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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 …
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 …
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 …
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 …
Introductory Problem Courses in Analysis and Topology
Strange Phenomena in Convex and Discrete Geometry
Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing …
Vector Analysis Versus Vector Calculus
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge …
Numerical Range
The theories of quadratic forms and their applications appear in many parts of mathematics and the sciences. All students of mathematics have the opportunity to encounter such …
Space-Filling Curves
The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like …