Format: Hardback, 472 pages, height x width: 235x155 mm, 117 Illustrations, color; 35 Illustrations, black and white
Pub. Date: 20-Jan-2026
ISBN-13: 9783032099990
Description
Motivated by curiosity and a deep love for the subject, this self-contained number theory text is designed primarily for advanced undergraduates and graduate students. It assumes a level of mathematical maturity found among students in physics, engineering, and mathematics. Covering the content of a full-year number theory course, the book can serve either as a primary textbook or as a supplementary reference in advanced topics courses. With its comprehensive scope and depth, it also offers an efficient resource for anyone seeking to explore the central currents of number theory.
The exposition begins with elementary concepts and gradually advances to more sophisticated material. Proofs are presented in full detail, ensuring clarity and rigor. The selection of topics is broad, and over 150 illustrations provide visual insight, particularly where geometry enriches understanding. More than 400 exercises, ranging in difficulty, are included to reinforce mastery of the material.
The book is organized into three parts. Part I introduces topics typically encountered in an advanced undergraduate course in number theory, with the later sections of the part extending to graduate-level material. Part II presents the foundations of major branches of number theory, including algebraic, analytic, ergodic, and probabilistic approaches. Part III covers advanced results, featuring proofs of the prime number theorem, the Birkhoff ergodic theorem, and the unsolvability of the general quintic, among others. The author also discusses possible uses of the book in non-number theory courses and in fields outside mathematics. Nine appendices supplement the main text with related material that, while valuable, would otherwise disrupt the narrative flow.
Table of Contents
Preface.-
Part 1 Introduction to Number Theory.-
1. A Quick Tour of Number Theory.-
2. The Fundamental Theorem of Arithmetic.-
3. Linear Diophantine Equations.-
4. Number Theoretic Functions.-
5. Modular Arithmetic and Primes.-
Part 2 Current in Number Theory: Algebraic, Probabilistic, and Analytic.-
6. Continued Fractions.-
7. Fields, Rings, and Ideals.-
8. Factorization in Rings.-
9. Ergodic Theory.-
10. Three Maps and the Real Numbers.- Part 3 Topics in Number Theory.-
11. The Cauchy Integral Formula.-
12. The Prime Number Theorem.-
13. Primes in Arithmetic Progressions.-
14. The Birkhoff Ergodic Theorem.-
15. The Unsolvability of the Quintic.-
A. The Metallic Means.-
B. Three Gaps and Denjoy-Koksma.-
C. Prime Towers.-
D. The Logarithm as a Moving Constant.-
Bibliography.-
Index.
Format: Hardback, 390 pages, height x width: 235x155 mm, 230 Illustrations, black and white
Series: Springer Proceedings in Mathematics & Statistics
Pub. Date: 23-Feb-2026
ISBN-13: 9783032094599
Description
This volume brings together selected contributions from the conference "Functor and Tensor Categories, Models and Systems" (Santiago de Compostela, Spain, June 2024), along with several invited contributions. As a satellite conference of the 9th European Congress of Mathematics, it attracted many participants and excellent speakers, some of whose presentations form the basis of the papers collected in this volume.
Table of Contents
Colocalizing subcategories on differentially graded algebras.-
A module-theoretic introduction to abstract elementary classes.-
The dark side of categorical Banach space theory.-
The Ziegler spectrum for enriched ringoids and schemes.-
Distributive laws in a non associative setting.-
Universal enveloping of certain types of structures of Lie and Leibniz algebras.-
Finite-order distributions: A purely algebraic approach.-
Cotilting dualities for Artinian rings.- On covering theory and its applications.-
On the computation of the vanishing locus of a finitely presented functor.-
Pp-types in additive structures.- On the classification of centralizers of ODOs: An effective differential algebra approach.-
Controllability and vector potential.-
Morphisms determined by objects and the minimal determiners.
Format: Hardback, 175 pages, height x width: 235x155 mm, 211 Illustrations, color; 13 Illustrations, black and white
Pub. Date: 22-Feb-2026
ISBN-13: 9783032101945
Description
Mastering ordinary differential equations (ODE) is crucial for success in numerous fields of science and engineering, as these powerful mathematical tools are indispensable for modeling and understanding the world around us. From the motion of celestial bodies to the flow of electric currents, ODEs provide the language to describe dynamic systems.
To truly grasp the concepts and techniques of differential equations, practice is paramount. "A Problem-Solving Approach to Ordinary Differential Equations" is your essential guide, offering a comprehensive, four-volume set filled with plenty of meticulously solved, step-by-step problems designed to build your skills and deepen your understanding. This book empowers you to confidently tackle any ODE, transforming challenges into triumphs.
Table of Contents
Partial Fraction Decomposition.- The Gamma Function.- The Laplace
Transform.- The Inverse Laplace Transform.- Solving Differential Equations
with the Laplace Transform.- Impulse, Step, and Frequency Responses.- A
Review of Differential Equation Solution Techniques.
Format: Hardback, height x width: 240x168 mm, Approx. 150 p.
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 07-Apr-2026
ISBN-13: 9783032101730
Description
This book provides an introduction to frame theory in Banach and Hilbert spaces, with a particular focus on the Banach space aspects of the frame theory and its applications. The authors present main developments from recent decades in the theory of frames, dilations, operator-valued measures, sampling, and related applications. By bridging topics from Banach space geometry, applied harmonic analysis, and quantum information theory, the book highlights a novel perspective: frame theory not only serves as a powerful and central tool in mathematics and engineering, but is also deeply intertwined with the structure and theory of Banach spaces. Rather than providing an exhaustive treatment, the book offers a broadly relevant and accessible overview that enables researchers across various fields to quickly grasp the foundational ideas and explore related research directions.
Table of Contents
Frames in Hilbert Spaces.- Frames in Banach Spaces.- Approximation
Properties.- Banach Dilation.- Nonselfadjoint Dilation and Generalized
Choi-Kraus Representation.- Quantum Detection and Phase Retrieval.
Format: Hardback, 200 pages, height x width: 235x155 mm, XII, 200 p.
Pub. Date: 12-Apr-2026
ISBN-13: 9789819535538
Description
In this book, the author considers several extended applications of the well-known half-discrete Hardy-Hilberts inequality with two internal variables, by using the techniques of real analysis, the way of introduced parameters and the weight function. The book first considers the basic results of half-discrete Hardy-Hilberts inequality. Then it obtains some new inequalities involving upper limit functions, derivative functions and partial sums, and studies the equivalent conditions of the best possible constant factors related to the parameters by 8 chapters. The author constructs a large kind of half-discrete Hardy-Hilberts inequalities for building their extended applications. The lemmas and theorems in this book provide an extensive account of this kind of inequalities and applications. This book will be helpful to researchers who are interested in half-discrete Hardy-Hilberts inequality.
Table of Contents
Chapter 1. Introduction.
Chapter 2. Half-Discrete Hardy-Hilberts Inequalities with Two Internal Variables.
Chapter 3. Half-Discrete Hardy-Hilberts Inequalities Involving One Upper LimitFunction.
Chapter 4. Half-Discrete Hardy-Hilberts Inequalities Involving One Derivative Function.
Chapter 5. Half-Discrete Hardy-Hilberts Inequalities Involving One Multiple Upper LimitFunction.
Chapter 6. Half-Discrete Hardy-Hilberts Inequalities Involving One Derivative Functionof Higher-Order.
Chapter 7. Half-Discrete Hardy-Hilberts Inequalities Involving One Upper Limit Function and One Partial Sum.
Chapter 8. Half-Discrete Hardy-Hilberts Inequalities Involving One Derivative Functionand One Partial Sum.-
Chapter 9. Half-Discrete Hardy-Hilberts Inequalities Involving One Multiple Upper Limit Function and One Partial Sum.
Chapter 10. Half-Discrete Hardy-Hilberts Inequalities Involving One Derivative Functionof Higher-Order and One Partial Sum.
Format: Paperback / softback, height x width: 240x168 mm, 379 Illustrations, color; 12 Illustrations, black and white
Pub. Date: 24-Apr-2026
ISBN-13: 9783662724026
Description
This book invites you to marvel: discover how, for example, Archimedes was able to determine the area of a parabolic segment 1,800 years before the invention of classical integral calculus, derive a summation formula for square numbers with Ibn al-Haitham, or explore quaternions with Hamilton. The 21 selected ideas are vividly developed with the help of numerous colour illustrations you will be astonished by the thought processes of mathematicians long since passed! Many ingenious approaches have been almost entirely forgotten by posterity for instance, the polymaths from the Islamic cultural sphere are scarcely known in Europe today, despite their significant contributions to the development of mathematics. Each chapter therefore also provides information about the lives of these individuals and the eras in which they lived, notes and explanations on further questions they addressed, as well as extensive references to additional literature that is generally accessible. The chapters can be read independently of one another where appropriate, connections to other chapters are indicated. Most topics can be followed with a solid background in upper or middle school mathematics, making the book suitable for anyone with an interest in mathematics but also for school study groups and as inspiration for extended essays. This book is a translation of the original German 2nd edition Mathematik einfach genial! by Heinz Klaus Strick, published by Springer-Verlag GmbH, DE, part of Springer Nature in 2025. The translation was done with the help of artificial intelligence. In the subsequent editing, the author, with the friendly support of John O'Connor, St Andrews University, Scotland, tried to make it closer to a conventional translation. Still, the book may read stylistically differently from a conventional translation.
Table of Contents
Pythagoras of Samos - Sect Leader and Philosopher.- Archimedes of
Syracuse - Mathematician, Physicist and Engineer.- Diophantus of Alexandria
Virtuoso Beginnings of Algebra and Number Theory.- Muhammed al-Khwarizmi -
Father of Algebra.- Thabit ibn Qurra Brilliant Translator and Creative
Mathematician.- Ali al-Hasan Ibn al-Haitham - Father of Optics.- Abu Arrayhan
al-Biruni - Universal Scholar from Afghanistan.- Omar Khayyam -
Mathematician, Philosopher, and Poet.- Jamshid al-Kashi - The Last
Significant Mathematician of the Islamic Middle Ages.- Niccolņ Tartaglia and
Girolamo Cardano - Who Deserves the Credit?- John Napier - Master of
Calculation.- René Descartes - Founder of Analytic Geometry.- Pierre de
Fermat - Misjudged Mathematical Genius from the Provinces.- Blaise Pascal -
Profound Theologian and Mathematician.- Abraham de Moivre - A Brilliant
Frenchman in English Exile.- Leonhard Euler - "our master par excellence".-
Joseph-Louis Lagrange - Versatile Mathematician and Physicist.- Jean Baptiste
Joseph Fourier - from the French Revolution to the Revolution in the Theory
of Heat.- William Rowan Hamilton - an Unhappy Genius from Ireland.- Georg
Cantor - Explorer of the Infinite- Giuseppe Peano Versatile Mathematician
and Logician.
Pages: 568
ISBN: 978-981-98-1958-4 (hardcover)
ISBN: 978-981-98-2047-4 (softcover)
Description
This calculus-based introduction to probability covers all of the traditional topics, along with a secondary emphasis on Monte Carlo simulation. Examples that introduce applications from a wide range of fields help the reader apply probability theory to real-world problems. The text covers all of the topics associated with Exam P given by the Society of Actuaries.
Over 100 figures highlight the intuitive and geometric aspects of probability. Over 800 exercises are used to reinforce concepts and make this text appropriate for classroom use.
Contents:
Preface
Introduction
Probability
Random Variables
Common Discrete Distributions
Common Continuous Distributions
Joint Distributions
Functions of Random Variables
Limiting Distributions
Index
Readership:
For introductory undergraduate calculus-based course in probability.
Pages: 460
ISBN: 978-981-98-1839-6 (hardcover)
Description
This book is about the nonlinear dynamics of single linear-bivariate cubic dynamical systems. For such cubic dynamical systems, the inflection-flows and third-order parabola flows exist for appearing bifurcations. The inflection-flows are for appearing bifurcations of two parabola flows on the same direction. The third-order parabola flows are for the appearing bifurcation of inflection and parabola flows, and for the appearing bifurcations of up, down and up-parabola flows or down, up and down-parabola flows. Third-order parabola flow are for the appearing bifurcation among the up and down-parabola flows. There are four types of infinite-equilibriums: (i) The inflection-source and sink infinite-equilibriums are for the switching bifurcations of two parabola flows on the two-directions. (ii) The parabola-source and sink infinite-equilibriums are for the switching bifurcations of parabola and inflection flows on the two-directions. (iii) The inflection-saddle infinite-equilibriums are for the switching bifurcation of two inflection flows in two directions. (iv) The parabola-saddle infinite-equilibriums are for the switching bifurcations of parabola and inflection flows on the two-directions are the switching bifurcations for parabola and inflection flows. Such switching bifurcations for 1-dimensional flow are based on the infinite-equilibriums, which will help one understand global dynamics in nonlinear cubic systems.
Contents:
Constant and Single-Linear-Bivariate Cubic Systems:
Constant and Single-Linear-Bivariate Cubic Vector Fields
Proof of Theorem 1.1
Inflection and Parabola Flows
Parabola Flows Series
Single-Linear-Bivariate Linear and Cubic Systems:
Single-Linear-Bivariate Linear and Cubic Vector Fields
Proof of Theorem 2.1
Third-Order Singular Single-Linear-Bivariate Cubic Systems
Parabola Flows Series and Switching Bifurcations
Single-Linear-Bivariate Quadratic and Cubic Systems:
Single-Linear-Bivariate Quadratic and Cubic Vector Fields
Proof of Theorem 3.1
Second-Order Singular Quadratic and Cubic Systems
Singular Parabola Flows and Infinite-Equilibriums
Single-Linear-Bivariate Double-Cubic Systems:
Two Single-Linear-Bivariate Cubic Vector Fields
Proof of Theorem 4.1
Singular Single-Linear Bivariate Cubic Systems
Singular Parabola Flows and Infinite-Equilibriums
Readership
Advanced undergraduates, graduate students and researchers in mathematics, physics, mechanical and control engineering; as well as those studying dynamical systems and control in these disciplines.
Pages: 308
ISBN: 978-981-98-1881-5 (hardcover)
ISBN: 978-981-98-1883-9 (ebook)
Description
Graphs are foundational to combinatorics, modeling relationships across disciplines, from communication networks and social systems to molecular biology. This book presents the first comprehensive treatment of extremal problems in edge-colored graphs, a rapidly developing area at the intersection of graph theory, combinatorics, and applied mathematics.
Focusing on the existence of rainbow and properly colored subgraphs, the text explores classical and contemporary topics including anti-Ramsey theory, Gallai–Ramsey results, and rainbow Turán-type problems. It offers a unified framework for understanding how coloring constraints affect graph structure, while drawing connections to Latin squares, transversals, and real-world network models.
Rich in theory and application, this accessible and in-depth resource serves as both a reference for researchers and a guide for graduate students, bringing together decades of literature into a coherent and insightful narrative.
Contents:
Preface
Introduction
Cycle
Path, Matching, Tree and Clique
Host Graphs with Certain Color Patterns
Anti-Ramsey Theory
Gallai-Ramsey Results and the Multicolor Erdős–Hajnal Conjecture
Rainbow Turán Problem
Uniformly Edge-Colored Graphs
Transversal in Graph System
Color-Bias Problem
Bibliography
Readership:
Graduate students and advanced undergraduates in mathematics and theoretical computer science, seeking a thorough and accessible introduction to edge-colored graph theory and its current research directions. Researchers and academics in graph theory, combinatorics, and discrete mathematics looking for a comprehensive reference that consolidates decades of developments in the field. Scientists and professionals in engineering, computer science, biology, physics, and chemistry who apply graph-theoretical methods to model communication networks, biological systems, and data structures.
Pages: 200
ISBN: 978-981-98-1728-3 (hardcover)
Description
The domination problem in graph theory is to find a minimum sized vertex subset in a graph such that every vertex not in this set is adjacent to at least one vertex in this set. The domination problem and its variations serve as good models for many real problems including location problems in operations research.
This comprehensive volume introduces domination and its variations in graphs from an algorithmic point of view. It examines the structures of various graph classes, including trees, chordal graphs, strongly chordal graphs, interval graphs, comparability graphs, permutation graphs, distance-hereditary graphs and generalizations of these graphs. These structure properties provide concepts for designing the algorithms.
This useful reference text benefits researchers, academics, and graduate students in theoretical computer science, combinatorics, and operations research.
Contents:
Introduction to Domination in Graphs
Design and Analysis of Algorithms
Trees
Chordal Graphs
Interval Graphs
Strongly Chordal Graphs
Cocomparability Graphs and Asteroidal Triple-Free Graphs
Permutation Graphs
Distance-hereditary Graphs
Readership:
Researchers, professionals, academics and graduate students in theoretical computer science, combinatorics and operations research.