Copyright Year 2021
ISBN 9780367743758
March 16, 2021 Forthcoming by Chapman and Hall/CRC
435 Pages 521 B/W Illustrations
Graph theory is the study of interactions, conflicts, and connections. The relationship between collections of discrete objects can inform us about the overall network in which they reside, and graph theory can provide an avenue for analysis.
This text, for the first undergraduate course, will explore major topics in graph theory from both a theoretical and applied viewpoint. Topics will progress from understanding basic terminology, to addressing computational questions, and finally ending with broad theoretical results.
Examples and exercises will guide the reader through this progression, with particular care in strengthening proof techniques and written mathematical explanations.
Current applications and exploratory exercises are provided to further the reader's mathematical reasoning and understanding of the relevance of graph theory to the modern world.
The first chapter introduces graph terminology, mathematical modeling using graphs, and a review of proof techniques featured throughout the book
The second chapter investigates three major route problems: eulerian circuits, hamiltonian cycles, and shortest paths.
The third chapter focuses entirely on trees - terminology, applications, and theory.
Four additional chapters focus around a major graph concept: connectivity, matching, coloring, and planarity. Each chapter brings in a modern application or approach.
Hints and Solutions to selected exercises provided at the back of the book.
Chapter 1: Graph Models, Terminology, and Proofs
Chapter 2: Graph Routes
Chapter 3: Trees
Chapter 4: Connectivity and Flow
Chapter 5: Matching and Factors
Chapter 6: Graph Coloring
Chapter 7: Planarity
Appendix
Selected Hints and Solutions
Dr. Karin R. Saoub is an Associate Professor of Mathematics at Roanoke College in Salem, Virginia. She received her PhD in Mathematics from Arizona State University and a Bachelor of Arts degree from Wellesley College. Her research focuses on graph coloring and on-line algorithms applied to tolerance graphs. She is also the author of A Tour Through Graph Theory, published by CRC Press.
Copyright Year 2021
ISBN 9780367684730
March 4, 2021 Forthcoming by Chapman and Hall/CRC
288 Pages 29 B/W Illustrations
Book Description
This book is intended for a first linear algebra course. The text includes all essential topics in a concise manner and can therefore be fully covered in a one term course. After this course, the student is fully equipped to specialize further in their direction(s) of choice (advanced pure linear algebra, numerical linear algebra, optimization, multivariate statistics, or one of the many other areas of linear algebra applications).
Linear Algebra is an exciting area of mathematics that is gaining more and more importance as the world is becoming increasingly digital. It has the following very appealing features:
It is a solid axiomatic based mathematical theory that is accessible to a large variety of students.
It has a multitude of applications from many different fields, ranging from traditional science and engineering applications to more edaily lifef applications (internet searches, guessing consumer preferences, etc.).
It easily allows for numerical experimentation through the use of a variety of readily available software (both commercial and open source).
This book incorporates all these aspects throughout the whole text with the intended effect that each student can find their own niche in the field.
Several suggestions of different software are made. While MATLAB is certainly still a favorite choice, open source programs such as Sage (especially among algebraists) and the Python libraries are increasingly popular. This text guides the student through different programs by providing specific commands.
Table of Contents
Preface
1 Matrices and Vectors
2 Subspaces in Rn, basis and dimension.
3 Matrix Algebra
4 Determinants
5 Vector Spaces
6 Linear Transformations
7 Eigenvectors and Eigenvalues
8 Orthogonality
Appendix
Index
Author(s)
Hugo J. Woerdeman,@PhD, professor, Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, USA, is also the author of Advanced Linear Algebra, published by CRC Press, and co-author of Matrix Completions, Moments, and Sums of Squares, published by Princeton University Press. He also serves as Vice President of two societies of researchers: The International Linear Algebra Society and The International Workshop on Operator Theory and its Applications.
Copyright Year 2021
ISBN 9780367562182
April 8, 2021 Forthcoming by Chapman and Hall/CRC
256 Pages 19 B/W Illustrations
Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master's or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals etc.)
Offers a self-contained discussion of wavelet theory
Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists
Provides researchers with detailed proofs
Provide guides for readers to help them understand and practice wavelet analysis in different areas.
Chapter 1. Introduction. Chapter 2. Wavelets on Euclidean Spaces. 2.1. Introduction. 2.2. Wavelets on R. 2.3. Multi-Resolution Analysis. 2.4. Wavelet Algorithms. 2.5. Wavelet Basis. 2.6. Multidimensional Real Wavelets. 2.7. Examples of Wavelet Functions and MRA. 2.8. Exercise. 3. Wavelets Extended. 3.1. Affine Group Wavelets. 3.2. Multiresolution Analysis on The Interval. 3.3 Wavelets on The Sphere. 3.4. Exercise. 4. Clifford Wavelets. 4.1. Introduction. 4.2. Different Constructions of Clifford Algebra. 4.3. Graduation in Clifford Algebra. 4.4. Some useful operations of Clifford Algebra. 4.5. Clifford Functional Analysis. 4.6. Existence of Monogenic Extensions. 4.7. Clifford-Fourier Transform. 4.8. Some Experimentations. 4.9. Exercise. 5. Quantum Wavelets. 5.1. Introduction. 5.2. Bessel Functions. 5.3. Bessel Wavelets. 5.4. Fractional Bessel Wavelets. 5.5. Quantum Theory Toolkit. 5.6. Some Quantum Special Functions. 5.7. Quantum Wavelets. 5.8. Exercise. 6. Wavelets in Statistics. 6.1 Introduction. 6.2. Wavelet Analysis of Time Series. 6.3. Wavelet Variance and Covariance. 6.4. Wavelet Decimated and Stationary Transforms. 6.5. Wavelet Density Estimation. 6.6. Wavelet Thresholding. 6.7. Application to Wavelet Density Estimations. 6.8. Exercise. 7. Wavelets for Partial Differential Equations. 7.1. Introduction. 7.2. Wavelet Collocation Method. 7.3. Wavelet Galerkin Approach. 7.4. Reduction of the Connection Coefficients Number. 7.5. Two Main Applications for Solving PDEs. 7.6. Appendix. 7.7. Exercise. 8. Wavelets for Fractal and Multifractal Functions. 8.1. Introduction. 8.2. Hausdorff Measure and Dimension. 8.3. Wavelets for The Regularity Of Functions. 8.4. The Multifractal Formalism. 8.5. Similar Type Functions. 8.6. Application to Financial Index Modeling. 8.7. Appendix. 8.8. Exercise.
Sabrine Arfaoui is the assistant professor of mathematics at the Faculty of Sciences, University of Monastir. Her main interests include wavelet harmonic analysis, especially in the Clifford algebra/analysis framework and their applications in other fields such as fractals, PDEs, bio-signals/bio-images. Currently Dr. Arfaoui is associated with the University of Tabuk, Saudi Arabia in a technical cooperation project.
Anouar Ben Mabrouk is currently working as the professor of mathematics. He is also the associate professor of Mathematics at the University of Kairouan, Tunisia, the Faculty of Sciences, University of Monastir. His main research interests are are wavelets, fractals, probability/statistics, PDEs and related fields such as financial mathematics, time series, image/signal processing, numerical and theoretical aspects of PDEs. Dr. Ben Mabrouk is currently associated with the University of Tabuk, Saudi Arabia in a technical cooperation project.
Carlo Cattani is currently the professor of Mathematical Physics and Applied Mathematics at the Engineering School (DEIM) of University of Tuscia. His scientific interests include but are not limited to wavelets, dynamical systems, fractals, fractional calculus, numerical methods, number theory, stochastic integro-differential equations, competition models, time-series analysis, nonlinear analysis, complexity of living systems, pattern analysis, computational biology, biophysics, history of science. He has (co)authored more than 150 scientific articles on international journals as well as several books.
Copyright Year 2021
ISBN 9780367248963
May 3, 2021 Forthcoming by CRC Press
376 Pages 32 B/W Illustrations
Linear Algebra: An Inquiry-based Approach is written to give instructors a tool to teach students to develop a mathematical concept from first principles. The Inquiry-based Approach is central to this development. The text is organized around and offers the standard topics expected in a first undergraduate course in linear algebra.
In our approach, students begin with a problem and develop the mathematics necessary to describe, solve, and generalize it. Thus students learn a vital skill for the 21st century: the ability to create a solution to a problem.
This text is offered to foster an environment that supports the creative process. The twin goals of this textbook are:
Providing opportunities to be creative,
Teaching "ways of thinking" that will make it easier for to be creative.
To motivate the development of the concepts and techniques of linear algebra, we include more than two hundred Activities on a wide range of problems, from purely mathematical questions, through applications in biology, computer science, cryptography, and more.
Introduction and Features. For the Student . . . and Teacher. Prerequisites. Suggested Sequences. 1. Tuples and Vectors. 1.1. Tuples. 1.2. Vectors. 1.3. Proofs. 1.4. Directed Distances. 1.5. Magnitude. 1.6. Direction. 1.7. Unit and Orthogonal Vectors. 2. Systems of Linear Equations. 2.1. Standard Form. 2.2. Solving Systems. 2.3. Coefficient Matrices. 2.4. Free and Basic Variables. 2.5. Computational Considerations. 2.6. Applications of Linear Algebra. 3. Transformations. 3.1. Geometric Transformations. 3.2. Vector Transformations. 3.3. The Transformation Matrix. 3.4. Domain, Codomain, and Range. 3.5. Discrete Time Models. 3.6. Linear Transformations. 3.7. Transformation Arithmetic. 3.8. Cryptography. 4. Matrix Algebra. 4.1. Scalar Multiplication. 4.2. Matrix Addition. 4.3. Matrix Multiplication. 4.4. Elementary Matrices. 4.5. More Transformations. 4.6. Matrix Inverses. 4.7. Complex Matrices. 5. Vector Spaces. 5.1. Vector Spaces. 5.2. Kernels and Null Spaces. 5.3. Span. 5.4. Linear Independence and Dependence. 5.5. Change of Basis. 5.6. Orthogonal Bases. 5.7. Normed Vector Spaces. 5.8. Inner Product Spaces. 5.9. Applications. 5.10. Least Squares. 6. Determinants. 6.1. Linear Equations. 6.2. Transformations. 6.3. Inverse. 6.4. The Determinant. 6.5. A Formula for the Determinant. 6.6. The Determinant Formula. 6.7. More Properties of the Determinant. 6.8. More Computations of the Determinant. 6.9. Use(lesses) of the Determinant. 6.10. Uses of the Determinant. 6.11. Permutations. 7. Eigenvalues and Eigenvectors. 7.1. More Transformations. 7.2. The Eigenproblem. 7.3. Finding Eigenvalues: Numerical Methods. 7.4. Eigenvalues and Eigenvectors for a 2 x 2 Matrix. 7.5. The Characteristic Equation. 7.6. Stochastic Matrices. 7.7. A Determinant-Free Approach. 7.8. Generalized Eigenvalues. 7.9. Symmetric Matrices. 7.10. Graphs. 8. Decomposition. 8.1. LU-Decomposition. 8.2. QR-Decomposition. 8.3. Eigendecompositions. 8.4. Singular Value Decomposition. 9. Extras. 9.1. Properties of Polynomials. 9.2. Complex Numbers. 9.3. Mod-N Arithmetic. 9.4. Polar Coordinates. Bibliography. Index.
Jeff Suzuki is Associate Professor of Mathematics at Brooklyn College and holds a Ph.D. from Boston University. His research interests include mathematics education, history of mathematics, and the application of mathematics to society and technology. He is a two-time winner of the prestigious Carl B. Allendoerfer Award for expository writing. His publications have appeared in The College Mathematics Journals; Mathematics Magazine; Mathematics Teacher; and the American Mathematical Society's blog on teaching and learning mathematics. His YouTube channel (http://youtube.com/jeffsuzuki1) includes videos on mathematical subjects ranging from elementary arithmetic to linear algebra, cryptography, and differential equations.