This up-to-date introductiontotypetheory and homotopytypetheory will be e...This up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and...more
The beginning graduate student inhomotopytheory is confronted with a vast li...The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable...more
Category theory provides structure for the mathematical world and is seen ever...Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book the author bridges the gap between pure category theory and its numerous applications in homotopy theory providing the...more
Despite its seemingly deterministic nature the study of whole numbers especial...Despite its seemingly deterministic nature the study of whole numbers especially prime numbers has many interactions with probability theory the theory of random processes and events. This surprising connection was first discovered around 1920 but...more
Reproducing kernel Hilbert spaces have developed into an important tool in man...Reproducing kernel Hilbert spaces have developed into an important tool in many areas especially statistics and machine learning and they play a valuable role in complex analysis probability group representation theory and the theory of integral...more
This concise introductionto ring theory module theory and number theory is id...This concise introduction to ring theory module theory and number theory is ideal for a first year graduate student as well as being an excellent reference for working mathematicians in other areas. Starting from definitions the book introduces...more
This book gives a general outlook on homotopytheory; fundamental concepts suc...This book gives a general outlook on homotopy theory; fundamental concepts such as homotopy groups and spectral sequences are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in...more
Through the fundamental work of Deligne and Lusztig in the 1970s further devel...Through the fundamental work of Deligne and Lusztig in the 1970s further developed mainly by Lusztig the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods...more
Representation theory has applications to number theory combinatorics and many...Representation theory has applications to number theory combinatorics and many areas of algebra. The aim of this text is to present some of the key results in the representation theory of finite groups. Professor Alperin concentrates on local...more
Prime numbers are the multiplicative building blocks of natural numbers. Under...Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is...more
Volume II on formal (ZFC) set theory incorporates a self-contained chapter 0 o...Volume II on formal (ZFC) set theory incorporates a self-contained chapter 0 on proof techniques so that it is based on formal logic in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough...more
This book describes various approaches to the Inverse Galois Problem a classic...This book describes various approaches to the Inverse Galois Problem a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory algebraic geometry and number theory...more
This book describes various approaches to the Inverse Galois Problem a classic...This book describes various approaches to the Inverse Galois Problem a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory algebraic geometry and number theory...more
This book gives a general outlook on homotopytheory; fundamental concepts suc...This book gives a general outlook on homotopy theory; fundamental concepts such as homotopy groups and spectral sequences are developed from a few axioms and are thus available in a broad variety of contexts. Many examples and applications in...more
Incorporated in this volume are the first two books in Mukai s series on Modul...Incorporated in this volume are the first two books in Mukai s series on Moduli Theory. The notion of a moduli space is central to geometry. However its influence is not confined there; for example the theory of moduli spaces is a crucial ingredient...more