Dilip P Patil (Indian Institute of Science, India)
Uwe Storch (Ruhr University, Germany)

INTRODUCTION TO ALGEBRAIC GEOMETRY AND COMMUTATIVE ALGEBRA

This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.

Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

Contents:

Finitely Generated Algebras
K-spectrum and the Zariski Topology
Prime Spectra and Dimension
Schemes
Projective Schemes
Regular, Normal, Smooth Points
Riemann-Roch Theorem

200pp (approx.) Pub. date: Scheduled Spring 2010
ISBN: 978-981-4304-56-6
ISBN: 978-981-4307-58-1(pbk)

Bruce Shawyer (Memorial University of Newfoundland, Canada)

EXPLORATIONS IN GEOMETRY

This book covers the basic topics in geometry (including trigonometry) that are accessible and valuable to senior high school and university students. It also includes materials that are very useful for problem solving in mathematical competitions, from relatively easy to advanced levels, including the International Mathematical Olympiad.

Contents:

Basic Euclidean Geometry
Trigonometry including Hyperbolic Functions
Concurrency and Collinearity Results
Circumcircle
Inradius and Semi-Perimeter Formulae
Conic Sections
Constructabilty including Some “Folk Theorems”
Less Known Recent Results including the Broken Chord Theorem
Splitter and Cleavers, and Remarkable Concurrences


318pp (approx.) Pub. date: Scheduled Spring 2010
ISBN: 978-981-4295-85-7
ISBN: 978-981-4295-86-4(pbk)

Donald Yau (The Ohio State University at Newark, USA)

LAMBDA-RINGS

The book gives a self-contained introduction to the theory of lambda-rings and closely related topics, including Witt vectors, integer-valued polynomials, and binomial rings. Many of the purely algebraic results about lambda-rings presented in this book have never appeared in book form before. This book concludes with a chapter on open problems related to lambda-rings.

Contents:

λ-Rings
Universal λ-Rings
Adams Operations
Witt Vectors
Binomial Rings
Filtered λ-Rings, I
Filtered λ-Rings, II
Open Problems

Readership: Advanced mathematics undergraduates, graduate students and researchers in the fields of homotomy theory, algebraic K-theory, algebraic geometry and representation theory.

204pp Pub. date: Mar 2010
ISBN: 978-981-4299-09-1