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Review of Intermediate Algebra
Reviewed by a reader, from Portland,
OR United States
I absolutely agree with the review by Stephen Armstrong below.
It doesn't take 50  100 problems for the average student to
grasp a simple, basic algebraic concept. I see no reason for
this book to be over 700 pages; the authors clearly ignored
the need for simplicity and relevance in presenting their material.
Of the several books I've used for algebra, this one has the
most distracting presentation. It's hard to figure out what
really matters and where the student should focus. And it's
hard to discern how the concepts presented relate to each other.
It seems that in the authors' desire to be thorough, they lost
perspective.
Reviewed by sugar_pansy, from Singapore,
South East Asia.
After having completed a course in Beginning Algebra, the next
textbook, Intermediate Algebra really smoothed everything out.
The topics it covers are basically quite the same as Beginning
Algebra (same author), but it goes into deeper depth that are
peasy to pick up (especially with the examples in the start
of each section). One thing I particularly like about Lial and
Hornsby mathematics textbooks are the summaries they provide
at the end of each chapter you complete. They give a concept
covered in the chapter, a couple of examples, and therefore
serve as a revision page before a test or exam.
Reviewed by Joyce Kwok, from a noncivilized
place
This is a terrific book. It makes me feel that I shouldn't bother
to attend my math class in school. The book explains concepts
clearly. You don't even need a mentor. You can manage the book
all by yourself, for the book itself is your teacher, your mentor.
There is an abundance of exercises for you to practise. They
never run out of it. It makes you feel that math is fun. It
is the simply the best way to learn math. The best part of the
book is the review after every chapter. I can learn back whatever
I've missed. I'm an 8th grader only, but I can still manage
the 2nd year of high school algebra. The book has helped a lot.
The book is perfect for talented 8th graders.
Reviewed by Stephen Armstrong, from Hadley,
MA
Lial and Hornsby have written a collegelevel intermediate algebra
text that demonstrates the best and the worst of US math instruction.
On the positive side, this is a lavishly produced book: great
detail, lots of graphs and clearly ordered explanations, excellent
colors, nearly 1 1/4 inches thick with what they consider the
11 essentials of intermediate algebra (listed above in the Amazon.com
notes). The books comes from AddisonWesleyLongman, from which
you can purchase an integrated set of videos and CDROM of testing
problems (not used or viewed for this review). Theirs truly
is a work of love. On the other hand, they represent the most
tedious part of American math instruction, which is interminable
problems5,921, to be exactwhich roll through the book, section
after section. Their extraordinary work makes me wonder how
any college math teacher in a 3credit course could hope to
get through 2% of the problems in a semester. Many of the problems
are repetitious, going over the same features (of problem solving)
again and again. I fear that only the grinds and math gearheads
will appreciate this.Even more worrisome, however, is the absence
of conceptual integration, other than that these 11 topics are
"important" if you want to go to advanced algebra
or college geometry. The one pertinent conceptual comment was
that polynomials are to algebra as numbers are to arithmetic,
but the authors never followed up on this. It is not clear,
for example, why inverse functions are related (or not) to conic
sections. The handling of systems of linear equations borrowed
liberally from matrix algebra, but the authors chose not to
demonstrate more general solutions and stuck with solving the
problems "manually."More than concepts in math, American
students know how to solve problems, which presumably is why
this book, reflecting its intended audience, is so problemsaturated.
Even so, when we test our best students against the best from
other countries, we do not fare too well. Perhaps it is because
we ignore the structure of the thinking in math, and substitute
problemsolving instead. The result is that attentive students
will know the notes, and some will know the notes quite well,
but not the music.
Review of Cracking the Golden State Exam: 1st Year Algebra (Princeton Review Series)
Editorial review
PROVEN TECHNIQUES FOR SCORING HIGHER FROM THE WORLD'S #1 TESTPREP
COMPANYWe Know the Golden State 1st Year Algebra ExamThe experts
at The Princeton Review study the Golden State Exams to make
sure you get the most uptodate, thoroughly researched book
possible.We Know StudentsEach year we help more than two milion
students score higher with our courses, bestselling books, and
awardwinning software.We Get ResultsStudents who take our courses
for the SAT, GRE, LSAT, and many other tests see score improvements
that have been verified by independent accounting firms. The
proven techniques we teach in our courses are in this book.And
If It's on the Golden State 1st Year Algebra Exam, It's in This
BookWe don't try to teach you everything there is to know about
algebraonly what you'll need to know to score higher on the
Golden State 1st Year Algebra Exam. There's a big difference.
In Cracking the Golden State Exam, 1st Year Algebra, we'll teach
you how to think like the testmakers and*Use process of elimination
to eliminate answer choices that look right but are planted
to fool you*Improve your score by focusing on the material most
likely to appear on the test*Test your knowledge with review
questions for each algebra concept coveredPractice your skills
on the four fulllength sample tests inside. The questions are
just like the ones you'll see on the actual Golden State 1st
Year Algebra Exam, and we fully explain every answer.
Reviewed by Adam Miller, from Los Angeles,
CA
This book is a fantastic review of first year algebra. I struggled
all year with my awful teacher, Mr. Dougherty. I couldn't figure
out x to save my life. Now thanks to Mr. Sliter, I know that
x marks the spot for success!
Review of Cracking the Virginia Sol Algebra II: Eoc Algebra II
Editorial review
Steve Leduc has been teaching at the university level since
the age of 19, earned his Sci. B. in theoretical mathematics
from MIT at the age of 20, and his M.A. in mathematics from
UCSD at the age of 22. After completing his graduate studies,
Steve cofounded Hyperlearning, Inc., an educational services
company that provided supplemental courses in undergraduate
math and science for students from the University of California,
where he lectures on 17 different courses in mathematics and
physics. He's published two math books, Differential Equations
in 1995, and Linear Algebra in 1996. He also published Cracking
the AP Physics B & C in 2000. Hyperlearning merged with
The Princeton Review in 1996, and Steve now holds the position
of National Director of Research and Development for Hyperlearning,
the medical division of The Princeton Review.
Review of College Algebra, With Problems and Solutions
Editorial review
Advanced monograph treats lattices (the title spells out the
intended meaning of that term), and stands as a contribution
to the literature of algebraic group theory. Considered by the
author to descend from M.S. Raghunaathan's Discrete subgroups
of Lie groups (Springer, 1972), and to complement R.L. Zimmer's
Ergodic theory and semisimple groups (Birkhauser, 1985). (NW)
Annotation copyright Book News, Inc. Portland, Or.
Reviewed by a reader, from Oxford, UK
As I read this masterpiece of 20th century mathematics, I couldn't
help thinking of its relation to the book that defines modern
group theory, RJ Zimmer's Ergodic Theory and Semisimple Groups.
Coincidence? I think not. Robert Zimmer's book is simply the
best there is, and Margoulis' brilliant work is an excellent
supplement to that standard mathematical text. As the great
Swiss mathematician Armand Borel once said, "Margoulis'
masterpiece, while inferior to some of my own work, is an excellent
supplement to Zimmer's classic. Zimmer's book is the standard
to which all mathematicians should aspire (along with myself,
bien sur). Other than my own work, Margoulis' comes as close
as possible to reaching that standard."
Review of Equimultiplicity and Blowing Up: An Algebraic Study (Universitext)
Editorial review
Content and Subject Matter: This research monograph deals with
two main subjects, namely the notion of equimultiplicity and
the algebraic study of various graded rings in relation to blowing
ups. Both subjects are clearly motivated by their use in resolving
singularities of algebraic varieties, for which one of the main
tools consists in blowing up the variety along an equimultiple
subvariety. For equimultiplicity a unified and selfcontained
treatment of earlier results of two of the authors is given,
establishing a notion of equimultiplicity for situations other
than the classical ones. For blowing up, new results are presented
on the connection with generalized CohenMacaulay rings. To
keep this part selfcontained too, a section on local cohomology
and local duality for graded rings and modules is included with
detailed proofs. Finally, in an appendix, the notion of equimultiplicity
for complex analytic spaces is given a geometric interpretation
and its equivalence to the algebraic notion is explained. The
book is primarily addressed to specialists in the subject but
the selfcontained and unified presentation of numerous earlier
results make it accessible to graduate students with basic knowledge
in commutative algebra.
Review of Algebra I: Basic Notions of Algebra (Encyclopedia of Mathematical Sciences, No. 11)
Editorial review
An absolutely splendid little book, a worthy companion to volumes
which comprise what is in fact a splendid series. Provides young
mathematicians and notsoyoung nonexperts with a deeply informed
broad survey of the topics which today comprise "algebra".
Formal things are said formally and correctly, but the emphasis
is on the generative issues and motivating examples/problemsin
short: upon the illuminatingly concrete. The volume is unintmidatingly
compact, yet the coverage is remarkably comprehensive. And the
graceful style calculated to delight even experts in the field.
Beautifully produced, with good figures, useful references.
Translated from the Russian edition of 1986. (NW) Annotation
copyright Book News, Inc. Portland, Or.
Review of College Algebra Homework Assignments
Editorial review
Development of the complexity theory of bilinear mappings in
a uniform and coordinatefree manner. Main topic is the bilinear
complexity of finite dimensional associative algebras with unity:
Upper bounds for the complexity of matrix multiplication and
a general lower bound for the complexity and algebraic structure
in the case of algebras of minimal rank is shown. Final chapter
is on the study of isotropy groups of bilinear mappings and
the structure of the variety of optimal algorithms for bilinear
mapping.
Review of Algebra I: Chapters 13 (Elements of Mathematics)
Editorial review
This series was originally published in French in the 1970s
as Elements de mathematique. It comprises ten works (some subjects
occupy more than one volume), five of which are cited in this
issue of SciTech (see entries at QA251, QA387, QA611). The series
takes up mathematics at the beginning, and gives complete proofs.
It is directed to those who have a good knowledge of at least
the content of the first year or two of a university math course.
The method of exposition is axiomatic and abstract, proceeding
from the general to the particular, a choice dictated by the
main purpose of the treatise, which is to provide a solid foundation
for the whole body of modern math. The first six books are numbered,
and, in general, every statement assumes as known only those
results which have been discussed in preceding volumes. This
volume is composed of three of ten chapters on algebra, covering
specifically: algebraic structures; linear algebra; and tensor,
exterior, and symmetric algebras. Annotation copyright Book
News, Inc. Portland, Or.
Review of SsmCollege Algebra 5e
Editorial review
This volume presents the lectures given by fourteen specialists
in algorithms for linear algebraic systems during a NATO Advanced
Study Institute held at Il Ciocco, Barga, Italy, September 1990.
The lectures give an uptodate and fairly complete coverage
of this fundamental field in numerical mathematics. Topics related
to sequential formulation include a review of classical methods
with some new proofs, and extensive presentations of complexity
results, of algorithms for linear least squares, of the recently
developed ABS methods, of multigrid methods, of preconditioned
conjugate gradient methods for Hmatrices, of domain decomposition
methods, of hierarchical basis methods, and of splitting type
methods. With reference to implementations on multiprocessors,
topics include algorithms for general sparse systems, factorization
methods for dense matrices, Gaussian elimination on systolic
arrays, and methods for linear systems arising in optimization
problems. The book will be useful as an introduction to a field
still in rapid growth and as a reference to the most recent
results in the field.
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