» » Linear and Geometric Algebra
Download Linear and Geometric Algebra epub book
Author: Alan Macdonald
ISBN13: 978-1453854938
Title: Linear and Geometric Algebra
Format: mobi lit doc lrf
ePUB size: 1723 kb
FB2 size: 1209 kb
DJVU size: 1966 kb
Language: English
Category: Mathematics
Publisher: CreateSpace Independent Publishing Platform (January 19, 2011)
Pages: 219

Linear and Geometric Algebra by Alan Macdonald

Macdonald does not show off how much more he knows about this topic than you do. The linear algebra material in this book was well known to me from my undergraduate courses, and I use most of it regularly in physics; still I (re)learned a great deal about.

Linear and Geometric Algebra by Alan Macdonald. Geometric algebra and its extension to geometric calculus simplify, unify, and generalize vast areas of mathematics that involve geometric ideas. Geometric algebra is an extension of linear algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. And geometric algebra does much more, as it incorporates the complex, quaternion, and exterior algebras, among others. 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.

Geometric algebra (based on Clifford algebra) - Leo Dorst, Daniel Fontijne, Intelligent Autonomous Systems, University of Amsterdam. Geometric algebra is a very convenient representational and computational system for geometry. We firmly believe that it is going to be the way computer science deals with geometrical issues. Companion site to the book Geometric Algebra For Computer Science, An Object Oriented Approach to Geometry (Morgan Kaufmann). The Grassmann Algebra Book - John Browne. This is the companion site for the book Grassmann Algebra: Exploring extended vector algebra with Mathematica and for the Mathematica-based software package GrassmannAlgebra. Geometric Algebra and Geometric Calculus playlists - Alan Macdonald, Luther College. Tutorial on Clifford's Geometric Algebra playlist - Chris Squibb. Lectures by Eckhard Hitzer.

Alan Macdonald's selected publications on Mathematics, Geometric Algebra, Foundations of Physics, Relativity, Quantum Theory, and Thermal Physics. Alan Macdonald is Professor Emeritus of Mathematics at Luther College in Decorah, Iowa. in mathematics from The University of Michigan in 1970.

Linear and Geometric Algebra book. Details (if other): Cancel. Thanks for telling us about the problem. Linear and Geometric Algebra.

and Geometric Calculus. Luther College, Decorah, IA 52101 USA macdonaler. My purpose is to demonstrate some of the scope and power of geometric algebra and geometric calculus. I will illustrate this for linear algebra, multivariable calculus, real analysis, complex analysis, and several geometries: euclidean, noneuclidean, projective, and conformal. I will also outline several applications. Geometric algebra is nothing less than a new approach to geometry.

Linear algebra: Introduction Proper linear algebra deals with vector spaces and linear transformations between them. It will rigorously develop the theory of nxn matrices and determinants and apply them to geometrical and algebraic contexts. dp/0130084514 This book offers a very modern introduction to linear algebra. Geometric algebra for computer science by Dorst, Fontijne, Mann This is an alternative for MacDonald. Don’t be turned down by computer science in the title, this is a really nice book that offers a lot of neat intuition on geometric algebra. It covers a lot more of Geometric algebra than MacDonalds book.

Alan Macdonald - 2012 - North Charleston, SC: CreateSpace. Linear Transformations in Unitary Geometric Algebra. Garret Sobczyk - 1993 - Foundations of Physics 23 (10):1375-1385. A Geometric Proof of the Completeness of the Łukasiewicz Calculus. Giovanni Panti - 1995 - Journal of Symbolic Logic 60 (2):563-578. Imaginary Numbers Are Not Real-The Geometric Algebra of Spacetime. Stephen Gull, Anthony Lasenby & Chris Doran - 1993 - Foundations of Physics 23 (9):1175-1201. An Einstein Addition Law for Nonparallel Boosts Using the Geometric Algebra of Space-Time. B. Tom King - 1995 - Foundations.

No current Talk conversations about this book.

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 fourth corrected printing. Chapter 6 has been rearranged. There is a new chapter on the conformal model. The chapter is also available for download at the book's web page. Visit the book's web page at faculty.luther.edu/~macdonal/laga to download its table of contents, preface, and index.There is a sequel, Vector and Geometric Calculus, by the same author.See faculty.luther.edu/~macdonal/vagc/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
Reviews: 7
Alan Macdonald has prepared for this for a long time. His personal web site at Luther College in Iowa includes an extensive list of his papers. That work shows clearly that he has both the mathematical and physical chops for this task. His detailed survey of geometric algebra and geometric calculus, which can be found on that site, has been worked and reworked since he first developed it in 2002. It is quite thorough in that it covers not just the fundamentals of the algebra, but also incorporates quite a few physical applications for motivation. For example, at this point it's well understood that quantum spin is really a geometric property of the particles themselves. Macdonald's survey covers that clearly and concisely.

Here he develops the first undergraduate text to cover the essentials of linear algebra, and its extension to geometric algebra. The terse statements from the above survey are expanded, in this elegant book, into rigorous proofs. Given the care with which that's done, however, it easily rewards those students for whom this is a first introduction to the abstract concepts inherent in linear vector spaces - and the higher dimensional analogues where the multi-vectors of geometrical algebra live.

I believe, as Macdonald does, that the geometric interpretation of Clifford algebras, and its extension to geometric calculus "unify, simplify, and generalize vast areas of mathematics". I'd strongly recommend this book to engineering, computer science, and physics teachers. It provides a solid grounding in this important and emerging area of mathematics.
Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers, given that geometric algebra is not a standard part of the undergraduate mathematics, physics, or engineering curriculum.

Like most everyone else, I first became aware of geometric algebra through David Hestenes: his American Journal of Physics articles, his books, and the many materials available at his web site, all of which I can recommend. I've also spent considerable time with the geometric algebra book by Doran and Lasenby, as well the book by Dorst, Fontijne, and Mann. The aforementioned books can help you understand why it might be worth your while to learn geometric algebra. Should you decide geometric algebra is worth your while, and furthermore, decide to develop some pencil-and-paper proficiency with it, I recommend Macdonald's book as a great way to get started. It won't help you discover new applications of geometric algebra, but it will give you the mathematical background and confidence you need to move on to the more difficult books and articles with applications to science/engineering.

Macdonald writes in a consistently friendly, but serious, voice that suggests he cares whether or not a reader understands the reasoning behind proofs and appreciates the significance of the results obtained from them. This is not a high-powered mathematics monograph for graduate students and researchers--this a book for first-time learners. Macdonald does not show off how much more he knows about this topic than you do. The linear algebra material in this book was well known to me from my undergraduate courses, and I use most of it regularly in physics; still I (re)learned a great deal about the nature of mathematical proof that was helpful later in the geometric algebra half of the book. It was great to have a consistent voice throughout both sections. I did a number of the 200+ exercises/problems, and felt the preceding sections had just what I needed to get an exercise/problem done.

There are remarkably few typographical errors--the few I did find were minor and did not obscure the meaning of the text. Some books on geometric algebra are full of typographical errors, to the point that I could imagine readers giving up in exasperation; the editors and authors of those books did not do their jobs. Macdonald's book has no such defect. Amazon allows you to look at a great number of pages from Macdonald's book on-line (today I could look at 90+ pages on-line). Read a section or two--note the many helpful diagrams.

This is not a book about physics, yet there are a few informative asides pertaining to physics, an example of which is a set of photographs showing an everyday situation where a rotation by 720 degrees is required to return a system to its original state. Also, as mentioned in the book's preface, some standard techniques in linear algebra are not covered (one uses a computer to carry out these calculations anyway) because the digressions necessary to cover them would have drawn attention away from making the transition to geometric algebra. If you only want to learn linear algebra in order to crunch numbers, this probably isn't your book. On the other hand, if money motivates you, the section on the $25,000,000,000 eigenvalue just might make this book a profitable purchase.

I hope Macdonald will find time to write a comparable book on geometric calculus, which is what I really need and want to know, but have found difficult to learn from other sources.
Linear algebra is really a foundational course. If it doesn't explain so much about the world, it explains a very great deal about the way mathematicians think about the world. This book is written at exactly the level to give students a first view into the subject. So, it collects the facts in a very concise and straightforward way. A freshman or sophomore in college (or even a good high school student) could use this as a fine introduction.

It was particularly insightful and very necessary for the author to include geometric algebra as a second half of the book. It goes beyond the regular curriculum and gives insight into mathematics that is very useful for computer applications and for general calculation. It is really a way of the future, and students are brought in on the ground floor.

Most people would see nothing to object to in this book. I would like to have seen a more detailed and constructive presentation. The author states (correctly) a basis of G^3 without going into detail of why the stated elements do form a basis. How does a beginner know they're linearly independent? (They look independent, isn't that enough????) If he had been willing to be more careful and constructive, I think it would have been a great book. As it is, the book is useful and ought to be considered at many schools, although I think there are certainly much better linear algebra texts (Linear Algebra Done Right, for example). None of the better texts give the huge advantage of including geometric algebra, as they really ought to do.
I would certainly agree with all of the other "5 star" reviewers. I've read this book and worked nearly every problem - the book is well written, in my opinion deserving of the term "pithy." His approach of integrating exercises into the flow of the text makes for a much more interactive experience. If all such books were written as well as this one I would be much further along in my acquisition of knowledge mathematical and otherwise!