LINEAR ALGEBRA FOR ALL UNDERGRADUATES BY D. C. MURDOCH – ONE OF THE FIRST COMPREHENSIVE, MODERN LINEAR ALGEBRA TEXTS, OUT OF PRINT FOR NEARLY 5 DECADES!
NOW AVAILABLE AGAIN AS BOTH A KINDLE AND INEXPENSIVE PAPERBACK BY BLUE COLLAR SCHOLAR!
NOW, THIS CLASSIC TEXTBOOK, A PRECIOUS LOST LINEAR ALGEBRA COURSE BOOK IS BACK IN PRINT FOR PURCHASE AT A PRICE ALL STUDENTS AND TEACHERS CAN AFFORD!
BEST OF ALL, BOTH A BRAND NEW PREFACE & COMPREHENSIVE SUPPLEMENTARY BIBILIOGRAPHY HAS BEEN WRITTEN BY KARO MAESTRO AKA THE MATHEMAGICIAN!
Reviews For Murdoch:
Elementary in treatment, the new book keeps abstract ideas to a minimum, while geometric motivations and applications for the abstract algebraic theorems are stressed. [There are]chapters devoted to: Vectors and vector spaces; matrices, rank, and systems of linear equations; further algebra of matrices; further geometry of real vector spaces; transformations of coordinates and linear transformation in a vector space; similar matrices and diagonalization theorems; reduction of quadratic forms; and vector spaces over the complex field. Largely written for the student, [Linear Algebra for All Undergraduates] contains material of use to physicists, engineers, mathematicians, and statisticians. Dr. Murdoch avoids abstract algebra in his treatment of the properties of matrices and quadratic forms of importance to physicists. He also includes some applications to differential equations and physical problems. The author…. recognizes that matrix methods are being used increasingly in engineering, especially in the theory of vibrations, elasticity, and electrical networks………..
Richard Cook
More Reviews For Murdoch
This textbook has been written for students reading mathematics and the physical sciences. They are supposed to have reached a standard something like the D.O.E. Advanced Level in this country, but not yet to be ready for the mathematically sophisticated point of view taken in modern abstract algebra…………One has the impression throughout that the text has been carefully written and clearly displayed, and that it reflects the experience of a good teacher. As some of the chapter headings indicate, there is a development by stages which match the reader’s growing feeling for the subject………This text should appeal to many students in this country. They will find exercises which are mostly straightforward and sometimes indicate further theoretical ideas. Answers are provided. There is a good index.– J. W. ARCHBOLD
Even More Reviews For Murdoch:
[The problem of] Bridging the [considerable] gap between College Algebra as it is traditionally presented and the abstractions of Modern Algebra is difficult……………….Professor Murdoch would introduce a transition course to bridge the gap and he presents [Linear Algebra for All Undergraduates] as a text for such a course. The subject matter of the book furnishes necessary information for any young mathematician. [The book presents] much of the material usually covered in a course in Determinants and Matrices……[The author well-covers] the algebra of matrices and [ develops] the general theory of matrices…….include such topics as similarity, diagonalization and reduction of quadratic forms………This reviewer, then, recommends this book as one whose subject matter is highly desirable and whose presentation might well be a solution to the problem of easing the first contact with the concepts of modern mathematics. -John W. Riner, St. Louis University
Yet More Reviews For Murdoch
Dr. Murdock has written a modern algebra text that satisfies a definite undergraduate need. [He treats] linear algebra, theory of matrices, and quadratic forms. Although the book emphasizes algebraic proof , it never allows the reader to wander too far from the concrete geometric interpretation of the algebraic statements….. [The author writes]in a good clear expository style……………………….There are many illustrative examples to point up the definitions and the theorems as well as a good deal of interesting problem material………………This book is not too difficult for the serious undergraduate who has had college algebra, analytic geometry, and a little extra time for these courses to settle. There are some excellent tips to the student on how to read algebraic material which should enable him to ease him-self into the reading of algebra as painlessly as possible.—Augusta Schurrer, Iowa State Teachers College, Cedar Falls, Iowa.
This book is …..a simple introduction to linear algebra. However, some exercises at the end of each section demand more of the reader. In particular in these exercises, the author expects the student to be be familiar with the basics of differential and integral calculus as well as Lagrange equations of mechanics. On this basis, he will easily follow the formal remarks on systems of linear differential equations with constant coefficients (without integration by eAt), the Wronskian determinant,as well as normal coordinates of an oscillating system. However, these are short and can be ignored…….-H. Schwerdtfeger , ZMATH
Another User Friendly Classic
Blue Collar Scholar makes yet another wonderful out of print textbook available to everyone at a price everyone can afford with this outstanding linear algebra text. Firstly, Murdoch’s book was one of the first textbooks that tried to give a broad presentation of linear algebra for well-prepared sophomores or juniors of average ability which was both mathematically careful and rich in applications.
At the time Murdoch wrote his text,as is important for modern students to realize, is there were almost no books on the subject for undergraduates. Previously, the theory of vector spaces was for mathematics graduate students learning abstract algebra, differential geometry or functional analysis.
Moreover,treatments still using 19th century formulations of vector and tensor analysis in geometry, physics and many other sciences.Obviously, undergraduate mathematics is a very different beast today.One of the reasons for this is the major role linear transformations currently play. The post-World War II years experienced an explosive growth of linear algebra across the board in both pure and applied mathematical research. Consequently, this created an urgent need for a much earlier, more accessible and thorough introduction to linear algebra for students. Murdoch’s text was one of the first to attempt to fulfill this need.
Written for The Beginner
Secondly, this book emphasizes the relationship between linear algebra and the classical geometry of low dimensional spaces. Many modern linear algebra texts emphasize abstract vector spaces and linear maps. In contrast, Murdoch completely avoids abstract vector spaces in the main text. Scalar fields are limited to R and C. This allows a careful presentation of the subject without recourse to abstract algebra concepts. Also, a familiar context is provided most students at this level should have at least a passing acquaintance with.
Thirdly,the author presents the generalization to abstract fields briefly in an appendix. Although the book’s overall emphasis is on linear transformations, matrices are discussed at length first. For example, the book gives complete presentations of linear systems of n variables, n x n matrices and determinants. Simultaneously, the text gives many applications of these topics. Since the presentation emphasizes concreteness, this is the natural way to go. This is because one does most applications and calculations in linear algebra via operations on matrices. As a result,the book drives home the role of matrices as linear transformations with a specific choice of basis. Therefore, Murdoch explores this relationship only after the reader gains a great deal of experience with manipulating matrices.
Some Topics in the Text
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- Vector spaces and their elementary properties
- Classical geometry
- Inner products and orthogonality, relations (complements and projections) in real spaces
- Abstract linear transformations in low dimensions and the relationship to matrices under a change of basis
- Spectral analysis-i.e. characteristic equation of a linear system
- Eigenvalues and their resulting eigenvectors
- Diagonalization and the Jordan form of a matrix
- Quadratic forms
- Complex vector spaces, adjoints and Hermitian matrices
In addition, Blue Collar Scholar founder and editor has added his usual personal 2018 edition preface. This preface details the gradual evolution of the linear algebra course in American universities. Therefore, it provides a historical context for the writing of Murdoch. He has also added a new Recommended Reading section for the purpose of suggesting further reading in linear algebra. Hence, both teachers and students will have a guide to the literature on this important subject.
A Teacher’s Text For Linear Algebra
As said above, the prerequisites for a course based on Murdoch are very minimal. In fact, those prerequisites are just
high school algebra and geometry. In addition, you’ll need a non-rigorous single variable calculus course for the more difficult exercises. Therefore,it’s also ideal for self study. As expected in a first linear algebra course, no experience with rigorous mathematics or proof techniques is necessary.
It’s quite important to understand why this is true in a historical context. When Murdoch wrote this book, it would be 20 years before linear algebra courses were mandatory for mathematics students. Previously, students taking linear algebra were graduate students or gifted undergraduates only at the top programs. Programs offering experimental courses like Murdoch’s were extremely rare.
In fact, this course assumes slightly more background and uses more rigor then most texts written today. However, it’s definitely not a pure theoretical presentation by any means. Hence, it would therefore be an accessible first course to most undergraduates without sacrificing any rigor.
Why Murdoch And Why Now?
Which brings us to the major reason we’re reissuing this text. Because of the Space Race,there was considerable upgrading of mathematics requirements in the 1960’s. So both linear and abstract algebra became required undergraduate courses. Subsequently,today’s undergrads have largely regressed at least to the pre-World War II preparation level. Consequently, the audience for modern linear algebra courses is mostly in non-theoretical courses. This limits purely theoretical courses in linear algebra to honors courses.
It is the belief of the publisher that both theory and applications are of equal importance in linear algebra. Therefore, we strongly recommend balanced textbooks that stress both aspects equally.We are providing precisely that kind of text in Murdoch.
As a result,the republication of this book at such an inexpensive price encourages these goals in linear algebra courses. This careful, rich and inexpensive text is a fantastic choice either for a linear algebra text or self-study. Therefore, it’s a great text for students who need to learn linear algebra for either applications or the theory.
The prerequisites are only high school algebra and geometry. A prior course in calculus, while helpful, is not really necessary. It should become a classic in rapid course for anyone interested in teaching or learning this beautiful,basic subject.
At any rate, buy this book to help fuel this movement in academia!
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