From Combinatorics to Number Theory, $p$-adic Analysis, Commutative andNon-Commutative Algebra
This book presents the theory of integer-valued polynomials, as transformed by the work of Manjul Bhargava in the late 1990s. Building from the core ideas in commutative algebra and number theory, the author weaves a panoramic perspective that encompasses results in combinatorics, ultrametric analysis, probability, dynamical systems, and ......
This richly illustrated text guides readers to discover the beautiful structure of mathematical billiards. Centered around expertly designed problem sets, the book incrementally builds up ideas through threads of related problems, fostering curiosity, exploration, and conversation. Working through the problems, the reader builds an understanding ......
Inverse problems are those where, from ""external"" observations of a hidden ""black box"" system (a patient's body, nontransparent industrial object, interior of the Earth, etc.), one needs to recover the unknown parameters of the system. A prototypical example is the by now classical Calderon problem, forming the basis of Electrical Impedance ......
Deep learning uses multi-layer neural networks to model complex data patterns. Large models-with millions or even billions of parameters-are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, ......
Inverse problems are those where, from ""external"" observations of a hidden ""black box"" system (a patient's body, nontransparent industrial object, interior of the Earth, etc.), one needs to recover the unknown parameters of the system. A prototypical example is the by now classical Calderon problem, forming the basis of Electrical Impedance ......
Deep learning uses multi-layer neural networks to model complex data patterns. Large models-with millions or even billions of parameters-are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, ......
Optimal control theory concerns the study of dynamical systems where one operates a control parameter with the goal of optimizing a given payoff function. This textbook provides an accessible, examples-led approach to the subject. The text focuses on systems modeled by differential equations, with applications drawn from a wide range of topics, ......
Scenes from the Early History of Algebraic Number Theory
In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose in the formative years of algebraic number theory and played a major role in the early development of the field. When nineteenth-century mathematicians set out to generalize E. E. Kummer's theory of ideal divisors in ......
This volume consists of surveys on topics to which Bernd Sturmfels has contributed over his mathematical career: invariant theory, Grobner bases, toric ideals and varieties, algebraic methods in discrete and convex optimization, hypergeometric systems, algebraic statistics, likelihood geometry, tropical geometry, chemical reaction networks, ......
