Babbage, peacock and modern algebra

Modern Algebra

Algebra is the study of mathematical manipulations that preserve something (like equality –when solving equations). The areas in which Algebra finds application are quite diverse, from Ancient Greek Geometry through to Modern Information Protection and Security (error correcting codes, data compression, and cryptography). This course begins with topics that should be familiar (such as rulerand-...

Modern Algebra with Applications

18.703 Modern Algebra, Cosets

Consider the group of integers Z under addition. Let H be the subgroup of even integers. Notice that if you take the elements of H and add one, then you get all the odd elements of Z. In fact if you take the elements of H and add any odd integer, then you get all the odd elements. On the other hand, every element of Z is either odd or even, and certainly not both (by convention zero is even and...

Dickson on Modern Algebra

with the concluding sentence of the preface: "The field is indeed a most fascinating one, and I believe a course of this character must be given in all our colleges and universities if we are to be fair to our students." The reviewer believes that departments of mathematics, where they have competent instructors, should take the lead in organizing such courses. This book could well furnish a pa...

S. Babbage 7,

This documents states the research agenda for the future of cryptology. We show which areas deserve more research bridging the gap between applications and research. For more detailed problems see the STORK document “D6 – Open Problems in Cryptology”.