Maciej (Professor of Mathematical Physics Dunajski Professor of Mathematical Physics Department of Applied Mathematics and Theoretical Physics University of Cambridge)
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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and profess
This book is designed as a text for a first-year graduate algebra course. As necessary background we would consider a good undergraduate linear algebra course. An undergraduate abstract algebra course
Covers material from function theory up to residue calculus, including discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations from their c
A clean, elegant, absolutely lovely text derived from a course which the author has taught for many years at Caltech, conceived as a companion to his Introduction to analytic number theory , and diff
This book provides an introduction to combinatorial commutative algebra with particular emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determin
Based on a translation of the 6th edition of Gewohnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as w
"An excellent up-to-date introduction to the theory of groups. It is general yet comprehensive, covering various branches of group theory. The 15 chapters contain the following main topics: free group
From the reviews: "The book is well written. We find here many examples. Each chapter is followed by exercises, and at the end of the book there are outline solutions to some of them. [...] I especial
The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applicatio
This text provides an introduction to basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas: for instance,
This volume is intended as an introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover all parts of numerical analysis, t
Written by an authority with great practical and teaching experience in the field, this book addresses a number of topics in computational number theory. Chapters one through five form a homogenous su
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition.
An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician.
The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrodinger operators
This introduction to algebraic number theory via "Fermat's Last Theorem" follows its historical development, beginning with the work of Fermat and ending with Kummer theory of "ideal" factorization. I
Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two
This book is an introductory text in functional analysis. Unlike many modern treatments, it begins with the particular and works its way to the more general. From the reviews: "This book is an excelle
