The goal is to record most books written or edited by the Department of Mathematics faculty. We will start by entering the most recent publications first and work our way back to older books. There is a WMU Authors section in Waldo Library, where most of these books can be found.
With a few exceptions, we do not have the rights to put the full text of the book online, so there will be a link to a place where you can purchase the book.
If you are a faculty member and have a book you would like to include in the WMU book list, please contact wmu-scholarworks@wmich.edu/
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Graphs & Digraphs
Gary Chartrand, Ping Zhang, Heather Jordon, and Vincent Vatter
Now streamlined from previous editions, a new author team brings in a fresh look to this classic textbook and at how graph theory courses have evolved. When the first edition of this precursor text was published, there were few undergraduate courses offered. The text assisted in the establishment of the undergraduate course, while also offering enough coverage for a graduate course. Graph theory is not a seminal course in all combinatorics programs taught in universities and colleges throughout the world. This text has remained among the top three best-sellers. The book is famous for the quality of the writing and presentation. We have two best-sellers for his course, including Gross, etal.'s Graph Theory and Its Applications. This one-two punch in this course means we can go against any and all texts and compete successfully.
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Scalar and Vector Risk in the General Framework of Portfolio Theory: A Convex Analysis Approach
Qiji Zhu
This book is the culmination of the authors' industry-academic collaboration in the past several years. The investigation is largely motivated by bank balance sheet management problems. The main difference between a bank balance sheet management problem and a typical portfolio optimization problem is that the former involves multiple risks. The related theoretical investigation leads to a significant extension of the scope of portfolio theories. The book combines practitioners' perspectives and mathematical rigor. For example, to guide the bank managers to trade off different Pareto efficient points, the topological structure of the Pareto efficient set is carefully analyzed. Moreover, on top of computing solutions, the authors focus the investigation on the qualitative properties of those solutions and their financial meanings. These relations, such as the role of duality, are most useful in helping bank managers to communicate their decisions to the different stakeholders. Finally, bank balance sheet management problems of varying levels of complexity are discussed to illustrate how to apply the central mathematical results. Although the primary motivation and application examples in this book are focused in the area of bank balance sheet management problems, the range of applications of the general portfolio theory is much wider. As a matter of fact, most financial problems involve multiple types of risks. Thus, the book is a good reference for financial practitioners in general and students who are interested in financial applications. This book can also serve as a nice example of a case study for applied mathematicians who are interested in engaging in industry-academic collaboration.
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Irregularity in Graphs
Akbar Ali, Gary Chartrand, and Ping Zhang
Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure. During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.
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Chromatic Graph Theory
Gary Chartrand and Ping Zhang
With Chromatic Graph Theory, Second Edition , the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition.
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Elementary mathematics curriculum materials: designs for student learning and teacher enactment
Ok-Kyeong Kim
The book presents comparative analyses of five elementary mathematics curriculum programs used in the U.S. from three different perspectives: the mathematical emphasis, the pedagogical approaches, and how authors communicate with teachers. These perspectives comprise a framework for examining what curriculum materials are comprised of, what is involved in reading and interpreting them, and how curriculum authors can and do support teachers in this process. Although the focus of the analysis is 5 programs used at a particular point in time, this framework extends beyond these specific programs and illuminates the complexity of curriculum materials and their role in teaching in general. Our analysis of the mathematical emphasis considers how the mathematics content is presented in each program, in terms of sequencing, the nature of mathematical tasks (cognitive demand and ongoing practice), and the way representations are used. Our analysis of the pedagogical approach examines explicit and implicit messages about how students should interact with mathematics, one another, the teacher, and the textbook around these mathematical ideas, as well as the role of the teacher. In order to examine how curriculum authors support teachers, we analyze how they communicate with teachers and what they communicate about, including the underlying mathematics, noticing student thinking, and rationale for design elements. The volume includes a chapter on curriculum design decisions based on interviews with curriculum authors.
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Advanced Calculus: Theory and Practice
John Srdjan Petrovic
Advanced Calculus: Theory and Practice, Second Edition, expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book explains how various topics in calculus may seem unrelated but in reality have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems.
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How to Label a Graph
Gary Chartrand, Ping Zhang, and Cooroo Egan
This book depicts graph labelings that have led to thought-provoking problems and conjectures. Problems and conjectures in graceful labelings, harmonious labelings, prime labelings, additive labelings, and zonal labelings are introduced with fundamentals, examples, and illustrations. A new labeling with a connection to the four color theorem is described to aid mathematicians to initiate new methods and techniques to study classical coloring problems from a new perspective. Researchers and graduate students interested in graph labelings will find the concepts and problems featured in this book valuable for finding new areas of research.
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From Domination to Coloring: Stephen Hedetniemi's Graph Theory and Beyond
Gary Chartrand, Ping Zhang, Teresa Haynes, and Michael A. Henning
This book is in honor of the 80th birthday of Stephen Hedetniemi. It describes advanced material in graph theory in the areas of domination, coloring, spanning cycles and circuits, and distance that grew out of research topics investigated by Stephen Hedetniemi. The purpose of this book is to provide background and principal results on these topics, along with same related problems and conjectures, for researchers in these areas. The most important features deal with material, results, and problems that researchers may not be aware of but may find of interest. Each chapter contains results, methods and information that will give readers the necessary background to investigate each topic in more detail.
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Convex Duality and Financial Mathematics
Peter Carr and Qiji Zhu
This book provides a concise introduction to convex duality in financial mathematics.Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization. Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims
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Convex Duality and Financial Mathematics
Peter Carr and Qiji Jim Zhu
This book provides a concise introduction to convex duality in financial mathematics. Convex duality plays an essential role in dealing with financial problems and involves maximizing concave utility functions and minimizing convex risk measures. Recently, convex and generalized convex dualities have shown to be crucial in the process of the dynamic hedging of contingent claims. Common underlying principles and connections between different perspectives are developed; results are illustrated through graphs and explained heuristically. This book can be used as a reference and is aimed toward graduate students, researchers and practitioners in mathematics, finance, economics, and optimization.
Topics include: Markowitz portfolio theory, growth portfolio theory, fundamental theorem of asset pricing emphasizing the duality between utility optimization and pricing by martingale measures, risk measures and its dual representation, hedging and super-hedging and its relationship with linear programming duality and the duality relationship in dynamic hedging of contingent claims.
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Mathematical Proofs: A Transition to Advanced Mathematics
Gary Chartrand, Albert D. Polimeni, and Ping Zhang
Mathematical Proofs: A Transition to Advanced Mathematics, 4th Edition introduces students to proof techniques, analyzing proofs, and writing proofs of their own that are not only mathematically correct but clearly written. Written in a student-friendly manner, it provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as optional excursions into fields such as number theory, combinatorics, and calculus. The exercises receive consistent praise from users for their thoughtfulness and creativity. They help students progress from understanding and analyzing proofs and techniques to producing well-constructed proofs independently. This book is also an excellent reference for students to use in future courses when writing or reading proofs.
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Knowledge and Interaction: A Synthetic Agenda for the Learning Sciences
Mariana Levin
Decades of research in the cognitive and learning sciences have led to a growing recognition of the incredibly multi-faceted nature of human knowing and learning. Up to now, this multifaceted nature has been visible mostly in distinct and often competing communities of researchers. From a purely scientific perspective, "siloed" science--where different traditions refuse to speak with one another, or merely ignore one another--is unacceptable. This ambitious volume attempts to kick-start a serious, new line of work that merges, or properly articulates, different traditions with their divergent historical, theoretical, and methodological commitments that, nonetheless, both focus on the highly detailed analysis of processes of knowing and learning as they unfold in interactional contexts in real time. Knowledge and Interaction puts two traditions in dialogue with one another: Knowledge Analysis (KA), which draws on intellectual roots in developmental psychology and cognitive modeling and focuses on the nature and form of individual knowledge systems, and Interaction Analysis (IA), which has been prominent in approaches that seek to understand and explain learning as a sequence of real-time moves by individuals as they interact with interlocutors, learning environments, and the world around them. The volume's four-part organization opens up space for both substantive contributions on areas of conceptual and empirical work as well as opportunities for reflection, integration, and coordination.
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The Fascinating World of Graph Theory
Arthur Benjamin, Gary Chartrand, and Ping Zhang
The fascinating world of 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. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory's development and the vibrant individuals responsible for the field's growth.
Introducing graph theory's fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight's Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor.
An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.
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Graphs & Digraphs
Ping Zhang
Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text: Adds more than 160 new exercises Presents many new concepts, theorems, and examples Includes recent major contributions to long-standing conjectures such as the Hamiltonian Factorization Conjecture, 1-Factorization Conjecture, and Alspachs Conjecture on graph decompositions Supplies a proof of the perfect graph theorem Features a revised chapter on the probabilistic method in graph theory with many results integrated throughout the text At the end of the book are indices and lists of mathematicians¿ names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numbered exercises. A complete solutions manual is available with qualifying course adoption. Graphs & Digraphs, Sixth Edition remains the consummate text for an advanced undergraduate level or introductory graduate level course or two-semester sequence on graph theory, exploring the subjects fascinating history while covering a host of interesting problems and diverse applications.
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Advanced Calculus: Theory and Practice
John Srdjan Petrovic
Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves studentse(tm) problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics.
The book takes a motivating approach that makes ideas less abstract to students. It explains how various topics in calculus may seem unrelated but in reality have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems as well as help students develop the necessary skills to closely examine the theorems. Proofs are also presented in an accessible way to students.
By strengthening skills gained through elementary calculus, this textbook leads students toward mastering calculus techniques. It will help them succeed in their future mathematical or engineering studies.
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Mathematical Proofs: A Transition to Advanced Mathematics
Gary Chartrand, Albert Polimeni, and Ping Zhang
Mathematical Proofs: A Transition to Advanced Mathematics, Third Edition, prepares students for the more abstract mathematics courses that follow calculus. Appropriate for self-study or for use in the classroom, this text introduces students to proof techniques, analyzing proofs, and writing proofs of their own. Written in a clear, conversational style, this book provides a solid introduction to such topics as relations, functions, and cardinalities of sets, as well as the theoretical aspects of fields such as number theory, abstract algebra, and group theory. It is also a great reference text that students can look back to when writing or reading proofs in their more advanced courses.
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Introduction to Mathematical Statistics
Robert V. Hogg, Joseph W. McKean, and Allen T. Craig
Introduction to Mathematical Statistics, Seventh Edition, offers a proven approach designed to provide you with an excellent foundation in mathematical statistics. Ample examples and exercises throughout the text illustrate concepts to help you gain a solid understanding of the material.
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Graphs & Diagraphs
Gary Chartrand, Ping Zhang, and Linda Lesniak
Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics.
New to the Fifth Edition
- New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings
- New examples, figures, and applications to illustrate concepts and theorems
- Expanded historical discussions of well-known mathematicians and problems
- More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book
- Reorganization of sections into subsections to make the material easier to read
- Bolded definitions of terms, making them easier to locate
Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject’s fascinating history and presents a host of interesting problems and diverse applications.
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Modern Classical Homotopy Theory
Jeffrey Strom
The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.
From Amazon.com
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Discrete Mathematics
Ping Zhang and Gary Chartrand
Chartrand and Zhang's Discrete Mathematics presents a clearly written, student-friendly introduction to discrete mathematics. The authors draw from their background as researchers and educators to offer lucid discussions and descriptions fundamental to the subject of discrete mathematics. Unique among discrete mathematics textbooks for its treatment of proof techniques and graph theory, topics discussed also include logic, relations and functions (especially equivalence relations and objective functions), algorithms and analysis of algorithms, introduction to number theory, combinatorics (counting, the Pascal triangle, and the binomial theorem), discrete probability, partially ordered sets, lattices and Boolean algebras, cryptography, and finite-state machines. This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business. Some of the major features and strengths of this textbook: Numerous carefully explained examples and applications facilitate learning, More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises, Descriptions of proof techniques are accessible and lively, Students benefit from the historical discussions throughout the textbook, An Instructor's Solutions Manual contains complete solutions to all exercises.
From Amazon.com
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A 5-Year Study of the First Edition of the Core-Plus Mathematics Curriculum
Harold Schoen, Steven Ziebarth, and Christian R. Hirsch
A volume in Research in Mathematics Education Series Editor Barbara J. Dougherty, Iowa State University The study reported in this volume adds to the growing body of evaluation studies that focus on the use of NSF-funded Standards-based high school mathematics curricula. Most previous evaluations have studied the impact of field-test versions of a curriculum. Since these innovative curricula were so new at the time of many of these studies, students and teachers were relative novices in their use. These earlier studies were mainly one year or less in duration. Students in the comparison groups were typically from schools in which some classes used a Standards-based curriculum and other classes used a conventional curriculum, rather than using the Standards-based curriculum with all students as curriculum developers intended. This volume reports one of the first studies of the efficacy of Standards-based mathematics curricula with all of the following characteristics: · The study focused on fairly stable implementations of a first-edition Standards-based high school mathematics curriculum that was used by all students in each of three schools. · It involved students who experienced up to seven years of Standards-based mathematics curricula and instruction in middle school and high school. · It monitored students’ mathematical achievement, beliefs, and attitudes for four years of high school and one year after graduation. Prior to the study, many of the teachers had one or more years of experience teaching the Standards-based curriculum and/or professional development focusing on how to implement the curriculum well. · In the study, variations in levels of implementation of the curriculum are described and related to student outcomes and teacher behavior variables. Item data and all unpublished testing instruments from this study are available at www.wmich.edu/ cpmp/evaluation.html for use as a baseline of instruments and data for future curriculum evaluators or Core-Plus Mathematics users who may wish to compare results of new groups of students to those in the present study on common tests or surveys. Taken together, this volume, the supplement at the CPMP Web site, and the first edition Core-Plus Mathematics curriculum materials (samples of which are also available at the Web site) serve as a fairly complete description of the nature and impact of an exemplar of first edition NSF-funded Standards-based high school mathematics curricula as it existed and was implemented with all students in three schools around the turn of the 21st century. (description from amazon.com)
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Chromatic Graph Theory
Gary Chartrand and Ping Zhang
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.
This self-contained book first presents various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. The remainder of the text deals exclusively with graph colorings. It covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings, and many distance-related vertex colorings.
With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.
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Mathematical Proofs: A Transition to Advanced Mathematics (2nd Edition)
Gary Chartrand, Albert D. Polimeni, and Ping Zhang
Mathematical Proofs: A Transition to Advanced Mathematics, 2/e,prepares students for the more abstract mathematics courses that follow calculus. This text introduces students to proof techniques and writing proofs of their own. As such, it is an introduction to the mathematics enterprise, providing solid introductions to relations, functions, and cardinalities of sets.KEY TOPICS: Communicating Mathematics, Sets, Logic, Direct Proof and Proof by Contrapositive, More on Direct Proof and Proof by Contrapositive, Existence and Proof by Contradiction, Mathematical Induction, Prove or Disprove, Equivalence Relations, Functions, Cardinalities of Sets, Proofs in Number Theory, Proofs in Calculus, Proofs in Group Theory.MARKET: For all readers interested in advanced mathematics and logic.
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Teachers Engaged in Research: Inquiry in Mathematics Classrooms, Grades 9-12
Laura R. Van Zoest
This book provides examples of the ways in which 9-12 grade mathematics teachers from across North America are engaging in research. It offers a glimpse of the questions that capture the attention of teachers, the methodologies that they use to gather data, and the ways in which they make sense of what they find. The focus of these teachers' investigations into mathematics classrooms ranges from students' understanding of content to pedagogical changes to social issues. Underlying the chapters is the common goal of enabling students to develop a deep understanding of the mathematics they learn in their classrooms. By opening their analysis of their classroom practice to our inspection, these courageous teachers have invited us to think along with them and to learn more about our own teaching as a result. By sharing their work, they have given the mathematics education community an important opportunity. Everyone who reads this book-teachers, researchers, teacher-researchers, policy makers, administrators, and others interested in mathematics education-can learn from the findings and the light that they shed on issues important to mathematics education. opportunity to step back and reflect on what can be learned about research from teachers who have engaged in the process. Areas of insight include: (a) the importance of collaboration and participation in communities that value research, (b) the potential of teacher research as a way to warrant teacher practice, (c) the power of video and other artifacts of teaching to support classroom inquiry, (d) connections between teaching and research, and (e) the publication process as professional development.
