This book details the heart and soul of modern commutative and algebraic geometry. It covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. In addition to enhancing the text of the second edition, with over 200 pages reflecting changes to enhance clarity and...

Many colleges and universities offer a course in discrete mathematics. Students taking these courses are from many disciplines, one of the largest being computer science. As a part of the Mathematics Across the Curriculum project at Dartmouth, supported by the National Science Foundation,1 we proposed to create a discrete mathematics...

Quantitative Finance is expanding rapidly. One of the aspects ofthe recent financial crisis is that, given the complexity offinancial products, the demand for people with high numeracy skillsis likely to grow and this means more recognition will be given toQuantitative Finance in existing and new course structuresworldwide. Evidence has...

Calculus is one of the milestones of Western thought. Building on ideas of Archimedes, Fermat, Newton, Leibniz, Cauchy, and many others, the calculus is arguably the cornerstone of modern science. Any well-educated person  should at least be acquainted with the ideas of calculus, and a scientifically literateperson must know calculus...

In the first part of the...

Bundles, connections, metrics and curvature are the 'lingua franca' of modern differential geometry and theoretical physics. This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects.

Many of the tools used in differential topology are introduced and the...

The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing...

Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.

Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a...

Mathematical Statistics for Economics and Business, Second Edition, provides a comprehensive introduction to the principles of mathematical statistics which underpin statistical analyses in the fields of economics, business, and econometrics.  The selection of topics in this textbook is designed to provide students with a...