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Asymptotic, Algebraic and Geometric Aspects of Integrable Systems
This proceedings volume gathers together selected works from the 2018 “Asymptotic, Algebraic and Geometric Aspects of Integrable Systems” workshop that was held at TSIMF Yau Mathematical Sciences Center in Sanya, China, honoring Nalini Joshi on her 60th birthday. The papers cover recent advances in asymptotic, algebraic and geometric methods in the study of discrete integrable systems. The workshop brought together experts from fields such as asymptotic analysis, representation theory and geometry, creating a platform to exchange current methods, results and novel ideas. This volume's articles reflect these exchanges and can be of special interest to a diverse group of researchers and graduate students interested in learning about current results, new approaches and trends in mathematical physics, in particular those relevant to discrete integrable systems.
Discrete Painlevé Equations
Discrete Painlevé equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics. This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and National Science Foundation conference in Texas in 2016. Instead of technical theorems or complete proofs, the book relies on providing essential points of many arguments through explicit examples, with the hope that they will be useful for applied mathematicians and physicists.
The Kitchen Pantry Scientist Math for Kids
Math for Kids, the fourth book of The Kitchen Pantry Scientist series, brings math to life through biography and creative engagement. Go beyond counting. Solve puzzles, learn a magic trick, and play a ton of games. This engaging guide offers a series of snapshots of 20+ mathematicians, from ancient history through today, paired with related hands-on projects perfect for a kitchen or a classroom. Each lab tells the story of a mathematician along with some background about the importance of their work, and a description of where it is still being used or reflected in today’s world. A step-by-step illustrated game or activity paired with each story offers kids an opportunity to engage directl...
Love & (Mellow) Drama
Gayatri Kulkarni: A gen Z girl who has always lived under the shadow of her elder brother Sharad; so much so that she even chose her degree and college following in his footsteps. Although she doesn’t regret it, she wishes her parents would understand her dream to pursue her one true passion - DANCE. Varun Agarwal: A millennial who believes there are no shortcuts in life. He has learned the hard way that being born into a wealthy family comes with more cons than the world would ever understand. She belongs to a Maharashtrian middle-class family from the suburbs. He hails from an affluent family in South Bombay. The only common point between them - being Mumbaikars. How do their paths cross...
Fifty Years of Women in Mathematics
The Association for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Fu...
Discrete Systems and Integrability
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thorough list of references will benefit upper-level undergraduate, and beginning graduate students as well as researchers from other disciplines.
Discrete Painlevé Equations
Discrete Painlevé equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic geometry, Coxeter groups, topology, special functions theory, and mathematical physics. This book necessarily starts with introductory material to give the reader an accessible entry point to this vast subject matter. It is based on lectures that the author presented as principal lecturer at a Conference Board of Mathematical Sciences and Nation.
Smart Girls
Are girls taking over the world? It would appear so, based on magazine covers, news headlines, and popular books touting girls’ academic success. Girls are said to outperform boys in high school exams, university entrance and graduation rates, and professional certification. As a result, many in Western society assume that girls no longer need support. But in spite of the messages of post-feminism and neoliberal individualism that tell girls they can have it all, the reality is far more complicated. Smart Girls investigates how academically successful girls deal with stress, the “supergirl” drive for perfection, race and class issues, and the sexism that is still present in schools. Describing girls’ varied everyday experiences, including negotiations of traditional gender norms, Shauna Pomerantz and Rebecca Raby show how teachers, administrators, parents, and media commentators can help smart girls thrive while working toward straight As and a bright future.
Surgery Theory
This monograph provides a comprehensive introduction to surgery theory, the main tool in the classification of manifolds. Surgery theory was developed to carry out the so-called Surgery Program, a basic strategy to decide whether two closed manifolds are homeomorphic or diffeomorphic. This book provides a detailed explanation of all the ingredients necessary for carrying out the surgery program, as well as an in-depth discussion of the obstructions that arise. The components include the surgery step, the surgery obstruction groups, surgery obstructions, and the surgery exact sequence. This machinery is applied to homotopy spheres, the classification of certain fake spaces, and topological ri...
Framing Global Mathematics
This open access book is about the shaping of international relations in mathematics over the last two hundred years. It focusses on institutions and organizations that were created to frame the international dimension of mathematical research. Today, striking evidence of globalized mathematics is provided by countless international meetings and the worldwide repository ArXiv. The text follows the sinuous path that was taken to reach this state, from the long nineteenth century, through the two wars, to the present day. International cooperation in mathematics was well established by 1900, centered in Europe. The first International Mathematical Union, IMU, founded in 1920 and disbanded in 1...
