MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7752-3
Expected availability date: August 07, 2024
Problem Books Volume: 38; 2024; 370 pp
Welcome to The Mathematical Playground, a book celebrating more than thirty years of the problems column in the MAA undergraduate magazine, Math Horizons. Anecdotes, interviews, and historical sketches accompany the puzzles, conveying the vibrancy of the gPlaygroundh community. The lively prose and humor used throughout the book reveal the enthusiasm and playfulness that have become the column's hallmark.
Each chapter features a theme that helps illustrate community: from the Opening Acts?chronicling how interesting questions snowball into original research?to the Posers and Solvers themselves. These stories add an engaging dimension beyond the ample mathematical challenge. A particular highlight is a chapter introducing the seven editors who have produced gThe Playgroundh, revealing the perspectives of the individuals behind the column.
The Mathematical Playground has plenty to offer both novice and experienced solvers. The lighthearted, conversational style, together with copious hints, a problem-solving primer, and a detailed glossary, welcomes newcomers, regardless of their background, to the puzzle-solving world. The more seasoned solver will find over twenty new problems plus open-ended challenges and suggestions for further investigation. Whether you're a long-time Math Horizons reader, or encountering gThe Playgroundh for the first time, you are invited into this celebration of the rich culture of recreational mathematics. Just remember the most important rule ... Have fun!
Anyone interested in recreational mathematics.
Chapters
Introduction
Phi, Pi, e, Fum! 3 constants
Picture perfect 5 portraits
Opening acts 7 starters
Prominent players 11 cameos
The zip line 13 adventures
Stumpers and bloopers 17 quandaries
Posers and solvers 19 contributions
Editors of the playground 23 questions
Games 29 challenges
Glossary of terms and theorems
Hints
Solutions
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7466-9
Expected availability date: August 11, 2024
Classroom Resource Materials Volume: 72;
2024; 351 pp
MSC: Primary 00; 97
This book offers engaging cross-curricular modules to supplement a variety of pure mathematics courses. Developed and tested by college instructors, each activity or project can be integrated into an instructorfs existing class to illuminate the relationship between pure mathematics and other subjects. Every chapter was carefully designed to promote active learning strategies.
The editors have diligently curated a volume of twenty-six independent modules that cover topics from fields as diverse as cultural studies, the arts, civic engagement, STEM topics, and sports and games. An easy-to-use reference table makes it straightforward to find the right project for your class. Each module contains a detailed description of a cross-curricular activity, as well as a list of the recommended prerequisites for the participating students. The reader will also find suggestions for extensions to the provided activities, as well as advice and reflections from instructors who field-tested the modules.
Teaching Mathematics Through Cross-Curricular Projects is aimed at anyone wishing to demonstrate the utility of pure mathematics across a wide selection of real-world scenarios and academic disciplines. Even the most experienced instructor will find something new and surprising to enhance their pure mathematics courses.
For additional material and updates on the book, visit www.ams.org/bookpages/clrm-72. The additional material and updates will be available after the book is published.
Undergraduate instructors interested in exposing their students to cross-curricular applications of the material that is taught in pure math courses.
Chapters
Investigating foundations of ancient Rapa Nui Houses
Kinship and group theory
Visualizing induction with African Sona designs
Japanese temple geometry
Abstract algebra in dance composition
Topological dance activities
Literary incarnations of topology
Solving with Sherlock
Mathematical dramaturgy: Making connections between mathematics and literature
Assessing the bikeability of bicycle infrastructure with graph theory
Ramping up campus accessibility through calculus
Whofs got the power? Measuring power in the U.S. legislative system
Order in the court! Spectral theory for an introductory linear algebra course
Double integrals and the human condition
Making mathematics relevant: Math in the news
Graph theoretical modeling of tile-based DNA self-assembly
Estimating the size and shape of a lung nodule from an x-ray image
Gradient descent methods in machine learning
Application-inspired real analysis: Image denoising
The seahorse reveals the waves
A topology scavenger hunt to introduce topological data analysis
Adventures in the SETR card game
Quads: A SET-like game with a twist
Eminently logical: The Monty Hall paradox as a teaching tool
Enumeration of the positive rational numbers using the Calkin-Wilf tree with application to the game Euclid
Get in the game with linear algebra
MAA Press: An Imprint of the American Mathematical Society
Expected availability date: August 15, 2024
Anneli Lax New Mathematical Library Volume: 56;
2024; 156 pp
MSC: Primary 52
Together with its clear mathematical exposition, the problems in this book take the reader from an introduction to discrete geometry all the way to its frontiers. Investigations start with easily drawn figures, such as dividing a polygon into triangles or finding the minimum number of gguardsh for a polygon (gart galleryh problem). These early explorations build intuition and set the stage. Variations on the initial problems stretch this intuition in new directions. These variations on problems together with growing intuition and understanding illustrate the theme of this book: gWhen you have answered the question, it is time to question the answer.h Numerous drawings, informal explanations, and careful reasoning build on high school algebra and geometry.
High school and undergraduate students interested in mathematics; instructors running summer programs and math circles.
Chapters
Beginning explorations
First variations
Further variations
Final explorations and connections
Answers to exercises
Softcover ISBN: 978-1-4704-7087-6
Expected availability date: August 18, 2024
Proceedings of Symposia in Pure Mathematics Volume: 109;
2024; 284 pp
MSC: Primary 53; 57
This volume contains the proceedings of the summer school and research conference gFrontiers in Geometry and Topologyh, celebrating the sixtieth birthday of Tomasz Mrowka, which was held from August 1?12, 2022, at the Abdus Salam International Centre for Theoretical Physics (ICTP).
The summer school featured ten lecturers and the research conference featured twenty-three speakers covering a range of topics. A common thread, reflecting Mrowka's own work, was the rich interplay among the fields of analysis, geometry, and topology.
Articles in this volume cover topics including knot theory; the topology of three and four-dimensional manifolds; instanton, monopole, and Heegaard Floer homologies; Khovanov homology; and pseudoholomorphic curve theory.
Researchers and graduate students interested in recent developments in low-dimensional topology.
Articles
Francesco Lin ? Lectures on families of Dirac operators and applications
Thomas Walpuski ? Lectures on generalised Seiberg?Witten equations
Nima Anvari ? A splitting formula in instanton Floer homology
Nima Anvari and Ian Hambleton ? Finite group actions on 4
-manifolds and equivariant bundles
Dave Auckly and Daniel Ruberman ? Exotic families of embeddings
John A. Baldwin and Steven Sivek ? An instanton take on some knot detection results
Hans U. Boden, Christopher M. Herald and Paul Kirk ? Examples of homology 3-spheres whose Chern-Simons function is not Morse-Bott
Lothar Gottsche ? Blowup formulas for Segre and Verlinde numbers of surfaces and higher rank Donaldson invariants
Kristen Hendricks, Jennifer Hom, Matthew Stoffregen and Ian Zemke ? A note on PL-disks and rationally slice knots
Robert Lipshitz and Sucharit Sarkar ? Khovanov homology of strongly invertible knots and their quotients
Paolo Lisca and Andrea Parma ? On almost complex embeddings of rational homology balls
Maggie Miller ? Explicitly describing fibered 3-manifolds through families of singularly fibered surfaces
Andras I. Stipsicz and Zoltan Szabo ? On the minimal genus problem in four-manifolds
Joshua Wang ? The Gysin sequence and the sl(N)
homology of T(2,m)
Claudius Zibrowius ? Heegaard Floer multicurves of double tangles
Softcover ISBN: 978-1-4704-7425-6
Expected availability date: August 29, 2024
Mathematical Surveys and Monographs Volume: 282;
2024; 278 pp
MSC: Primary 20; 51
This book offers an alternative proof of the Bestvina?Feighn combination theorem for trees of hyperbolic spaces and describes uniform quasigeodesics in such spaces. As one of the applications of their description of uniform quasigeodesics, the authors prove the existence of Cannon?Thurston maps for inclusion maps of total spaces of subtrees of hyperbolic spaces and of relatively hyperbolic spaces. They also analyze the structure of Cannon?Thurston laminations in this setting. Furthermore, some group-theoretic applications of these results are discussed. This book also contains background material on coarse geometry and geometric group theory.
Graduate students and researchers interested in hyperbolic geometry.
Chapters
Preliminaries on metric geometry
Graphs of groups and trees of metric spaces
Carpets, ladders, flow-spaces, metric bundles, and their retractions
Hyperbolicity of ladders
Hyperbolicity of flow-spaces
Hyperbolicity of trees of spaces: Putting everything together
Description of geodesics
Cannon?Thurston maps
Cannon?Thurston maps for elatively hyperbolic spaces
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Softcover ISBN: 978-1-4704-5618-4
Expected availability date: September 26, 2024
Courant Lecture Notes Volume: 32;
2024; Estimated: 205 pp
This book introduces the mathematical ideas connecting Statistical Mechanics and Conformal Field Theory (CFT). Building advanced structures on top of more elementary ones, the authors map out a well-posed road from simple lattice models to CFTs.
Structured in two parts, the book begins by exploring several two-dimensional lattice models, their phase transitions, and their conjectural connection with CFT. Through these lattice models and their local fields, the fundamental ideas and results of two-dimensional CFTs emerge, with a special emphasis on the Unitary Minimal Models of CFT. Delving into the delicate ideas that lead to the classification of these CFTs, the authors discuss the assumptions on the lattice models whose scaling limits are described by CFTs. This produces a probabilistic rather than an axiomatic or algebraic definition of CFTs.
Suitable for graduate students and researchers in mathematics and physics, Lattice Models and Conformal Field Theory introduces the ideas at the core of Statistical Field Theory. Assuming only undergraduate probability and complex analysis, the authors carefully motivate every argument and assumption made. Concrete examples and exercises allow readers to check their progress throughout.
Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Researchers interested in probability, mathematical physics, statistical mechanics, and high-energy physics.
Introduction
Lattice models, phase transitions, and critical exponents
Statistical and quantum field theories
Conformal field theory
Conformal field theory: Minimal models on the plane
Local fields and correlations
Stress-energy tensor and conformal Ward identities
Unitarity and radial quantization
Primary fields and conformal families
Unitary minimal models, lattice models, and loop models
Bibliography
Index