc_facbooks/27Mon, 03 Feb 2014 11:35:39 PST
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
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Clive L. Dym et al.Engineering Design: A Project-Based Introduction
https://scholarship.claremont.edu/hmc_facbooks/26
https://scholarship.claremont.edu/hmc_facbooks/26Mon, 03 Feb 2014 11:35:37 PST
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.
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Clive L. Dym et al.Engineering Design: A Project-Based Introduction
https://scholarship.claremont.edu/hmc_facbooks/25
https://scholarship.claremont.edu/hmc_facbooks/25Mon, 03 Feb 2014 11:35:35 PST
Focus on the Methods and Techniques Needed for Conceptual Design Engineering Design: A Project-Based Introduction by Clive L. Dym and Patrick Little introduces conceptual design methods and project management tools in the context of a team working on a design project initiated by a client. Two design projects are consistently drawn upon to illustrate the design methods and management tools. The book also summarizes means of reporting the results of a design project and provides useful insights into team behaviors and dynamics. The Design Process This extended, five-stage, "linear" model of the design process is integrated throughout the text. Following the steps outlined in this model allows the reader to learn how to examine the problem at hand and develop an effective design solution. This includes developing an engineering statement of what the client wants, progressing through several design stages, and finally documenting the fabrication specifications and their justification.
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Clive L. Dym et al.Engineering Design: A Project-Based Introduction
https://scholarship.claremont.edu/hmc_facbooks/24
https://scholarship.claremont.edu/hmc_facbooks/24Mon, 03 Feb 2014 11:25:37 PST
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.
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Clive L. Dym et al.Engineering Design: Representation and Reasoning
https://scholarship.claremont.edu/hmc_facbooks/23
https://scholarship.claremont.edu/hmc_facbooks/23Mon, 03 Feb 2014 11:25:35 PST
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.
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Clive L. Dym et al.Fundamentals of Modeling and Analyzing Engineering Systems
https://scholarship.claremont.edu/hmc_facbooks/22
https://scholarship.claremont.edu/hmc_facbooks/22Mon, 03 Feb 2014 11:25:34 PST
This text, aimed at beginning engineering students, offers a broad-based introduction to engineering systems that incorporates material from mechanical, electrical, aerospace, and chemical engineering. The overall theme that distinguishes the text from others is its unified treatment of disparate physical systems, emphasizing similarities in both the modeling and behavior of lumped-element systems. Chapters cover linear graph theory, analysis of system dynamics organized by behavioral characteristics rather than by engineering subdisciplines, the Laplace transform, and feedback systems. Every chapter includes examples and exercise problems, drawn from real-world mechanical, electrical, hydraulic, chemical, and thermal systems.
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Philip D. Cha et al.Structural Modeling and Analysis
https://scholarship.claremont.edu/hmc_facbooks/21
https://scholarship.claremont.edu/hmc_facbooks/21Mon, 03 Feb 2014 11:25:32 PST
The study of structural analysis and design is a central subject in civil, aeronautical, and mechanical engineering. This book presents a modern and unified introduction to structural analysis, with a strong emphasis on how structures actually behave. The unifying theme is the application of energy methods, developed without the formal mathematics of the calculus of variations. The energy approach makes it possible to articulate the logical relationship between equilibrium and compatibility; emphasize the unity of structural analysis, particularly for indeterminate structures; and identify the roles of idealization and discretization in structural modeling. Thus, energy methods also serve as a prelude to the main ideas behind modern computational approaches to structural analysis and design. As an aid to upper-level undergraduate students in mastering this material, the text includes numerous worked examples, as well as homework problems.
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Clive L. DymEngineering Design: A Synthesis of Views
https://scholarship.claremont.edu/hmc_facbooks/20
https://scholarship.claremont.edu/hmc_facbooks/20Mon, 03 Feb 2014 11:25:30 PST
Design is a central activity in engineering. It is both a creative process not easily defined and a thought process that can, with increasing success, be externalized, articulated, and modeled. This book aims to clarify the issues, providing an operational definition of engineering design and an explication of design as a discipline. In particular, the book focuses on the contribution of AI (artificial intelligence) to engineering design. With its clear presentation of the main ideas of recent AI-based models of design, set within the context of inductive design models, the book offers an integrated view of current thinking about design. Also included is a brief review of some key AI-based problem-solving methods and classical design tools. The author closes with a look ahead at the roles that symbolic representation and knowledge-based (expert) systems can play in engineering design in practice and in education.
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Clive L. DymEnergy and Finite Element Methods in Structural Mechanics
https://scholarship.claremont.edu/hmc_facbooks/19
https://scholarship.claremont.edu/hmc_facbooks/19Mon, 03 Feb 2014 11:25:29 PST
This book is the outcome of material used in senior and graduate courses for students in civil, mechanical and aeronautical engineering. To meet the needs of this varied audience, the author have laboured to make this text as flexible as possible to use.consequently, the book is divided into three distinct parts of approximately equal size. Part I is entitled foundations of solid mechanics and variational methods, part II is entitled structural mechanics; and part III is entitled finite elements.depending on the background of the students and the aims of the course selected portions can be used from some or all of the three parts of the text to form the basis of an individual course.the purpose of this useful book is to afford the student a sound foundation in variational calculus and energy methods before delving into finite elements. He goal is to make finite elements more understandable in terms of fundamentals and also to provide the student with the background needed to extrapolate the finite element method to areas of study other than solid mechanics. In addition, a number of approximation techniques are made available using the quadratic functional for a boundary-value problem.finally, the authors; aim is to give students who go through the entire text a balanced and connected exposure to certain key aspects of modern structural and solid mechanics.
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Irving H. Shames et al.