Algebraic Methods II: Theory, Tools and Applications

Algebraic Methods II: Theory, Tools and Applications
Author: Jan A. Bergstra
Publisher: Springer Science & Business Media
Total Pages: 448
Release: 1991-04-10
Genre: Computers
ISBN: 9783540539124

The proper treatment and choice of the basic data structures is an important and complex part in the process of program construction. Algebraic methods provide techniques for data abstraction and the structured specification, validation and analysis of data structures. This volume originates from a workshop organized within ESPRIT Project 432 METEOR, An Integrated Formal Approach to Industrial Software Development, held in Mierlo, The Netherlands, September 1989. The volume includes five invited contributions based on workshop talks given by A. Finkelstein, P. Klint, C.A. Middelburg, E.-R. Olderog, and H.A. Partsch. Ten further papers by members of the METEOR team are based on talks given at the workshop. The workshop was a successor to an earlier one held in Passau, Germany, June 1987, the proceedings of which were published as Lecture Notes in Computer Science, Vol. 394.

The algebra of logic

The algebra of logic
Author: Louis Couturat
Publisher: BoD - Books on Demand
Total Pages: 96
Release: 2022-12-15
Genre: Mathematics
ISBN:

Louis Couturat (French: [kutyʁa]; 17 January 1868 – 3 August 1914) was a French logician, mathematician, philosopher, and linguist. Couturat was a pioneer of the constructed language Ido. He was the French advocate of the symbolic logic that emerged in the years before World War I, thanks to the writings of Charles Sanders Peirce, Giuseppe Peano and his school, and especially to The Principles of Mathematics by Couturat's friend and correspondent Bertrand Russell. Like Russell, Couturat saw symbolic logic as a tool to advance both mathematics and the philosophy of mathematics. In this, he was opposed by Henri Poincaré, who took considerable exception to Couturat's efforts to interest the French in symbolic logic. With the benefit of hindsight, we can see that Couturat was in broad agreement with the logicism of Russell, while Poincaré anticipated Brouwer's intuitionism. His first major publication was Couturat (1896). In 1901, he published La Logique de Leibniz, a detailed study of Leibniz the logician, based on his examination of the huge Leibniz Nachlass in Hanover. Even though Leibniz had died in 1716, his Nachlass was cataloged only in 1895. Only then was it possible to determine the extent of Leibniz's unpublished work on logic. In 1903, Couturat published much of that work in another large volume, his Opuscules et Fragments Inedits de Leibniz, containing many of the documents he had examined while writing La Logique. Couturat was thus the first to appreciate that Leibniz was the greatest logician during the more than 2000 years that separate Aristotle from George Boole and Augustus De Morgan. A significant part of the 20th century Leibniz revival is grounded in Couturat's editorial and exegetical efforts. This work on Leibniz attracted Russell, also the author of a 1900 book on Leibniz, and thus began their professional correspondence and friendship. In 1905, Couturat published a work on logic and the foundations of mathematics (with an appendix on Kant's philosophy of mathematics) that was originally conceived as a translation of Russell's Principles of Mathematics. In the same year, he published L'Algèbre de la logique, a classic introduction to Boolean algebra and the works of C.S. Peirce and Ernst Schröder.

Algebraic Methods II: Theory, Tools and Applications

Algebraic Methods II: Theory, Tools and Applications
Author: Jan A. Bergstra
Publisher: Springer
Total Pages: 436
Release: 1991-04-10
Genre: Mathematics
ISBN: 9783540539124

The proper treatment and choice of the basic data structures is an important and complex part in the process of program construction. Algebraic methods provide techniques for data abstraction and the structured specification, validation and analysis of data structures. This volume originates from a workshop organized within ESPRIT Project 432 METEOR, An Integrated Formal Approach to Industrial Software Development, held in Mierlo, The Netherlands, September 1989. The volume includes five invited contributions based on workshop talks given by A. Finkelstein, P. Klint, C.A. Middelburg, E.-R. Olderog, and H.A. Partsch. Ten further papers by members of the METEOR team are based on talks given at the workshop. The workshop was a successor to an earlier one held in Passau, Germany, June 1987, the proceedings of which were published as Lecture Notes in Computer Science, Vol. 394.

Problems and Proofs in Numbers and Algebra

Problems and Proofs in Numbers and Algebra
Author: Richard S. Millman
Publisher: Springer
Total Pages: 0
Release: 2016-10-06
Genre: Mathematics
ISBN: 9783319357232

Focusing on an approach of solving rigorous problems and learning how to prove, this volume is concentrated on two specific content themes, elementary number theory and algebraic polynomials. The benefit to readers who are moving from calculus to more abstract mathematics is to acquire the ability to understand proofs through use of the book and the multitude of proofs and problems that will be covered throughout. This book is meant to be a transitional precursor to more complex topics in analysis, advanced number theory, and abstract algebra. To achieve the goal of conceptual understanding, a large number of problems and examples will be interspersed through every chapter. The problems are always presented in a multi-step and often very challenging, requiring the reader to think about proofs, counter-examples, and conjectures. Beyond the undergraduate mathematics student audience, the text can also offer a rigorous treatment of mathematics content (numbers and algebra) for high-achieving high school students. Furthermore, prospective teachers will add to the breadth of the audience as math education majors, will understand more thoroughly methods of proof, and will add to the depth of their mathematical knowledge. In the past, PNA has been taught in a "problem solving in middle school” course (twice), to a quite advanced high school students course (three semesters), and three times as a secondary resource for a course for future high school teachers. PNA is suitable for secondary math teachers who look for material to encourage and motivate more high achieving students.