Book Description
A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE. ... Read more

Customer Reviews (2)

Full of mistakes
This text is based upon lecture notes (written either by Rota and then bound by Birkhoff or vice versa) and it is VERY apparant that the authors spent little time on checking for mistakes.It seems as though every fourth problem has a typographical error or is completely incorrect.This textbook does not take an intuitive approach to the subject and the many errors gives me reason to rate it low.

Nothing is more frustrating to a student than to have a text make a claim, ask you to prove it, and then you find out the claim is false.This is not a unique occurance.Steer clear of this textbook.

Good text but watch for errors
This is a good text for a course in ODE after the computational course is completed.This book covers many topics in ODE, but be careful and watchfor errors; especially near the end of the text.Most of the errors comein the excercises.For instance: you are asked to show that "everyfinite sequence of eigenfunctions of a S-L system is bounded".Duh! This is trivial until one realizes that every infinite sequence is alsobounded. ... Read more

Book Description
The purpose of the third edition is threefold: to make the deeperideas of lattice theory accessible to mathematicians generally,to portray its structure, and to indicate some of its mostinteresting applications.

This 1996 reprint includes expanded and updated AdditionalReferences. ... Read more

Product Description
This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses. ... Read more

Customer Reviews (2)

This is how algebra texts ought to be written
I have just started reading this book, and already I am
enthralled by the beauty and elegance of the authors'
exposition. Assuming nothing more than an acquaintance with
school algebra and a little geometry, they develop
the basic properties of central algebraic structures, including
rings, groups and fields. These are treated by reference to
familiar examples, such as the ring of integers and the
rational, real and complex fields. Everything that one learned
in school algebra is to be found here, though, as is to be
expected, each topic is treated at a rigorous, mathematically
sophisticated level. In the first two chapters, the properties
of the integers and rational numbers are gradually examined,
ultimately down to the definition of addition and multiplication
on the basis of Peano postulates. The authors then consider
polynomials, the real and complex numbers, vector spaces, linear
algebra and other topics.
The writing style is clear, concise and elegant, with each new
concept being carefully defined as it is introduced. The proofs
achieve a satisfying balance between detail and brevity. Indeed,
reading the proofs and completing the exercises would do much, I
am sure, to enhance a reader's mathematical facility.

If you are interested in acquiring a deeper understanding of
algebra, this book should serve as an excellent introduction.

A smorgousborg of symmetries of the square
Modern algebra is an extraordinary topic and Birkhoff and MacLane do a superb job of exploring it. However, as is often the case with mathematical texts, the material can be somewhat dry. ... Read more

Book Description

An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics.

This Source Book, a sequel to D. J. Struik's Source Book in Mathematics, 1200-1800, draws together more than eighty selections from the writings of the most influential mathematicians of the period. Thirteen chapters, each with an introduction by the editor, highlight the major developments in mathematical thinking over the century. All material is in English, and great care has been taken to maintain a high standard of accuracy both in translation and in transcription. Of particular value to historians and philosophers of science, the Source Book should serve as a vital reference to anyone seeking to understand the roots of twentieth-century mathematical thought.