Copyright Year 2023
ISBN 9781032424545
March 6, 2023 Forthcoming by A K Peters/CRC Press
210 Pages 90 B/W Illustrations
Mathematical Puzzle Tales from Mount Olympus uses fascinating tales from Greek Mythology as the background for introducing mathematics puzzles to the general public. A background in high school mathematics will be ample preparation for using this book, and it should appeal to anyone who enjoys puzzles and recreational mathematics.
Combines the arts and science, and emphasizes the fact that mathematics straddles both domains.
Great resource for students preparing for mathematics competitions, and the trainers of such students
1. The Boxing Matches. 2. The First and Second Labors of Heracles. 3. The Third and Fourth Labors of Heracles. 4. The Fifth and Sixth Labors of Heracles. 5. The Seventh and Eighth Labors of Heracles. 6. The Ninth and Tenth Labors of Heracles. 7. The Loss of the Pigs. 8. The Planting of Barley. 9. The Fifteen Fruit Pies. 10. The Palace Admittance Questionnaire. 11. The Midas Touch. 12. The Collapsing Beams. 13. The Seating Plan. 14. The Forty-Nine Danaids. 15. The Quarrelsome Residents. 16. The Bears in the Caves. 17. The Phrygian Music Festival. 18. The Banquet Tickets. 19. The Eleventh and Twelfth Labors of Heracles. 20. The Summer Festival. 21. The Great Amoeba Escape. 22. The Rolling Stones. 23. The Conscientious Birds. 24. The Archipelago Tour. 25. The Fireballs and Lightningbolts. 26. The Leaded Spears. 27. The Triangular Palace. 28. The Matching of Boxes and Keys. 29. The Number-and-Coin Tricks. 30. The Unguarded Gate. 31. The Rearrangement of the Suitresses. 32. The Wily Prisoners. 33. The Selection of the Argonauts. 34. The Beef Feast. 35. The Huntersf Competitions. 36. The First Rebellion of the Giants. 37. The Second Rebellion of the Giants. 38. The Third Rebellion of the Giants. 39. The Ungrateful Refugees. 40. The Pandora Box. Appendix Source of the Problems.
January 16, 2023
Paperback ISBN: 9780323954228
The Boolean functions may be iterated either asynchronously, when their coordinates are computed independently of each other, or synchronously, when their coordinates are computed at the same time. In Boolean Systems: Topics in Asynchronicity, a book addressed to mathematicians and computer scientists interested in Boolean systems and their use in modelling, author Serban E. Vlad presents a consistent and original mathematical theory of the discrete-time Boolean asynchronous systems. The purpose of the book is to set forth the concepts of such a theory, resulting from the synchronous Boolean system theory and mostly from the synchronous real system theory, by analogy, and to indicate the way in which known synchronous deterministic concepts generate new asynchronous nondeterministic concepts. The reader will be introduced to the dependence on the initial conditions, periodicity, path-connectedness, topological transitivity, and chaos. A property of major importance is invariance, which is present in five versions. In relation to it, the reader will study the maximal invariant subsets, the minimal invariant supersets, the minimal invariant subsets, connectedness, separation, the basins of attraction, and attractors. The stability of the systems and their time-reversal symmetry end the topics that refer to the systems without input. The rest of the book is concerned with input systems. The most consistent chapters of this part of the book refer to the fundamental operating mode and to the combinational systems (systems without feedback). The chapter Wires, Gates, and Flip-Flops presents a variety of applications. The first appendix addresses the issue of continuous time, and the second one sketches the important theory of Daizhan Cheng, which is put in relation to asynchronicity. The third appendix is a bridge between asynchronicity and the symbolic dynamics of Douglas Lind and Brian Marcus.
April 1, 2023
Paperback ISBN: 9780128234709
Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.
1. Matrices
2. Vector Spaces
3. Linear Transformations
4. Eigenvalues, Eigenvectors, and Differential Equations
5. Euclidean Inner Product
Appendix
A. Determinants
B. Jordan Canonical Forms
C. Markov Chains
D. The Simplex Method, an Example
E. A Word on Numerical Techniques and Technology
Answers And Hints To Selected Problems
Copyright Year 2023
ISBN 9781032330471
December 29, 2022 Forthcoming by Chapman & Hall
428 Pages 146 B/W Illustrations
Probability and statistics courses are more popular than ever. Regardless of your major or your profession, you will most likely use concepts from probability and statistics often in your career.
The primary goal behind this book is offering the flexibility for instructors to build most undergraduate courses upon it. This book is designed for either a one-semester course in either introductory probability and statistics (not calculus-based) and/or a one-semester course in a calculus-based probability and statistics course.
The book focuses on engineering examples and applications, while also including social sciences and more examples. Depending on the chapter flows, a course can be tailored for students at all levels and background.
Over many years of teaching this course, the authors created problems based on real data, student projects, and labs. Students have suggested these enhance their experience and learning. The authors hope to share projects and labs with other instructors and students to make the course more interesting for both.
R is an excellent platform to use. This book uses R with real data sets. The labs can be used for group work, in class, or for self-directed study. These project labs have been class-tested for many years with good results and encourage students to apply the key concepts and use of technology to analyze and present results.
1. Introduction to Statistical Modeling and Models and R
2. Introduction to Data
3. Statistical Measures
4. Classical Probability
5. Discrete Distributions
6. Continuous Probability Models
7. Other Continuous Distribution (some calculus required): Triangular, Unnamed, Beta, Gamma
8. Sampling Distributions
9. Estimating Parameters
10. One Sample Hypothesis Testing
11. Two Sample Hypothesis Testing
12. Reliability Modeling
13. Introduction to Regression Techniques
14. Advanced Regression Models: Nonlinear, Sinusoidal, and Binary Logistics Regression using R
15. ANOVA in R
16. Two-way ANCOVA using R
Copyright Year 2023
ISBN 9781032229478
February 17, 2023 Forthcoming by Chapman & Hall
414 Pages 141 Color Illustrations
This textbook offers a guided tutorial that reviews the theoretical fundamentals
while going through the practical examples used for constructing the computational
frame, applied to various real-life models.
Computational Optimization: Success in Practice will lead the readers through the entire process. They will start with the simple calculus examples of fitting data and basics of optimal control methods and end up constructing a multi-component framework for running PDE-constrained optimization. This framework will be assembled piece by piece; the readers may apply this process at the levels of complexity matching their current projects or research needs.
By connecting examples with the theory and discussing the proper "communication" between them, the readers will learn the process of creating a "big house." Moreover, they can use the framework exemplified in the book as the template for their research or course problems ? they will know how to change the single "bricks" or add extra "floors" on top of that.
This book is for students, faculty, and researchers.
The main optimization framework builds through the course exercises and centers on MATLABR
All other scripts to implement computations for solving optimization problems with various models use only open-source software, e.g., FreeFEM
All computational steps are platform-independent; readers may freely use Windows, macOS, or Linux systems
All scripts illustrating every step in building the optimization framework will be available to the readers online
Each chapter contains problems based on the examples provided in the text and associated scripts. The readers will not need to create the scripts from scratch, but rather modify the codes provided as a supplement to the book
This book will prove valuable to graduate students of math, computer science, engineering, and all who explore optimization techniques at different levels for educational or research purposes. It will benefit many professionals in academic and industry-related research: professors, researchers, postdoctoral fellows, and the personnel of R&D departments.
Chapter 1. Introduction to Optimization
Chapter 2. Minimization Approaches for Functions of One Variable
Chapter 3. Generalized Optimization Framework
Chapter 4. Exploring Optimization Algorithms
Chapter 5. Line Search Algorithms
Chapter 6. Choosing Optimal Step Size
Chapter 7. Trust Region and Derivative-Free Methods
Chapter 8. Large-Scale and Constrained Optimization
Chapter 9. ODE-based Optimization
Chapter 10. Implementing Regularization Techniques
Chapter 11. Moving to PDE-based Optimization
Chapter 12. Sharing Multiple Software Environments