Bøger af Harold M. Edwards

He [Kronecker] was, in fact, attempting to describe and to initiate a new branch of mathematics, which would contain both number theory and alge- braic geometry as special cases.-Andre Weil [62] This book is about mathematics, not the history or philosophy of mathemat- ics. Still, history and philosophy were prominent among my motives for writing it, and historical and philosophical issues will be major factors in determining whether it wins acceptance. Most mathematicians prefer constructive methods. Given two proofs of the same statement, one constructive and the other not, most will prefer the constructive proof. The real philosophical disagreement over the role of con- structions in mathematics is between those-the majority-who believe that to exclude from mathematics all statements that cannot be proved construc- tively would omit far too much, and those of us who believe, on the contrary, that the most interesting parts of mathematics can be dealt with construc- tively, and that the greater rigor and precision of mathematics done in that way adds immensely to its value.

In his new undergraduate textbook, Harold M. Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra. Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century.Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience.Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject. Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject.

Contents and treatment are fresh and very different from the standard treatmentsPresents a fully constructive version of what it means to do algebraThe exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader

Work on this book was supported in part by the James M. Vaughn, Jr., Vaughn Foundation Fund.

In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus.

Number theory is the equal of Euclidean geometry - some would say it is superior to Euclidean geometry - as a model of pure, logical, deductive thinking. This title explains number theory in a way that gives deductive reasoning, including algorithms and computations, the central role.

This is an introduction to Galois Theory along the lines of Galois's Memoir on the Conditions for Solvability of Equations by Radicals. It puts Galois's ideas into historical perspective by tracing their antecedents in the works of Gauss, Lagrange, Newton, and even the ancient Babylonians.

This work presents a modern approach to a remarkable algebraic technique. It should be of interest to both the mathematical historian and the working specialist in commutative algebra, number theory and algebraic geometry.