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Book Reviews

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 non-civilized 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 college-level 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 Addison-Wesley-Longman, from which you can purchase an integrated set of videos and CD-ROM 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 problems--5,921, to be exact--which roll through the book, section after section. Their extraordinary work makes me wonder how any college math teacher in a 3-credit 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 problem-saturated. 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 problem-solving 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 TEST-PREP 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 up-to-date, thoroughly researched book possible.We Know StudentsEach year we help more than two milion students score higher with our courses, bestselling books, and award-winning 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 algebra--only 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 test-makers 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 full-length 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 co-founded 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 self-contained 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 Cohen-Macaulay rings. To keep this part self-contained 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 self-contained 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 not-so-young non-experts 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/problems--in 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 coordinate-free 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 1-3 (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 Ssm-College 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 up-to-date 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 H-matrices, 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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