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Modern Algebra and Trigonometry, by Elbridge P. Vance
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- Sales Rank: #2333019 in Books
- Published on: 1962
- Format: Import
- Number of items: 1
- Binding: Hardcover
- 374 pages
Most helpful customer reviews
13 of 13 people found the following review helpful.
Answers to Exercises are Available in Some Versions
By Jimmy "Handyman" Jones
In its day, this was a widely used book across the US for teaching high school Trig and Algebra II. Mary P. Dolciani was a Math professor at Hunter College, NY, but more famously, an influential educator of Math teachers. Today, both an education center and an endowment bear her name in recognition her legacy. This is a review of the 1963 and 1965 editions of the book. The only substantive differences I noticed were in the last chapter on p. 599 and pp. 603-604 (practice tests). "Modern Algebra and Trigonometry Structure and Method Book 2" was published in four different versions. These are,
Teacher's Manual ("Teacher's Edition" is printed on the spine) - This has a separate teacher's manual (usually on green paper) at the beginning of the book along with teacher notes throughout the rest of the student text. Answers to exercises are in the back of the book.
Student Version ("With Answers" is printed on the spine) - Answers to odd and even-numbered exercises are in the back of the book.
Student Version ("With Odd-Numbered Answers" is printed on the spine) - Answers to odd-numbered exercises are in the back of the book.
Student Version (no additional annotation on the spine) - No answers to exercises.
However, those answers in the back exclude four types of exercises: 1) graphs, 2) proofs and "show thats," 3) exercises in the twelve "Extra for Experts" sections, and 4) exercises in two of the three transparency insert sections. If you desire the answers for 1, 2 and 3, they are included in a separate publication, viz., "Solution Key for Modern Algebra and Trigonometry Structure and Method Book 2" (no ISBN). I found it devilishly difficult getting hold of a copy of the Solution Key at a reasonable price.
There is significant overlap in the topics in Ch. 1-8 and Book 1 of this series. Ch. 9-16 are essentially new material with respect to Book 1. The plentiful exercises are all quite doable and are ordered in very gradually increasing levels of complexity. There are almost no compromises to mathematical rigor. Axioms and definitions are clearly presented, and proofs given for all theorems - except for one in Ch. 14, "Every polynomial equation with complex coefficients and nonzero degree n has exactly n complex roots." Sections dealing with interpolation for increasing accuracy when using four digit log and trig tables are now passé.
Ch 1 Sets of Numbers; Axioms
Ch 2 Open Sentences in One Variable
Ch 3 Systems of Linear Open Sentences
Ch 4 Polynomials and Factoring
Ch 5 Rational Numbers and Expressions
Ch 6 Relations and Functions
Ch 7 Irrational Numbers and Quadratic Equations
Ch 8 Quadratic Relations and Systems
Ch 9 Exponential Functions and Logarithms
Ch 10 Trigonometric Functions and Complex Numbers
Ch 11 Trigonometric Identities and Formulas
Ch 12 The Circular Functions and Their Inverses
Ch 13 Progressions and Binomial Expansions
Ch 14 Polynomial Functions
Ch 15 Matrices and Determinants
Ch 16 Permutations, Combinations and Probability
10 of 10 people found the following review helpful.
Best version of best Algebra II textbook of all time
By Richard J. Petti
After the Soviet Union launched Sputnik into orbit in 1957, America feared a potential missile base on the moon in the hands of a hostile superpower that America lacked the technology to reach. The federal government did something unusual in America: it asked top universities what should be taught in high schools to optimize the education of future scientists and engineers; and it used it influence to gain adoption for the new curriculum. In mathematics, this book and its cousins with first Author Mary Dolciani were the results.
The basic approach is to blend a set-theory approach to the foundations of mathematics with procedural math for doing computations. (That is why the subtitle is "Structure and Methods.") For example: (a) A function is a mapping from one set (the domain) to another (the range), and the set of all points that get mapped onto is called the "image." (Current high school terminology unfortunately uses the term “range” for what mathematicians call the image, which is a bad attempt to "simplify" the ideas.) (b) Addition and multiplication of real or complex numbers are associative commutative binary operations on pairs of real numbers to the real numbers.
The power of this approach is that students’ intuitions about integers and real numbers serve as foundations for higher mathematics, starting with matrices and linear algebra, calculus, function spaces, probability and literally everything.
A bit more history about how this occurred: Late in the nineteenth century, mathematics had outgrown use of equations and variables as the fundamental language of most of mathematics. There were two competing approaches to providing a stronger foundation: “lambda calculus” which formalized symbolic computation using symbolic logic (and which became the foundation of LISP), and set theory. Set theory proved far more flexible and powerful and it became the universal language for all mathematics in the twentieth century.
From 1960 to 19990, this approach to secondary mathematics was called “the new math.”
The Math Wars
In the 1970s and 1980s, this approach to high school mathematics was virtually eliminated from American high schools. Evidence clearly shows that most students do worse with the “new math” approach based on sets and mappings, and I believe this is accurate. You can see a review of the math wars at [...]
The unmentionable elephant in the room is that the mythical top 10% or so do much better with the new math approach. That is why the universities recommended this approach to the federal government after Sputnik, and why the federal government encouraged its adoption in schools. That is why all my friends at MIT found it a great help. That is why as a math tutor today, I find clients who like it and benefit from it. This approach works well because (a) it explains the complexities of ordinary math in such elementary terms that some students say it feels like they already know it and just have to rediscover that they know it (Plato’s concept of innate knowledge); and (b) when you move on to more advanced math, it is based on the same abstract concepts of sets and mappings, as are integers and real numbers.
I say “mythical top 10%” because the students who can benefit from the sets and mappings approach are not necessarily the ones with the best math grades. The key determinant of who benefits is ability to think abstractly and to relate the abstractions to concrete procedures. My experience is that some students, who have these abilities but do not do very well in math, like this approach benefit greatly from it.
The sets-and-mappings approach impairs performance of the majority of students because they do not make the connection between the abstractions and procedural math. As a result, these students have more material to learn, the new material does not help them understand and perform math procedures, and math procedures get a smaller share of student time than with the traditional approach.
It is a losing proposition to introduce curricula that meet the needs of the top 10% but impairs the learning of perhaps 70% of the student population, unless you restrict that curriculum to people who can benefit. That restriction is an important reason why AP courses survive in the current environment. Similarly, if you tried to introduce an MIT undergraduate curriculum in most colleges, it would be resoundingly rejected.
If you know a student or a whole class who can benefit from this, this book is the way to go.
1 of 1 people found the following review helpful.
Modern Algebra and Trigonometry: Structure and Method Book 2
By mike plott
I collect lots of Mary P. Dolciani math books. This one caught my eye as I never knew that this particular book title existed! I rate this book 5 stars! The book was in great shape! Good price too!
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