Format: Paperback / softback, 282 pages, height x width: 235x155 mm, 1 Illustrations, black and white; X, 282 p. 1 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2368
Pub. Date: 07-Jun-2025
ISBN-13: 9783031888779
This book offers a concise treatment of multiplicative ideal theory in the language of multiplicative monoids. It presents a systematic development of the theory of weak ideal systems and weak module systems on arbitrary commutative monoids. Examples of monoids that are investigated include, but are not limited to, Mori monoids, Laskerian monoids, Prufer monoids and Krull monoids. An in-depth study of various constructions from ring theory is also provided, with an emphasis on polynomial rings, Kronecker function rings and Nagata rings. The target audience is graduate students and researchers in ring and semigroup theory.
1. Basic Monoid Theory.-
2. The Formalism of Module and Ideal Systems.-
3. Prime and Primary Ideals and Noetherian Conditions.-
4. Invertibility, Cancellation and Integrality.-
5. Arithmetic of Cancellative Mori Monoids.-
6. Ideal Theory of Polynomial Rings.
Format: Paperback / softback, 215 pages, height x width: 235x155 mm, 7 Illustrations, black and white; X, 215 p. 7 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2369
Pub. Date: 18-Jun-2025
ISBN-13: 9783031889103
This book provides a concrete description of the identity connected components of the real and complex exceptional Lie groups. The constructions are elementary and improve on those of H. Freudenthal.
The complex simple Lie algebras were classified into classical (An, Bn, Cn, Dn) and exceptional (G2, F4, E6, E7, E8) types at the end of the 19th century by W. Killing and E. Cartan. These simple Lie algebras and the corresponding compact simple Lie groups arise in many settings in mathematics and physics. The exceptional Lie groups form an especially interesting class of objects that have attracted the attention of numerous mathematicians. Requiring no prior knowledge of composition algebras or Jordan algebras, the book will be valuable to anyone who wants to learn about the structure and realizations of these fascinating groups.
Chapter 1. Exceptional Lie group G2.
Chapter 2. Exceptional Lie group F4.
Chapter 3. Exceptional Lie group E6.
Chapter 4. Exceptional Lie group E7.
Chapter 5. Exceptional Lie group E8.
Format: Hardback, 589 pages, height x width: 235x155 mm, 100 Illustrations, color; 69 Illustrations,
black and white; XVI, 589 p. 169 illus., 100 illus. in color., 1 Hardback
Series: Trends in the History of Science
Pub. Date: 09-Jul-2025
ISBN-13: 9783031868696
This book explores the evolving relationship between the history and epistemology of mathematics and mathematics education over the past fifty years. Beginning with the international movement that emerged in the 1970s, it celebrates the enduring and expanding role of historical and epistemological perspectives in shaping teaching practices.
Organized into seven thematic sections, the volume examines core issues such as how historical and epistemological insights enhance understanding of mathematical concepts, interdisciplinarity as a tool for teaching, and innovative approaches to teacher training. It also delves into the use of historical problems, ancient texts, and textbooks as teaching resources, alongside an analysis of the social and political dimensions of mathematics education.
Special attention is given to the impact of the "modern mathematics" reform and its legacy in rekindling interest in the history of mathematics in education. Featuring contributions from diverse geographical and historical contexts, this book is an essential resource for teachers, researchers, and anyone passionate about the rich interplay of history, epistemology, and mathematics.
DALEMBERTS ENCYCLOPEDIC REFLECTIONS ON THE DISPUTE ABOUT THE SHAPE OF
THE EARTH.- EPISTEMOLOGICAL FUNCTIONS OF INSTRUMENTS IN TEACHING OF
EXPERIMENTAL GEOMETRY.- WHEN PRACTICAL MATHEMATICS MEETS SPECULATIVE
MATHEMATICS: PIERO DELLA FRANCESCA AND THE VOLUME OF THE VAULT.- SHAPING
CRITERIA FOR THE DIDACTICAL TRANSPOSITION OF HISTORICAL MATHEMATICAL
KNOWLEDGE.- THE CONTRIBUTIONS OF UBIRATAN D'AMBROSIO AND PAULUS GERDES TO THE
HISTORY AND EPISTEMOLOGY OF MATHEMATICS.- CALCULUS AS NEVER TOUCHED BEFORE.-
THE DIVISION OF PLANE FIGURES: HISTORICAL BACKGROUND, DIACHRONIC APPROACH AND
MATHEMATICAL SOLUTIONS.- ANCIENT PROBLEMS AND CONTEMPORARY IUSSUES.- THE
EPISTEMOLOGICAL ROLE OF SPATIAL THINKING IN THE CONSTRUCTION OF CONIC
SECTIONS. A SOCIAL APPROACH.- A CLASSROOM EXPERIENCE BETWEEN GEOMETRY AND
ALGEBRA WITH THE HELP OF THE HISTORY OF MATHEMATICS.- THE HISTORY OF
MATHEMATICS IN ITALY: THE ROLE OF APPLICATIONS.- TEACHING ON THE BORDER
BETWEEN MATHEMATICS AND PHYSICS THROUGH THE HISTORY OF MATHEMATICS: FAGNANOS
PROBLEM.- ALGORITHMS BEFORE COMPUTERS.- POTENTIAL OF COLLABORATION BETWEEN
HISTORY AND MATHEMATICS TEACHERS: EMPERICAL INVESTIGATION.- ENACTING THE
STORIES BEHIND THE CONCEPTS.- INCORPORATING HISTORY OF MATHEMATICS IN INITIAL
TEACHER EDUCATION IN REUNION AND MAYOTTE INCORPORATING HISTORY.- DESIGNING
HISTORY-INSPIRED LESSONS: AN ACTION RESEARCH WITH PRE-SERVICE MATHEMATICS
TEACHERS IN NORWAY.- THE HISTORY OF MATHEMATICS FOR TEACHING AND LEARNING
MATHEMATICS.- IN SEARCH FOR THE MODERATOR IN DIALOGUE ATTITUDE TOWARD THE
PAST.- HISTORY OF MATHEMATICS AS A COMPONENT OF MATHEMATICAL KNOWLEDGE FOR
TEACHING.- BOOK OF ALGEBRA IN ARITHMETICS AND GEOMETRY.- EUCLIDS INFLUENCE
ON 19TH CENTURY MATHEMATICS EDUCATION: SOME EXAMPLES FROM A NORWEGIAN
TEXTBOOK IN PLANE GEOMETRY.- BEYOND THE TEXTBOOK: REFLECTIONS ON HANDS-ON
APPROACH FROM JULES DALS?MES (1845-1904) PRODUCTION.- HISTORY OF MATHEMATICS
IN PORTUGUESE ANCIENT TEXTBOOKS OF VICENTE GON?ALVES AND SEBASTI?O E SILVA:
POTENTIALITIES FOR CURRENT TEACHING.- HISTORY OF MATHEMATICS IN BRAZILIAN
SECONDARY SCHOOL TEXTBOOKS.- MATHEMATICAL ICONS IN MATHEMATICS EDUCATION.-
ARGUING FOR EQUALITY: A WORKSHOP FOR SECONDARY SCHOOL EXPLORING THE POLITICAL
ARGUMENT STARTING FROM THE STRUCTURE OF THE GREEK DEMONSTRATION.- GORCEIX AND
THE MATHEMATICS IN BRAZIL FRENCH INFLUENCES IN THE XIX CENTURY.- A HIDDEN
THREAD: IDEAS AND PROPOSALS ON CHILDRENS MATHEMATICS EDUCATION IN THE LATE
MODERN AGE.- MATHEMATICS AS AN EDUCATIONAL OPPORTUNITY FOR CHILDREN WITH
INTELLECTUAL DISABILITIES: INSIGHTS FROM EDOUARD SEGUIN (1812-1880).- IN
SEARCH FOR THE EARLY ROOTS OF NEW MATH REFORM MOVEMENTS.- RECOVER, REPURPOSE,
REFORM.- DISTINCT APPROACHES TO INTEGERS IN TECHNICAL SCHOOLS AND IN LICEUS,
DURING MODERN MATHEMATICS IN PORTUGAL.- REBIRTH OF MATHEMATICAL LOGIC IN
ITALY DURING THE SECOND HALF OF THE 20TH CENTURY, AND ITS INTRODUCTION INTO
THE SCHOOL MATHEMATICS CURRICULUM.
Format: Hardback, 400 pages, height x width: 235x155 mm, Approx. 400 p., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 15-Jul-2025
ISBN-13: 9783031874680
Graph minor theory is one of the most influential and well-developed areas of graph theory, yet its key results, particularly the work of Robertson and Seymour, have remained scattered across numerous technical papers. This book fills an important gap by providing a comprehensive, structured treatment of the subject.
Divided into three main parts, the book first introduces the fundamentals of graph minor theory, focusing on the deep and powerful Minor Structure Theorem. It offers a clear roadmap for understanding the theorems proof, presenting its key ingredients while omitting only the most technical details. The second part explores a variety of applications, from algorithmic results to connections with the Linear Hadwiger Conjecture and graph coloring problems. The final section presents alternative approaches to graph minor theory that do not rely on the Minor Structure Theorem, covering topics such as sublinear separators, density, and isomorphism testing.
The exposition is rigorous yet accessible, striving to balance depth with readability. While some parts remain dense due to the complexity of the subject, the author provides valuable insights and explanations that make challenging concepts more approachable. The book not only serves as an excellent learning resource for graduate students and researchers entering the field but also as a long-lasting reference for experts.
Chapter 1. Introduction.- Part I. Understanding the structure theorem.-
Chapter 2. Tree decompositions and treewidth.
Chapter 3. Linkedness.-
Chapter 4. Graphs on surfaces.
Chapter 5. Towards the structure theorem.-
Chapter 6. Pointers and sources.- Part II. Using the structure theorem.-
Chapter 7. Low-treewidth colorings.
Chapter 8. Tighter grid theorem.-
Chapter 9. Topological minors.
Chapter 10. Minors in large connected graphs.
Chapter 11. Sources.- Part III. Avoiding the structure theorem.-
Chapter 12. Sublinear separators.
Chapter 13. Chordal partitions.
Chapter 14. Chromatic number.
Chapter 15. Product structure.
Chapter 16. Iterated layerings.
Chapter 17. Isomorphism testing.
Chapter 18. Sources.
Format: Hardback, 240 pages, height x width: 235x155 mm, 4 Illustrations, color; 41 Illustrations,
black and white; X, 240 p. 45 illus., 4 illus. in color., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 26-Jun-2025
ISBN-13: 9783031870460
This self-contained book offers an extensive state-of-the-art exposition of rotational integral geometry, a field that has reached significant maturity over the past four decades. Through a unified description of key results previously scattered across various scientific journals, this book provides a cohesive and thorough account of the subject. Initially, rotational integral geometry was driven by applications in fields such as optical microscopy. Rotational integral geometry has now evolved into an independent mathematical discipline. It contains a wealth of theorems paralleling those in classical kinematic integral geometry for Euclidean spaces, such as the rotational Crofton formulae, rotational slice formulae, and principal rotational formulae. The present book presents these for very general tensor valuations in a convex geometric setting. It also discusses various applications in the biosciences, explained with a mathematical audience in mind. This book is intended for a diverse readership, including specialists in integral geometry, and researchers and graduate students working in integral, convex, and stochastic geometry, as well as geometric measure theory.
1. Introduction.-
2. Convex Bodies and their Classical Integral Geometry.-
3. Integral Geometric Transformations.-
4. Rotational Crofton Formulae for Intrinsic Volumes.-
5. Rotational Crofton Formulae for Minkowski Tensors.-
6. Rotational Slice Formulae.-
7. Further Rotational Integral Geometric Formulae.-
8. Applications to Particle Populations.-
9. Implementation in Optical Microscopy.
Format: Paperback / softback, 230 pages, height x width: 235x155 mm, 27 Illustrations, color; 90 Illustrations,
black and white; X, 230 p. 117 illus., 27 illus. in color., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2365
Pub. Date: 22-Jun-2025
ISBN-13: 9783031872631
This volume covers a broad spectrum of topics in stochastic geometry, including percolation, tessellations, Gaussian fields and point processes. Based on lectures given at the Stochastic Geometry Days held by the Stochastic Geometry Research Group from 2019 to 2022, the book opens with an introduction to RussoSeymourWelsh theory for the study of percolation, before going on to explore random tessellations and their applications, the geometry of Gaussian random fields, and the zeros of analytic Gaussian fields. This discussion naturally leads to the concept of determinantal point processes, whose applications in signal processing are the focus of the final chapter. Providing a unique and accessible overview of active fields in stochastic geometry, their tools and models, this collection of lectures will encourage further research and applications.
1. An Introduction to Russo-Seymour-Welsh Theory.-
2. Random Tessellations - An Overview of Models.-
3. Gaussian Fields through Geometrical Properties.-
4. Complex Gaussian Zeros and Eigenvalues.-
5. Point Processes and Spatial Statistics in Time-Frequency Analysis.
Format: Paperback / softback, 170 pages, height x width: 235x155 mm, 49 Illustrations, color; 4 Illustrations,
black and white; X, 170 p. 53 illus., 49 illus. in color., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2366
Pub. Date: 05-Jul-2025
ISBN-13: 9783031872013
This book presents three short courses on topics at the intersection of Calculus of Variations, PDEs and Material Science, based on lectures given at the CIME summer school Variational and PDE Methods in Nonlinear Science, held in Cetraro (Italy), July 1014, 2023.
Fabrice Bethuel discusses aympototics for AllenCahn systems, providing an overview of classical methods and tools for the scalar case and further results for the two-dimensional vectorial case. An alternate monotonicity formula is described, and the still open parabolic vectorial case is considered. Angkana Ruland considers the modelling and analysis of microstructures in shape-memory alloys, including material on quasiconvexity, differential inclusions, rigidity of the two-well problem under BV-regularity assumptions, and recent results on the quantitative dichotomy between rigidity and flexibility. Duvan Henao focuses on existence theory in nonlinear elasticity, where a central role is played by the Jacobian determinant. The methods developed have implications for the analysis of magnetoelasticity and nematic elastomers.
The volume is aimed at graduate students and researchers interested in the applications of PDEs and the calculus of variations to the theory of phase transitions, fluid dynamics, materials science, and elasticity theory.
1. Scalar and Vectorial Allen-Cahn Equations and their Asymptotics.-
2. Microstructures in the Modelling of Shape-Memory Alloys: Rigidity, Flexibility and Scaling.-
3. Singular Minimizers in Nonlinear Elasticity.