Format: Paperback / softback, 254 pages, height x width: 240x168 mm, 14 Illustrations, color;
1 Illustrations, black and white; XIV, 254 p. 15 illus., 14 illus. in color., 1 Paperback / softback
Series: Oberwolfach Seminars 56
Pub. Date: 29-Jul-2025
ISBN-13: 9783031927300
This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on Computational Variational Flows in Machine Learning and Optimal Transport.
Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
1. A Dynamic Perspective of Optimal Transport.-
2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications.-
3. Wasserstein Dynamics in Mathematical Data Sciences.-
4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.
Format: Hardback, 104 pages, height x width: 240x168 mm, 16 Illustrations, color;
2 Illustrations, black and white; VIII, 104 p. 18 illus., 16 illus. in color., 1 Hardback
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 28-Jul-2025
ISBN-13: 9783031917127
This book presents a concise introduction to real and complex number systems and metric space theory. The goal is to help students bridge the gap between undergraduate courses in advanced calculus and graduate level material in analysis or related subjects such as differential geometry or probability. The unifying feature in all of these subject areas is the predominance of the limit, and metric space theory is the mathematical language in which limits are formulated. To understand analysis at a graduate level, students need to develop fluency in this language. To facilitate this development, exercises are incorporated into the main text, with many key results posed as problems. Solutions are provided to help readers fill in any gaps.
Real Numbers.- Complex Numbers and Series.- Metric Topology.- Functions
on Metric Spaces. Solutions to Exercises.- Index.
Format: Hardback, 314 pages, height x width: 235x155 mm, 1 Illustrations, black and white; X, 314 p. 1 illus., 1 Hardback
Series: Infosys Science Foundation Series in Mathematical Sciences
Pub. Date: 08-Aug-2025
ISBN-13: 9789819664702
This book describes research problems by unifying and generalizing some remote-looking objects through the functional equation and the parity relation of relevant zeta functions, known as the modular relation or RHB correspondence. It provides examples of zeta functions introduced as absolutely convergent Dirichlet series, not necessarily with the Euler product. The book generalizes this to broader cases, explaining the special functions involved. The extension of the ChowlaSelberg integral formula and the Hardy transform are key, substituting the Bochner modular relation in the zeta function of Maass forms. The book also develops principles to deduce summation formulas as modular relations and addresses Chowlas problem and determinant expressions for class numbers.
Many books define zeta functions using Euler products, excluding Epstein and Hurwitz-type zeta functions. Euler products are constructed from objects with a unique factorization domain property. This book focuses on using the functional equation, called the modular relation, specifically the ramified functional equation of the Hecker type. Here, the gamma factor is the product of two gamma functions, leading to the FourierWhittaker expansion, and reducing to the FourierBessel expansion or the ChowlaSelberg integral formula for Epstein zeta functions.
Introduction and preliminaries.- Ramified functional equations and
(CSIF).- Unified theory of Epstein zeta-functions & zeta-functions associated
with real-analytic automorphic forms.- A unifying principle for modular
relations and summation formulas.- Class numbers of Abelian fields and
(CPMD).- Historical remarks.
Format: Hardback, 146 pages, height x width: 279x210 mm, X, 146 p., 1 Hardback
Series: Sources and Studies in the History of Mathematics and Physical Sciences
Pub. Date: 01-Aug-2025
ISBN-13: 9783031890864
Calculating the sine of one degree, not possible with the tools of geometry alone, was a problem approached frequently in various ways in Hellenistic, Arabic, Persian, and European trigonometry. This book situates the problem and the iterative techniques often used to solve it in the context of Indian trigonometry, focusing on the Sanskrit text and manuscript that form the main subject of this study: the jyacapa section of the Siddhantakaustubha of Jagannatha. This text describes the approaches of Jamshid al-Kashi and Ulugh Beg of 15th-century Samarqand, and also includes innovations produced by astronomers of Jai Singh’s court in Jaipur.
This book contains translations and editions of two recensions of the manuscript's surviving prose texts, along with analyses of its mathematical content. The authors also trace the textual history of the mathematical methods in both Islamic and Sanskrit mathematical traditions.
Of timely interest to scholars in the history of early modern Islamic and Indian mathematical sciences, this book contributes an important text to the literature on the interactions between these cultures.
Introduction: The sine of 1 and its history.- Parallel editions and
translations of the jycpa excerpt.- Mathematical notes on the jycpa
excerpt.- Al-Brjand and his predecessors on sine 1 approximations.- Sine
1 iteration in the Sanskrit tradition.- Discussion.- Appendix A. Anonymous
Arabic treatise iteration calculations.- Bibliography.
Format: Paperback / softback, 395 pages, height x width: 235x155 mm, 25
Illustrations,
black and white; XVII, 395 p. 25 illus., 1 Paperback / softback
Series: Springer Undergraduate Mathematics Series
Pub. Date: 29-Jul-2025
ISBN-13: 9783031932595
This self-contained textbook, now in a thoroughly revised and expanded second edition, takes a matrix-oriented approach to Linear Algebra. It presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its derivation. Throughout, the book emphasizes the practical applicability of results. It therefore also covers special topics in Applied Linear Algebra, such as matrix functions, the singular value decomposition, the Kronecker product, and linear matrix equations. New to this edition are topics such as the Frobenius canonical form and a more detailed treatment of infinite-dimensional vector spaces, along with many additional exercises.
The books matrix-oriented approach enhances intuition and simplifies abstract concepts, making them easier to understand and to apply in real-world scenarios. Key applications are illustrated through detailed examples. Additionally, several "MATLAB Minutes" allow students to explore concepts and results through computational experiments, supported by a brief introduction to MATLAB fundamentals. Together with over 380 exercises, this encourages active engagement with the material.
Chapter 1. Linear Algebra in every day life.
Chapter 2. Basic mathematical concepts.
Chapter 3. Algebraic structures.
Chapter 4. Matrices.
Chapter 5. The echelon form and the rank of matrices.
Chapter 6. Linear systems of equations.
Chapter 7. Determinants of matrices.
Chapter 8. The characteristic polynomial and eigenvalues of matrices.
Chapter 9. Vector spaces.
Chapter 10. Linear maps.
Chapter 11. Linear forms and bilinear forms.
Chapter 12. Euclidean and unitary vector spaces.
Chapter 13. Adjoints of linear maps.
Chapter 14. Eigenvalues of endomorphisms.-
Chapter 15. Polynomials and the Fundamental Theorem of Algebra.
Chapter 16. Cyclic subspaces, duality and the Jordan canonical form.
Chapter 17. Matrix functions and systems of differential equations.
Chapter 18. Special classes of endomorphisms.
Chapter 19. The singular value decomposition.
Chapter 20. The Kronecker product and linear matrix equations.
Format: Hardback, 400 pages, height x width: 235x155 mm, 48 Illustrations, color; Approx. 400 p. 48 illus. in color., 1 Hardback
Pub. Date: 27-Aug-2025
ISBN-13: 9789819657148
This book is about hybrid networks of singular and non-singular, one-dimensional flows and equilibriums in crossing and product polynomial systems. The singular equilibriums and one-dimensional flows with infinite-equilibriums in product polynomial systems are presented in the theorem. The singular equilibriums are singular saddles and centers, parabola-saddles, and double-inflection-saddles. The singular one-dimensional flows are singular hyperbolic-flows, hyperbolic-to-hyperbolic-secant flows, inflection-source and sink flows, and inflection-saddle flows. The higher-order singular one-dimensional flows and singular equilibriums are for the appearing bifurcations of lower-order singular and non-singular one-dimensional flows and equilibriums. The infinite-equilibriums are the switching bifurcations for two associated networks of singular and non-singular, one-dimensional flows and equilibriums. The corresponding mathematical conditions are presented, and the theory for nonlinear dynamics of crossing and product polynomial systems is presented through a theorem. The mathematical proof is completed through the local analysis and the first integral manifolds. The illustrations of singular one-dimensional flows and equilibriums are completed, and the sampled networks of non-singular one-dimensional flows and equilibriums are presented in this book.
Constant and Product Polynomial Systems.- Proof of Theorem.- Singular
flows bifurcaions and networks.
Format: Hardback, 600 pages, height x width: 235x155 mm, 116 Illustrations, color;
174 Illustrations, black and white; XVI, 600 p. 290 illus., 116 illus. in color., 1 Hardback
Pub. Date: 18-Aug-2025
ISBN-13: 9783031890666
This textbook, now in its third edition, provides a broad and accessible introduction to both continuous and discrete dynamical systems, the theory of which is motivated by examples from a wide range of disciplines. It emphasizes applications and simulation utilizing MATLABR, SimulinkR, the Image Processing ToolboxR, the Symbolic Math ToolboxR, and the Deep Learning ToolboxR.
The text begins with a tutorial introduction to MATLAB that assumes no prior programming knowledge. Discrete systems are covered in the first part, after which the second part explores the study of continuous systems using delay, ordinary, and partial differential equations. The third part considers chaos control and synchronization, binary oscillator computing, Simulink, and the Deep Learning Toolbox. A final chapter provides examination- and coursework-type MATLAB questions for use by instructors and students.
For the Third Edition, all the material has been thoroughly updated in line with the most recent version of MATLAB, R2025a. New chapters have been added on artificial neural networks, delay differential equations, numerical methods for ordinary and partial differential equations, and the Deep Learning Toolbox. MATLAB program files, Simulink model files, and other materials are available to download from the authors website and through GitHub.
The hands-on approach of Dynamical Systems with Applications using MATLABR has minimal prerequisites, only requiring familiarity with ordinary differential equations. It will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a broad range of disciplines such as population dynamics, biology, chemistry, computing, economics, nonlinear optics, neural networks, and physics.
This book [ is] a valuable reference to the existing literature on dynamical systems, especially for the remarkable collection of examples and applications selected from very different areas, as well as for its treatment with MATLAB of these problems. -- Fernando Casas, zbMATH
[ The] vast compilation of applications makes this text a great resource
for applied mathematicians, engineers, physicists, and researchers. Instructors
will be pleased to find an aims and objectives section at the beginning
of each chapter where the author outlines its content and provides student
learning objectives. -- Stanley R. Huddy, MAA
A Tutorial Introduction to MATLAB.- Linear Discrete Dynamical Systems.-
Nonlinear Discrete Dynamical Systems.- Complex Iterative Maps.-
Electromagnetic Waves and Optical Resonators.- Fractals and Multifractals.-
Neural Networks and Neurodynamics.- Image and Signal Processing.-
Differential Equations.- Numerical Methods for Ordinary and Partial
Differential Equations.