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Women Who Count: Honoring African American Women Mathematicians is a children's activity book highlighting the lives and work of 29 African American women mathematicians. Although the book is geared toward a young audience, its content is appropriate for all ages. The book includes portrait sketches and biographies for the featured mathematicians, and highlights the important contributions of Drs. Martha Euphemia Lofton Haynes, Evelyn Boyd Granville, and Marjorie Lee Browne, the first three African American women to receive doctoral degrees in mathematics.
Generalized Ricci Flow by Mario Garcia Fernandez; Jeffrey D. StreetsThe generalized Ricci flow is a geometric evolution equation which has recently emerged from investigations into mathematical physics, Hitchin's generalized geometry program, and complex geometry. This book gives an introduction to this new area, discusses recent developments, and formulates open questions and conjectures for future study. The text begins with an introduction to fundamental aspects of generalized Riemannian, complex, and Kahler geometry. This leads to an extension of the classical Einstein-Hilbert action, which yields natural extensions of Einstein and Calabi-Yau structures as `canonical metrics' in generalized Riemannian and complex geometry. The book then introduces generalized Ricci flow as a tool for constructing such metrics and proves extensions of the fundamental Hamilton/Perelman regularity theory of Ricci flow. These results are refined in the setting of generalized complex geometry, where the generalized Ricci flow is shown to preserve various integrability conditions, taking the form of pluriclosed flow and generalized Kahler-Ricci flow, leading to global convergence results and applications to complex geometry. Finally, the book gives a purely mathematical introduction to the physical idea of T-duality and discusses its relationship to generalized Ricci flow. The book is suitable for graduate students and researchers with a background in Riemannian and complex geometry who are interested in the theory of geometric evolution equations.
100 years of Math Milestones : The Pi Mu Epsilon Centennial Collection by Stephan Ramon Garcia; Steven J. MillerThis book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes.
A First Journey through Logic by Martin Hils; François LoeserThe aim of this book is to present mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum. The book starts with a presentation of naive set theory, the theory of sets that mathematicians use on a daily basis. Each subsequent chapter presents one of the main areas of mathematical logic: first order logic and formal proofs, model theory, recursion theory, Gödel's incompleteness theorem, and, finally, the axiomatic set theory.
Boundary Value Problems For Fractional Differential Equations And Systems by Bashir Ahmad; Johnny Henderson; Rodica LucaThis book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
Wittgenstein on Mathematics by Severin SchroederThis book offers a detailed account and discussion of Ludwig Wittgenstein's philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege's logicist attempt to provide arithmetic with a foundation and Wittgenstein's criticisms of it, followed by sketches of Wittgenstein's early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein's mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity -- calculation -- rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which it can be resolved. Finally, there are chapters analysing and defending Wittgenstein's provocative views on Hilbert's Formalism and the quest for consistency proofs and on Gödel's incompleteness theorems.
The Impact and Legacy of The Ladies' Diary (1704-1840) : A Women's Declaration by Frank J. SwetzThe Ladies' Diary was an annual almanac published in England from 1704 to 1840. It was designed to provide useful information to women; the subtitle reveals the purpose, Containing New Improvements in Arts and Sciences, and Many Entertaining Particulars: Designed for the Use and Diversion of the Fair Sex. It contained meteorological and astronomical information, recipes, health and medical advice, scientific information, and mathematical puzzles and problems. Readers were encouraged to, and did, send solutions and original problems and puzzles of their own for publication in the next year's issue.
The Distribution of Prime Numbers by Dimitris KoukoulopoulosPrime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem.
Random Matrices by Alexei Borodin; Ivan Corwin; Alice Guionnet (Editors)Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits.