Copyright Year 2021
ISBN 9781032021799
ISBN 9781032007816 Paperback
June 29, 2021 Forthcoming by Chapman and Hall/CRC
248 Pages 69 B/W Illustrations
This book illustrates how MAPLE can be used to supplement a standard, elementary text in ordinary and partial differential equation. MAPLE is used with several purposes in mind.
The authors are firm believers in the teaching of mathematics as an experimental science where the student does numerous calculations and then synthesizes these experiments into a general theory.
Projects based on the concept of writing generic programs test a student's understanding of the theoretical material of the course. A student who can solve a general problem certainly can solve a specialized problem. The authors show MAPLE has a built-in program for doing these problems. While it is important for the student to learn MAPLE? in built programs, using these alone removes the student from the conceptual nature of differential equations.
The goal of the book is to teach the students enough about the computer algebra system MAPLE so that it can be used in an investigative way. The investigative materials which are present in the book are done in desk calculator mode DCM, that is the calculations are in the order command line followed by output line. Frequently, this approach eventually leads to a program or procedure in MAPLE designated by proc and completed by end proc.
This book was developed through ten years of instruction in the differential equations course.
1. Introduction to the Maple DEtools
2. First-order Differential Equations
3. Numerical Methods for First Order Equations
4. The Theory of Second Order Differential Equations with Con-
5. Applications of Second Order Linear Equations
6. Two-Point Boundary Value Problems, Catalytic Reactors and
7. Eigenvalue Problems
8. Power Series Methods for Solving Differential Equations
9. Nonlinear Autonomous Systems
10. Integral Transforms
Robert P. Gilbert holds a Ph.D. in mathematics from Carnegie Mellon University. He and Jerry Hile originated the method of generalized hyperanalytic function theory. Dr. Gilbert was professor at Indiana University, Bloomington and later became the Unidel Foundation Chair of Mathematics at the University of Delaware. He has published over 300 articles in professional journals and conference proceedings. He is the Founding Editor of two mathematics journals Complex Variables and Applicable Analysis. He is a three-time Awardee of the Humboldt-Preis, and. received a British Research Council award to do research at Oxford University. He is also the recipient of a Doctor Honoris Causa from the I. Vekua Institute of Applied Mathematics at Tbilisi State University.
George C. Hsiao holds a doctorate degree in Mathematics from Carnegie Mellon University. Dr. Hsiao is the Carl J. Rees Professor of Mathematics Emeritus at the University of Delaware from which he retired after 43 years on the faculty of the Department of Mathematical Sciences. Dr. Hsiao was also the recipient of the Francis Alison Faculty Award, the University of Delaware’s most prestigious faculty honor, which was bestowed on him in recognition of his scholarship, professional achievement and dedication. His primary research interests are integral equations and partial differential equations with their applications in mathematical physics and continuum mechanics. He is the author or co-author of more than 200 publications in books and journals. Dr. Hsiao is world-renowned for his expertise in Boundary Element Method and has given invited lectures all over the world.
Robert J. Ronkese holds a PhD in applied mathematics from the University of Delaware. He is a professor of mathematics at the US Merchant Marine Academy on Long Island. As an undergraduate, he was an exchange student at the Swiss Federal Institute of Technology (ETH) in Zurich. He has held visiting positions at the US Military Academy at West Point and at the University of Central Florida in Orlando.
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Copyright Year 2021
ISBN 9780367563035
ISBN 9780367565084 paperback
June 23, 2021 Forthcoming by Chapman and Hall/CRC
424 Pages 98 B/W Illustrations
Algebra & Geometry: An Introduction to University Mathematics provides a bridge between high school and undergraduate mathematics courses on algebra and geometry. The author shows students how mathematics is more than a collection of methods by presenting important ideas and their historical origins throughout the text. He incorporates a hands-on approach to proofs and connects algebra and geometry to various applications.
The text focuses on linear equations, polynomial equations, and quadratic forms. The first few chapters cover foundational topics, including the importance of proofs and a discussion of the properties commonly encountered when studying algebra. The remaining chapters form the mathematical core of the book. These chapters explain the solution of different kinds of algebraic equations, the nature of the solutions, and the interplay between geometry and algebra.
Several updated chapters, plus an all new chapter discussing the construction of the real numbers by means of approximations by rational numbers
Includes fifteen short ‘essays’ that are accessible to undergraduate readers, but which direct interested students to more advanced developments of the material
Expanded references.
Prolegomena. Section I. Ideas. 1. The Nature of Mathematics. 1.1. Mathematics in History. 1.2. Mathematics Today. 1.3. The Scope of Mathematics. 1.4. What They (Probably) Didn’t Tell You in School. 1.5. Further Reading. 2. Proofs. 2.1. Mathematical Truth. 2.2. Fundamental Assumption of Logic. 2.3. Five Easy Proofs. 2.4. Axioms. 2.5. Un Petit Peu De Philosophie. 2.6. Mathematical Creativity. 2.7. Proving Something False. 2.8. Terminology. 2.9. Advice on Proofs. 3. Foundations. 3.1. Sets. 3.2 Boolean Proofs. 3.3. Relations. 3.4. Functions. 3.5. Equivalence Relations. 3.6. Order Relations. 3.7. Quantifiers. 3.8. Proofs by Inductions. 3.9. Counting. 3.10. Infinite Numbers. 4. Algebra Redux. 4.1. Rules of the Game. 4.2. Algebraic Axioms for Real Numbers. 4.3. Solving Quadratic Equations. 4.4. Binomial Theorem. 4.5. Boolean Algebras. Characterizing Real Numbers. Section II. Theories. 5. Number Theory. 5.1. Remainder Theorem. 5.2. Greatest Common Divisors. 5.3. Fundamental Theorem of Arithmetic. 5.5. Continued Fractions. 6. Complex Numbers. 6.1. Complex Number Arithmetic. 6.2. Complex Number Geometry. 6.3 Euler’s Formula for Complex Numbers. 7. Polynomials. 7.1. Terminology. 7.2. The Remainder Theorem. 7.3. Roots of Polynomials. 7.4. Fundamental Theorem of Algebra. 7.5. Arbitrary Roots of Complex Number. 7.6. Greatest Common Divisors of Complex Numbers. 7.7. Irreducible Polynomials. 7.8 Partial Fractions. 7.9. Radical Solutions. 7.10. Algebraic and Transcendental Numbers. 7.11. Modular Arithmetic with Polynomials. 8. Matrices. 8.1. Matrix Arithmetic. 8.2. Matrix Algebra. 8.3. Solving Systems of Linear Equations. 8.4. Determinants. 8.5. Invertible Matrices. 8.6. Diagonalization. 8.7. Blankinship’s Algorithm. 9. Vectors. 9.1. Vectors Geometrically. 9.2. Vectors Algebraically. 9.3. Geometric Meaning of Determinants. 9.4. Geometry with Vectors. 9.5. Linear Functions. Algebraic Meaning of Determinants. 9.7. Quaternions. 10. The Principal Axis Theorem. 10.1. Orthogonal Matrices. 10.2. Orthogonal Diagonalization. 10.3. Conics and Quadrics. 11. What are the Real Numbers? 11.1 The Properties of the Real Numbers. 11.2. Approximating Real Numbers by Rational Numbers. 11.3. A Construction of the Real Numbers. Epilegomena. Bibliography. Index.
Mark V. Lawson is a professor in the Department of Mathematics at Heriot-Watt University. Prof. Lawson has published over 70 papers and has given seminars on his research work both at home and abroad. His research interests focus on algebraic semigroup theory and its applications. In 2017, he was awarded the Mahoney-Neumann-Room prize by the Australian Mathematical Society for one of his papers.
Copyright Year 2021
ISBN 9780367820435
June 29, 2021 Forthcoming by Chapman and Hall/CRC
516 Pages 95 B/W Illustrations
Many experiments have shown the human brain generally has very serious problems dealing with probability and chance. A greater understanding of probability can help develop the intuition necessary to approach risk with the ability to make more informed (and better) decisions.
The first four chapters offer the standard content for an introductory probability course, albeit presented in a much different way and order. The chapters afterward include some discussion of different games, different "ideas" that relate to the law of large numbers, and many more mathematical topics not typically seen in such a book. The use of games is meant to make the book (and course) feel like fun!
Since many of the early games discussed are casino games, the study of those games, along with an understanding of the material in later chapters, should remind you that gambling is a bad idea; you should think of placing bets in a casino as paying for entertainment. Winning can, obviously, be a fun reward, but should not ever be expected.
New chapter on Game Theory
New chapter on Sports Mathematics
The chapter on Blackjack, which was Chapter 4 in the first edition, appears later in the book.
Reorganization has been done to improve the flow of topics and learning.
New sections on Arkham Horror, Uno, and Scrabble have been added.
Even more exercises were added!
The goal for this textbook is to complement the inquiry-based learning movement. In my mind, concepts and ideas will stick with the reader more when they are motivated in an interesting way. Here, we use questions about various games (not just casino games) to motivate the mathematics, and I would say that the writing emphasizes a "just-in-time" mathematics approach. Topics are presented mathematically as questions about the games themselves are posed.
Preface
1. Mathematics and Probability
2. Roulette and Craps: Expected Value
3. Counting: Poker Hands
4. More Dice: Counting and Combinations, and Statistics
5. Game Theory: Poker Bluffing and Other Games
6. Probability/Stochastic Matrices: Board Game Movement
7. Sports Mathematics: Probability Meets Athletics
8. Blackjack: Previous Methods Revisited
9. A Mix of Other Games
10. Betting Systems: Can You Beat the System?
11. Potpourri: Assorted Adventures in Probability
Appendices
Tables
Answers and Selected Solutions
Bibliography
Dr. David G. Taylor is a professor of mathematics and an associate dean for academic affairs at Roanoke College in southwest Virginia. He attended Lebanon Valley College for his B.S. in computer science and mathematics and went to the University of Virginia for his Ph.D. While his graduate school focus was on studying infinite dimensional Lie algebras, he started studying the mathematics of various games in order to have a more undergraduate-friendly research agenda. Work done with two Roanoke College students, Heather Cook and Jonathan Marino, appears in this book! Currently he owns over 100 different board games and enjoys using probability in his decision-making while playing most of those games. In his spare time, he enjoys reading, cooking, coding, playing his board games, and spending time with his six-year-old dog Lilly.
Copyright Year 2021
ISBN 9780367486846
June 23, 2021 Forthcoming by Chapman and Hall/CRC
440 Pages 60 B/W Illustrations
The book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. These students tend not to realize the importance of linear algebra in applied sciences since traditional linear algebra courses tend to cover mathematical contexts but not the computational aspect of linear algebra or its applications to data science and bioinformatics.
The author presents the topics in a traditional course yet offers lectures as well as lab exercises on simulated and empirical data sets. This textbook provides students a theoretical basis which can then be applied to the practical R and Python problems, providing the tools needed for real-world applications.
Each section starts with working examples to demonstrate how tools from linear algebra can help solve problems in applied science. These exercises start from easy computations, such as computing determinants of matrices, to practical applications on simulated and empirical data sets with R so that students learn how to get started with R along with computational examples in each section and then they learn how to apply what they learn to problems in applied sciences.
This book is designed from first principles to demonstrate the importance of linear algebra through working computational examples with R and python including tutorials on how to install R in the Appendix. If a student has never seen R, they can get started without any additional help.
Since Python is one of the most popular languages in data science, optimization, and computer science, code supplements are available for students who feel more comfortable with Python. R is used primarily for computational examples to develop student’s practical computational skills.
Preface
List of Figures
List of Tables
1. Systems of Linear Equations and Matrices
2. Matrix Arithmetic
3. Deteminants
4. Vector Spaces
5. Inner Product Space
6. Eigen values and Eigen vectors
7. Linear Regression
8. Linear Programming
Network Analysis
Appendices
A) Introduction to RStudio via Amazon Web Service (AWS)
B) Introduction to R
Bibliography
Index
Dr. Ruriko Yoshida is an Associate Professor of Operations Research at the Naval Postgraduate School. She received her Ph.D. in Mathematics from the University of California, Davis. Her research topics cover a wide variety of areas: applications of algebraic combinatorics to statistical problems such as statistical learning on non-Euclidean spaces, sensor networks, phylogenetics, and phylogenomics. She teaches courses in statistics, stochastic models, probability, and data science.
Copyright Year 2021
ISBN 9780367507848
July 7, 2021 Forthcoming by A K Peters/CRC Press
592 Pages 319 B/W Illustrations
Linear algebra is growing in importance. 3D entertainment, animations in movies and video games are developed using linear algebra. Animated characters are generated using equations straight out of this book. Linear algebra is used to extract knowledge from the massive amounts of data generated from modern technology.
The Fourth Edition of this popular text introduces linear algebra in a comprehensive, geometric, and algorithmic way. The authors start with the fundamentals in 2D and 3D, then move on to higher dimensions, expanding on the fundamentals and introducing new topics, which are necessary for many real-life applications and the development of abstract thought. Applications are introduced to motivate topics.
The subtitle, A Geometry Toolbox, hints at the book’s geometric approach, which is supported by many sketches and figures. Furthermore, the book covers applications of triangles, polygons, conics, and curves. Examples demonstrate each topic in action.
This practical approach to a linear algebra course, whether through classroom
instruction or self-study, is unique to this book
Ten new application sections.
A new section on change of basis. This concept now appears in several places.
Chapters 14-16 on higher dimensions are notably revised.
A deeper look at polynomials in the gallery of spaces.
Introduces the QR decomposition and its relevance to least squares.
Similarity and diagonalization are given more attention as are eigenfunctions.
A longer thread on least squares, running from orthogonal projections to a solution via SVD and the pseudoinverse.
More applications for PCA have been added.
More examples, exercises, and more on the kernel and general linear spaces.
A list of applications has been added in Appendix A.
The book gives instructors the option of tailoring the course for the primary interests of their students: mathematics, engineering, science, computer graphics, and geometric modeling.
Preface
Descartes’ Discovery
Here and There: Points and Vectors in 2D
Lining Up: 2D Lines
Changing Shapes: Linear Maps in 2D
2 × 2 Linear Systems
Moving Things Around: A?ne Maps in 2D
Eigen Things
3D Geometry
Linear Maps in 3D
A?ne Maps in 3D
Interactions in 3D
Gauss or Linear Systems
Alternative System Solvers
General Linear Spaces
Eigen Things Revisited
The Singular Value Decomposition
Breaking It Up: Triangles
Putting Lines Together: Polylines and Polygons
Conics
Curves
Appendices
Gerald Farin (deceased) was a professor in the School of Computing, Informatics, and Design Systems Engineering (CIDSE) at Arizona State University. He received his doctoral degree in mathematics from the University of Braunschweig, Germany. His extensive experience in geometric design started at Daimler-Benz. He was a founding member of the editorial board for the journal Computer-Aided Geometric Design (Elsevier), and he served as co-editor in chief for more than 20 years. He published more than 100 research papers. Gerald also organized numerous conferences and authored or edited 29 books. This includes his much read and referenced textbook Curves and Surfaces for CAGD and his book on NURBS. In addition to this book, Gerald and Dianne co-authored The Essentials of CAGD, Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press.
Dianne Hansford, received her Ph.D. from Arizona State University. Her research interests are in the field of geometric modeling with a focus on industrial curve and surface applications related to mathematical definitions of shape. Together with Gerald Farin (deceased), she delivered custom software solutions, advisement on best practices, and taught on-site courses as a consultant. She is a co-founder of 3D Compression Technologies. She is now lecturer in the School of Computing, Informatics, and Design Systems Engineering (CIDSE) at Arizona State University, primarily teaching geometric design, computer graphics, and scientific computing and visualization. In addition to this book, Gerald and Dianne co-authored The Essentials of CAGD, Mathematical Principles for Scientific Computing and Visualization both also published by AK Peters/CRC Press.