Linear and Geometric Algebra

Linear and Geometric Algebra

This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book’s web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. — David Hestenes, Distinguished Research Professor, Arizona State University

Linear and Geometric Algebra

Superheroes of the Round Table

Superheroes of the Round Table

Few scholars nursed on the literary canon would dispute that knowledge of Western literature benefits readers and writers of the superhero genre. This analysis of superhero comics as Romance literature shows that the reverse is true–knowledge of the superhero romance has something to teach critics of traditional literature. Establishing the comic genre as a cousin to Arthurian myth, Spenser, and Shakespeare, it uses comics to inform readings of The Faerie Queene, The Tempest, Malory’s Morte and more, while employing authors like Ben Johnson to help explain comics by Alan Moore, Jack Kirby, and Grant Morrison and characters like Iron Man, the Hulk, the X-Men, and the Justice League. Scholars of comics, medieval and Renaissance literature alike will find it appealing.

Superheroes of the Round Table

Computability

Computability

In the 1930s a series of seminal works published by Alan Turing, Kurt Gdel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding. Some chapters focus on the pioneering work by Turing, Gdel, and Church, including the Church-Turing thesis and Gdel’s response to Church’s and Turing’s proposals. Other chapters cover more recent technical developments, including computability over the reals, Gdel’s influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics. Contributors:Scott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

Computability