Copyright 2025
Paperback
Hardback
ISBN 9781032560472
336 Pages 379 Color Illustrations
Published March 20, 2025 by A K Peters/CRC Press
The hexaflexagon is a folded paper strip of colored triangles that has long delighted people with how it “magically” changes its appearance when “flexed”. This hands-on, comprehensive book goes beyond the hexaflexagon, the standard version of this folded puzzle, exponentially expanding the barely explored field of flexagons as it brings new options and fresh insights to light.
● Learn over a dozen different flexes, and make dozens of different flexagons with the aid of step-by-step illustrated directions and templates to copy and print.
● Delve into the internal structure of flexagons and discover a universal way to describe and predict their behavior.
● Learn how to create your own custom flexagons with a special computer program.
● Understand how flexagons are connected to group theory, computer science, and topology.
● Have fun decorating flexagons and make flexagon books, puzzles, pop-ups, mazes, and more.
Written in a clear, easy-to-understand, and conversational style and enhanced with challenges and tips to broaden your flexagon skills and spark creativity, The Secret World of Flexagons: Fascinating Folded Paper Puzzles is a must for flexagon enthusiasts, teachers, students, libraries, mathematicians, and everyone who loves to solve a good puzzle.
Introduction
Part One: Symmetric Flexes
1: The Pinch Flex
2: General Tips
3: More Faces
4: Triangle Tetraflexagon and Octaflexagon
5: Different Triangles
6: Pinch Flex Variations
7: The Book Flex
8: The Box Flex
Part Two: Asymmetric Flexes
9: Flex Diagrams
10: The V-Flex
11: The Tuck Flex
12: The Flip Flex
13: The Pyramid Shuffle Flex
14: Breaking Down Flexes
15: Slot Flexes
Part Three: Learning about Flexagons
16: Flexagon Naming
17: State Diagrams
18: Flex Sequences
19: Pat Notation
20: Atomic Flex Theory
21: Defining Flexagon and Flex
22: Groups and Flexagons
23: Flexagon Computers
24: Conrad and Hartline’s Flexagon Theory
25: Les Pook’s Flexagon Theory
26: Topology
27: Templates and Labels
Part Four: Exploring Flexagons
28: Square Silver Octaflexagon
29: Hexagonal Bronze Dodecaflexagon
30: Hexagonal Silver Dodecaflexagon
31: Silver Bracelet
32: Octagonal Ring 14-flexagon
33: Flexagon Inspector
Part Five: Fun with Flexagons
34: Decorating Flexagons
35: Flexagon Books
36: Flexagon Puzzles and Mazes
37: Flexagon Pop-ups
38: Cutting Flexagons
Epilogue
Appendices
A: Definitions
B: Flexagon Charts
C: Flex Compendium
Bibliography
Copyright 2025
Paperback
Hardback
ISBN 9781032162003
192 Pages 383 Color Illustrations
July 4, 2025 by A K Peters/CRC Press
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things. Begun as a standard second edition by the original author team, it changed in scope following the passing of John Conway. This version of the book fulfills the original vision for the project: an elementary introduction to the orbifold signature notation and the theory behind it.
The Magic Theorem features all the material contained in Part I of The Symmetries of Things, now redesigned and even more lavishly illustrated, along with new and engaging material suitable for a novice audience. This new book includes hands-on symmetry activities for the home or classroom and an online repository of teaching materials.
1 Symmetries. 2 Planar Patterns. 3 The Magic Theorem. 4 Symmetries of Spherical Patterns. 5 The Seven Types of Frieze Patterns. 6 Why the Magic Theorems Work. 7 Euler’s Map Theorem. 8 The Classification of Surfaces. 9 Orbifolds. 10 A Bigger Picture. A Other Notations for the Plane and Spherical Groups.
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Copyright 2025
Hardback
ISBN 9781032765549
583 Pages 174 B/W Illustrations
May 27, 2025 by Chapman & Hall
This classic text appears here in a new edition for the first time in four decades. The new edition, with the aid of two new authors, brings it up to date for a new generation of mathematicians and mathematics students.
Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, duality in manifolds, and applications to classical theorems of point-set topology, this book is perfect for communicating complex topics and the fun nature of algebraic topology for beginners.
This second edition retains the essential features of the original book. Most of the notation and terminology are the same. There are some useful additions. There is a new introduction to homotopy theory. A new Index of Notation is included. Many new exercises are added.
Algebraic topology is a cornerstone of modern mathematics. Every working mathematician should have at least an acquaintance with the subject. This book, which is based largely on the theory of triangulations, provides such an introduction. It should be accessible to a broad cross-section of the profession?both students and senior mathematicians. Students should have some familiarity with general topology.
1 Homology Groups of a Simplicial Complex
1.1 Introduction
1.2 Simplices
1.3 Simplicial Complexes and Simplicial Maps
1.4 Abstract Simplicial Complexes
1.5 Review of Abelian Groups
1.6 Homology Groups
1.7 Homology Groups of Surfaces
1.8 Zero-Dimensional Homology
1.9 The Homology of a Cone
1.10 Relative Homology
1.11 ?Homology with Arbitrary Coefficients
1.12 ?The Computability of Homology Groups
1.13 Homomorphisms Induced by Simplicial Maps
1.14 Chain Complexes and Acyclic Carriers
2 Topological Invariance of the Homology Groups
2.1 Introduction
2.2 Simplicial Approximations
2.3 Barycentric Subdivision
2.4 The Simplicial Approximation Theorem
2.5 The Algebra of Subdivision
2.6 Topological Invariance of the Homology Groups
2.7 Homomorphisms Induced by Homotopic Maps
2.8 Review of Quotient Spaces
2.9 ?Application: Maps of Spheres
2.10 ?The Lefschetz Fixed Point Theorem
3 Relative Homology and the Eilenberg?Steenrod Axioms
3.1 Introduction
3.2 The Exact Homology Sequence
3.3 The Zig-Zag Lemma
3.4 The Mayer?Vietoris Sequence
3.5 The Eilenberg?Steenrod Axioms
3.6 The Axioms for Simplicial Theory
3.7 ?Categories and Functors
4 Singular Homology Theory
4.1 Introduction
4.2 The Singular Homology Groups
4.3 The Axioms for Singular Theory
4.4 Excisionin Singular Homology
4.5 ?Acyclic Models
4.6 Mayer?Vietoris Sequences
4.7 The Isomorphism Between Simplicial and Singular Homology
4.8 ?Application: Local Homology Groups and Manifolds
4.9 ?Application: The Jordan Curve Theorem
4.10 The Fundamental Group
4.11 More on Quotient Spaces
4.12 CW Complexes
4.13 The Homology of CW Complexes
4.14 ?Application: Projective Spaces and Lens Spaces
5 Cohomology
5.1 Introduction
5.2 The Hom Functor
5.3 Simplicial Cohomology Groups
5.4 Relative Cohomology
5.5 Cohomology Theory
5.6 The Cohomology of Free Chain Complexes
5.7 ?Chain Equivalences in Free Chain Complexes
5.8 The Cohomology of CW Complexes
5.9 Cup Products
5.10 Cohomology Rings of Surfaces
6 Homology with Coefficients
6.1 Introduction
6.2 Tensor Products
6.3 Homology with Arbitrary Coefficients
7 Homological Algebra
7.1 Introduction
7.2 The Ext Functor
7.3 The Universal Coefficient Theorem
7.4 Torsion Products
7.5 The Universal Coefficient Theorem for Homology
7.6 ?Other Universal Coefficient Theorems
7.7 Tensor Products of Chain Complexes
7.8 The Kunneth Theorem
7.9 TheEilenberg?Zilber Theorem
7.10 ?The Kunneth Theorem for Cohomolgy
7.11 ?Application: The Cohomology Ring of a Product Space
8 Duality in Manifolds
8.1 Introduction
8.2 The Join of Two Complexes
8.3 Homology Manifolds
8.4 The Dual Block Complex
8.5 Poincare Duality
8.6 Cap Products
8.7 A Second Proof of Poincare Duality
8.8 ?Application: Cohomology Rings of Manifolds
8.9 ?Application: Homotopy Classification of Lens Spaces
8.10 Lefschetz Duality
8.11 Alexander Duality
8.12 Natural Versions of Duality
8.13 ?ech Cohomology
8.14 Alexander?Pontryagin Duality
MAA Press: An Imprint of the American Mathematical Society
Product Code: CLRM/76.E
Expected availability date: June 27, 2025
Classroom Resource Materials, Volume: 76
2025; 128 pp
MSC: Primary 97; 26
PRACTIS (Precalculus Review and Calculus Topics In Sync) provides just-in-time resources to support Calculus I students. This volume contains worksheets which may be assigned to students for targeted remediation of the necessary material to be successful in Calculus.
Prepared by two highly-experienced instructors, the twenty-eight worksheets cover topics broadly divided into four categories:
limits,
differentiation,
applications of derivatives,
integration.
In addition, each worksheet comes with an answer key. The convenience of the worksheets is enhanced by
a table showing how the resources align with popular Calculus textbooks,
guidelines and suggestions for using the worksheets,
a handy table summarizing the topics of each worksheet.
Presentation slides, covering the precalculus/calculus topics from each worksheet, are also available for use by those instructors who wish to present these topics in the classroom, or who want to share them with students on their learning management system. These can be found at www.ams.org/bookpages/clrm-76. The additional material and updates will be available after the book is published.
Worksheets
Guidelines for using the PRACTIS worksheets & keys
Listing of worksheets by topic
Limits and derivatives
Rules of differentiation
Applications of differentiation
Antiderivatives and integrals
Worksheet keys
Limits and derivatives
Rules of differentiation
Applications of differentiation
Antiderivatives and integrals
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-6431-8
Product Code: SPEC/108
Expected availability date: July 15, 2025
Spectrum Volume: 108;
2025; Estimated: 158 pp
MSC: Primary 01; 05
This book gives an engaging overview of the advances in graph theory during the 20th century. The authors, all subject experts, considered hundreds of original papers, picking out key developments and some of the notable milestones in the subject. This carefully researched volume leads the reader from the struggles of the early pioneers, through the rapid expansion of the subject in the 1960s and 1970s, up to the present day, with graph theory now a part of mainstream mathematics.
After an opening chapter giving an overview of graph theory and its legacy from the 18th and 19th centuries, the book is organized thematically into seven chapters, each covering the developments made in a specified area. Topics covered in these chapters include map colorings, planarity, Hamiltonian graphs, matchings, extremal graph theory, and complexity. Each chapter is supplemented with copious endnotes, providing additional comments, bibliographic details, and further context.
Written as an accessible account of the history of the subject, this book is suitable not only for graph theorists, but also for anyone interested in learning about the history of this fascinating subject. Some basic knowledge of linear algebra and group theory would be helpful, but is certainly not essential.
Undergraduate and graduate students and researchers interested in the history of graph theory.
Setting the scene
Coloring maps and graphs
Graphs on surfaces
Graphs, linear algebra, and groups
Cycles, factorizations, and matchings
Minors, perfect graphs, and extremal graph theory
Graph enumeration and probability
Graph algorithms and complexity
Index
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Softcover ISBN: 978-1-4704-7732-5
Product Code: SURV/291
Expected availability date: July 24, 2025
Mathematical Surveys and Monographs, Volume: 291
2025; 107 pp
MSC: Primary 11
Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to
-adic
-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory.
The goal of this third part of the three-part publication is to present additional aspects of the cyclotomic Iwasawa theory of
-adic Galois representations.
Graduate students and researchers interested in number theory and arithmetic geometry.
Framework on Iwasawa theory for
-adic Galois deformations
Known results on Iwasawa theory for
-adic deformations
Appendix A
References
Index