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Algebraic Geometry
This book is built upon a basic second-year masters course given in 1991– 1992, 1992–1993 and 1993–1994 at the Universit´ e Paris-Sud (Orsay). The course consisted of about 50 …
Logic and Structure
Dirk van Dalen’s popular textbook Logic and Structure, now in its fifth edition, provides a comprehensive introduction to the basics of classical and intuitionistic logic, model …
An Invitation to Algebraic Geometry
The aim of this book is to describe the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that …
Galois Theory
The first edition aimed to give a geodesic path to the Fundamental Theorem of Galois Theory, and I still think its brevity is valuable. Alas, the book is now a bit longer, but I …
The Calculus of Variations
The calculus of variations has a long history of interaction with other branches of mathematics such as geometry and differential equations, and with physics, particularly …
Stochastic Differential Equations
This edition contains detailed solutions of selected exercises. Many readers have requested this, because it makes the book more suitable for self-study. At the same time new …
Algebraic Geometry over the Complex Numbers
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some …
Linear Programming Duality
The main theorem of Linear Programming Duality, relating a "pri- mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of …
Plane and Solid Geometry
Nature and the world around us that we ourselves design, furnish, and build contain many geometric patterns and structures. This is one of the reasons that geometry should be …
An Introduction to Infinite-Dimensional Analysis
In this revised and extended version of his course notes from a 1-year course at Scuola Normale Superiore, Pisa, the author provides an introduction – for an audience knowing basic …
Modern Analysis and Topology
The purpose of this book is to provide an integrated development of modern analysis and topology through the integrating vehicle of uniform spaces. It is intended that the material …
Introduction to Differentiable Manifolds
This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are …