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Review of The Beginnings and Evolution of Algebra
Editorial review
Exceptional complex Lie groups have become increasingly important
in various fields of mathematics and physics. As a result, there
has been interest in expanding the representation theory of
finite groups to include embeddings into the exceptional Lie
groups. Cohen, Griess, Lisser, Ryba, Serre and Wales have pioneered
this area, classifying the finite simple and quasisimple subgroups
that embed in the exceptional complex Lie groups. This work
contains the first major results concerning conjugacy classes
of embeddings of finite subgroups of an exceptional complex
Lie group in which there are large numbers of classes. The approach
developed in this work is character theoretic, taking advantage
of the classical subgroups of $E_8 (\mathbb C)$. The machinery
used is relatively elementary and has been used by the author
and others to solve other conjugacy problems. The results presented
here are very explicit. Each known conjugacy class is listed
by its fusion pattern with an explicit character afforded by
an embedding in that class.
Review of Adventures in Arithmetic for the Pre-Algebra Student
Editorial review
Proceedings of the Summer Research Institute on [title] held
at the U. of New Hampshire, Durham, July 1988. During the last
20 years operator theory has developed in several directions,
using new and powerful methods that have led to the solution
of previously inaccessible basic problems. Some of these developments
connect with other areas of mathematics, including algebraic
topology and index theory, complex analysis in one and several
variables, and probability theory. There have been direct applications
to systems theory, complex variables, and statistical mechanics.
These papers summarize progress and examine the common points
of view that now run through the subject. Annotation copyright
Book News, Inc. Portland, Or.
Review of Algebra
Editorial review
This book presents modern algebra from first principles and
is accessible to undergraduates or graduates. It combines standard
materials and necessary algebraic manipulations with general
concepts that clarify meaning and importance. This conceptual
approach to algebra starts with a description of algebraic structures
by means of axioms chosen to suit the examples, for instance,
axioms for groups, rings, fields, lattices, and vector spaces.
This axiomatic approach---emphasized by Hilbert and developed
in Germany by Noether, Artin, Van der Waerden, et al., in the
1920s---was popularized for the graduate level in the 1940s
and 1950s to some degree by the authors' publication of A Survey
of Modern Algebra. The present book presents the developments
from that time to the first printing of this book. This third
edition includes corrections made by the authors for this printing.
Reviewed by Pedro Lauridsen Ribeiro,
from Cotia, SP Brasil
After getting frustated by nearly all the so-called "authoritative"
books on abstract algebra (Lang, Hungerford, Jacobson), I really
can say that MacLane/Birkhoff is the best die-hard classic on
algebra. Now I must stress that this book IS NOT out-of-print:
the third edition is actually published by AMS/Chelsea.There's
an interesting thing about the evolution of this book: the first
edition has become famous among mathematicians, because it brought
for the first time an elementary exposition of categories and
universal constructions, directly from the horse's mouth (MacLane
founded the theory of categories together with S. Eilenberg;
Birkhoff was the creator of the theory of lattices), which is
used as a basic tool throughout the book; it also contained
unusual topics such as multilinear algebra and affine and projective
spaces, but no Galois theory. The second edition has gained
a chapter on Galois theory, but has lost the part on affine
and projective spaces. The third edition is the best! It has
recovered the part which was lost in the second edition, and
had its exposition considerably polished. While most other books
expose abstract algebra as a ugly, prawling monster, MacLane/Birkhoff
manage to explain quite esoterical topics (many of them created
and/or developed by themselves) in a surprisingly natural and
tasty way (compare it with the dry, encyclopaedic style of Hungerford
and Lang); although quite big, the book supports several ways
of reading and teaching its parts without sacrificing clarity.
Another great quality: it is INSPIRING, in the sense that it
develops a powerful algebraic intuition, which is, in my opinion,
the main obstacle one has to face to learn algebra.
Reviewed by profsd@aol.com, from Virginia
Beach VA
This text is a very readable presentation of first year graduate
abstract algebra. The material is presented with notations similar
to that of Jacobsen in his "Basic Algebra" texts,
and is useful as a review text for qualifiers, or for independent
study.
Review of Elementary Algebra: A Straightforward Approach
Editorial review
This volume contains many of the papers in the area of algebraic
geometry presented at the 1984 Solomon Lefschetz Centennial
Conference held in Mexico City. It is the first in a three volume
series. The conference focused on this topic along with the
areas of algebraic topology and differential equations where
Lefschetz made significant contributions. The proceedings begin
with two interesting articles: A Page of Mathematical Autobiography,
that has been reprinted from an early edition of the Bulletin
of the AMS, and "Solomon Lefschetz, a biography" by
William Hodge, that is reprinted from the Bulletin of the London
Mathematical Society.
Review of Pre-Algebra: A Laboratory Workbook
Editorial review
Comprehensive ... remarkably clear and explicit.
Review of College Algebra Workbook: Technology in the Classroom
Editorial review
From the Preface: "An accurate (though uninspiring) title
for this book would have been Applications of the Theory of
the Modular Forms $\eta(\tau)$ and $\vartheta(\tau)M$ to the
Number-Theoretic functions $p(n)$ and $r_s(n)$ respectively.
This is accurate because, except in the first two chapters,
we deal exclusively with these two modular forms and these two
number-theoretic functions. However, at the heart of these particular
applications to the treatment of these specific number-theoretic
functions lies the general theory of automorphic functions,
a theory of far-reaching significance with important connections
to a great many fields of mathematics. Indeed, together with
Riemann surface theory, analytic number theory has provided
the principal impetus for the development over the last century
of the theory of automorphic functions ... I have tried to keep
the book self-contained for those readers who have had a good
first-year graduate course in analysis; and, in particular,
I have assumed readers to be familiar with the Cauchy theory
and the Lebesgue theorem of dominated convergence."
Review of Basic Mathematics With Pre-Algebra (Test Yourself)
Reviewed by darisier@aol.com, from FT
LAUDERDALE FL
I WOULD LIKE TO HAVE THIS BOOK BUT I CANT GET TO ORDER IT HOW
DO YOU ORDER.AND ALSO FORGOTTON ALEBRA
Reviewed by a reader, from india
i had a very nice time with solving these problems
Review of Teach Yourself Algebra
Editorial review
Written by experts in the field, this valuable study guide goes
into great detail and serve as a valuable resource.
Reviewed by Kersi N. Billimoria, from
San Diego, California
I have the Asian paperback edition of this book. This text was
a standard in the 1960s for folks who wanted to bursh up on
their High School algebra. The format is pedagogical in the
British style from the 1940-50s era. I have always found this
to be a faithful companion when I find myself forgetting basic
algebraic tasks such as simultaneous equations, factoring, etc.
The writing is simple and easy to follow. There are numerous
exercises to reinforce the material. There is one drawback.
I have found quite a few errors in the solutions within the
text AND in some of the answers to exercises. However, if one
is familiar with the material these shortcomings can be easily
excused. If you are just beginning to learn algebra go with
"Practical Algebra " by Selby et al. However if you
have take the subject before and just want to brush up basic
High School algebra get this volume.
Reviewed by a reader, from Hsv ,al
i would suggest it to everyone it really helps you get your
way thruogh Math classes Iteches you the basics of Algebra
Review of Using Algebra
Reviewed by a reader, from Cleveland,
Ohio
This book is great. It shows everything from Pre-Algebra to
real Algebra. I really recommend it. I have a brand new copy.
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