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Pick up this book and dive into one of eight chapters relating mathematics to fiber arts! Amazing exposition transports any interested person on a mathematical exploration that is rigorous enough to capture the hearts of mathematicians.

Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book provides an introduction to the mathematical methods that form the foundations of machine learning and data science.

Offers a comprehensive history of the development of mathematics in the US and Canada. This first volume of a two-volume work takes the reader from the European encounters with North America in the fifteenth century up to the emergence of the United States as a world leader in mathematics in the 1930s.

Introduces a new notion of analytic space over a non-Archimedean field. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space.

Contains the proceedings of the conference String-Math 2016, held in June 2016 at College de France, Paris. The papers in this volume cover topics ranging from supersymmetric quantum field theories, topological strings, and conformal nets to moduli spaces of curves, representations, instantons, and harmonic maps, with applications to spectral theory and to the geometric Langlands program.

Contains the proceedings of the conference on Manifolds, $K$-Theory, and Related Topics, held in June, 2014. The articles are a collection of research papers featuring recent advances in homotopy theory, $K$-theory, and their applications to manifolds. Topics covered include homotopy and manifold calculus, structured spectra, and their applications to group theory and the geometry of manifolds.

This book starts with simple arithmetic inequalities and builds to sophisticated inequality results such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra is required of the student. The exposition is lean. Most of the learning occurs as the student engages in the problems posed in each chapter. And the learning is not "linear".

Provides an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas.

Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and this volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory.

This book, together with the companion volume, Fermat's Last Theorem: The Proof, presents in full detail the proof of Fermat's Last Theorem given by Wiles and Taylor. With these two books, the reader will be able to see the whole picture of the proof to appreciate one of the deepest achievements in the history of mathematics.

Provides a systematic exposition of the modern theory of Gaussian measures. It presents complete and detailed proofs fundamental facts about finite and infinite dimensional Gaussian distributions. Covered topics include linear properties, convexity, linear and nonlinear transformations, and applications to Gaussian and diffusion processes.

The work of Joseph Fels Ritt and Ellis Kolchin in differential algebra paved the way for exciting new applications in constructive symbolic computation, differential Galois theory, the model theory of fields, and Diophantine geometry. This book assembles Kolchin's mathematical papers.

Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.

Covers the classical theory of abstract Riemann surfaces. This book presents the requisite function theory and topology for Riemann surfaces. It also covers differentials and uniformization. For compact Riemann surfaces, it features topics such as divisors, Weierstrass points, and the Riemann-Roch theorem.

Operads are mathematical devices that describe algebraic structures of many varieties and in various categories. Operads are particularly important in categories with a good notion of 'homotopy', where they play a key role in organizing hierarchies of higher homotopies. This book offers an introduction describing the development of operad theory.

Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.

Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. This book presents an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. It is suitable for a year-long graduate course.

Focuses on the fundamentals of a theory, which is an analog of affine algebraic geometry for partial differential equations. This work describes applications of Secondary Calculus ranging from algebraic geometry to field theory, classical and quantum, including areas such as characteristic classes, differential invariants and variational calculus.

Treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. This book covers a wide range of topics of modern coordinate-free differential geometry.

Among nonlinear PDEs, dispersive and wave equations form an important class of equations, including the nonlinear Schrodinger equation, nonlinear wave equation, Korteweg de Vries equation, and the wave maps equation. This book offers an introduction to the methods and results used in the modern analysis of the Cauchy problem for such equations.

An introduction to stochastic processes studying certain elementary continuous-time processes. It includes a description of the Poisson process and related processes with independent increments as well as a brief look at Markov processes with a finite number of jumps.

The Ausdehnungslehre of 1862 is Grassmann's mature presentation of his extension theory. The work captured his mathematical achievements. This book includes development of the inner product and its relation to the concept of angle, the 'theory of functions' from the point of view of extension theory, and his contribution to the Pfaff problem.

Presents research on understanding, teaching, and learning mathematics at the post-secondary level. This book offers some preliminary results on student learning using technology when lessons are delivered via the Internet.

Presents the basics of linear algebra, with an emphasis on nonstandard and interesting proofs. This book features about 230 problems with solutions. It is suitable as a supplementary text for an undergraduate or graduate algebra course.

Includes a treatment of exponential, logarithmic, and trigonometric functions, progressions, and induction method, as well as an extensive introduction to differential and integral calculus.

A guide to the qualitative theory of foliations. It features topics including: analysis on foliated spaces, characteristic classes of foliations and foliated manifolds. It is suitable as a supplementary text for a topics course at the advanced graduate level.