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 correctness, this third edition of Ideals, Varieties and Algorithms includes: a significantly updated section on Maple; updated information on AXIOM, CoCoA, Macaulay 2, Magma, Mathematica and SINGULAR; and presents a shorter proof of the Extension Theorem.
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.
This book presents algorithmic tools for algebraic geometry, with experimental applications. It also introduces Macaulay 2, a computer algebra system supporting research in algebraic geometry, commutative algebra, and their applications.
This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.
Gillispie, C. C. 2000 Pierre-Simon Laplace, 1749–1827: A Life in Exact Science. Princeton University Press. Gouvea, F. Q. 2011 Was Cantor surprised? Am. Math. Monthly 118:198–209. Gray, J. J. 2000 The Hilbert Challenge: A Perspective on ...
Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives.
The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra.
The book also includes many exercises, both theoretical and practical. This is a book about Gröbner bases and their applications. It contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements.
First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.
This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms.