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Using Algebraic Geometry
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Ideals, Varieties, and Algorithms
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
The Poincaré Conjecture
The Poincaré Conjecture tells the story behind one of the world’s most confounding mathematical theories. Formulated in 1904 by Henri Poincaré, his Conjecture promised to describe the very shape of the universe, but remained unproved until a huge prize was offered for its solution in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O’Shea explains the maths behind the Conjecture and its proof, and illuminates the curious personalities surrounding this perplexing conundrum, along the way taking in a grand sweep of scientific history from the ancient Greeks to Christopher Columbus. This is an enthralling tale of human endeavour, intellectual brilliance and the thrill of discovery.
Programming for Mathematicians
Aimed at teaching mathematics students how to program using their knowledge of mathematics, the entire books emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: manipulation and enrichment of existing code; use of recurrent sequences; deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed, and the text concludes with an explanation of how a compiler works and how to compile "by hand" little programs. Intended for anyone who thinks mathematically and wants to program and play with mathematics.
Israel/Palestine and the Politics of a Two-State Solution
This is a dispassionate examination of the viability of a two-state solution in the Israeli-Palestinian conflict, based on the politics of Israel, Palestine and the United States. It includes instructive case studies from South Africa in Namibia and the Irish claim to Northern Ireland. The results of Israeli elections from 2001 to 2013 are analyzed (with the conclusion that the Likud will be in any government coalition for at least the midterm future, giving it a veto over policy). A chapter examining the history and ideology of the secular right over the last 90 years follows. There are three chapters of case studies: the Likud withdrawal from the Sinai in 1979-1982 and from Gaza in 2005, the withdrawal of South Africa from Namibia in 1988-1989, and the dropping of Ireland's constitutional claim to Northern Ireland in 1998 under a Fianna Fail government--the same party that wrote the constitution in 1937. A chapter examines Palestinian politics since the mandatory era and another, the American-Israeli alliance and American politics. A concluding chapter draws lessons from the case studies and the analysis.
Silent as the Dead
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The Six Pillars of Calculus: Biology Edition
The Six Pillars of Calculus: Biology Edition is a conceptual and practical introduction to differential and integral calculus for use in a one- or two-semester course. By boiling calculus down to six common-sense ideas, the text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem. This engaging process of discovery encourages students to wrestle with the material and understand the reasoning behind the techniques they are learning—to focus on when and why to use the tools of calculus, not just on how to apply formulas. Modeling and differential equations are front and center. Solut...
Algebraic Geometry
"Surveys and applies fundamental ideas and techniques in the theory of curves, surfaces, and threefolds to a wide variety of subjects. Furnishes all of the basic definitions necessary for understanding and provides interrelated articles that support and refer to one another."
Storming the Ivory Tower
A firsthand account of how Richard Corcoran, former education commissioner of Florida, successfully took on powerful progressive interest groups, broke their monopoly, and paved the way for higher education reform across America. Covid alerted the nation to the reality that K-12 schools—private and public alike—were infested with ideologues bent on indoctrinating children. Then, three years after the beginning of the pandemic, the shocking response to Hamas’s genocidal assault on Israel made Americans aware that the same tumor had wholly sickened our country’s colleges and universities. Now, conservatives—and increasingly, moderates and old-school liberals—want to know exactly ho...
Schnitzer O'Shea
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