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Re: Dolciani and SMSG
Posted:
Sep 18, 2011 6:08 PM
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On 18 Sept 2011, Guy Brandenburg wrote:
> That's what I'm asking you to do: examine and compare
> several books side by side
[snip]
This is an exercise that you must do on your own. After you have done this for my Euclidean Geometry textbook and for the Dolciani book, you should also do it for my 12th-grade Advanced Mathematics book [1] and the Dolciani book that replaced it in 1968 [2]. Fifteen years ago, I found out that Mr. Robert E. Millett, my superb teacher, had retired when he was forced to adopt the Dolciani atrocity.
[1] William E. Kline, Robert O. Oesterle, Leroy M. Willson, "Foundations of Advanced Mathematics," The American Book Company, New York (1959) 519p.
[Note: the second edition (1965) is identical to the original, with the exception of Chapter Review Tests that were added after page 500.]
Contents
Section I: Solid Geometry
1 Lines and Planes in Space 3
2 Dihedral and Polyhedral Angles 18
3 Polyhedrons, Prisms, and Pyramids 26
4 Cylinders and Cones 40
5 Spheres 48
Section II: Plane Trigonometry
6 Angles and Their Trigonometric Functions 60
7 Trigonometry of the Right Triangle 84
8 Reference Angles and Their Uses 96
9 Graphs of the Trigonometric Functions 106
10 Identities 120
11 Trigonometric Equations 130
12 Functions of the Sum of Two Angles 136
13 Inverse Trigonometric Relations 153
14 Logarithmic Solutions of the Right Triangle 161
15 Oblique Triangles 179
Section III: Analytic Geometry
16 Coordinate Geometry 192
17 The Line 211
18 Functions and Graphs 236
19 Locus 255
20 Exponential and Logarithmic Functions 265
21 Parametric and Polar Equations 271
22 The Conic Sections 286
Section IV: Calculus [We did not cover this Section]
23 The Calculus of Polynomial Functions 316
24 Applications of the Derivative 336
25 The Antiderivative 358
Section V: Statistics
26 Permutations and Selections [Combinations] 370
27 Probability 381
28 Set Theory and Probability 388
29 Descriptive Statistics 402
30 Statistical Inference 414
Section VI: Algebra
31 A Review of Algebra You Should Know 426
32 Mathematical Induction and the Binomial Theorem 450
33 Determinants 461
34 Complex Numbers 474
35 Theory of Equations 484
Tables 501
Index 513
The beginning of the textbook contains the following Note to the Student:
"One of the primary objectives of this text is to prepare you to take more advanced courses in mathematics. To succeed in these courses, one must learn to study! The following suggestions are offered for your consideration:
1. From the beginning of this text to the end, greater emphasis is progressively placed upon the necessity that you, the student, learn to read carefully. Many times questions are raised in the textual material and algebraic details are frequently omitted. Read the material carefully, attempt to answer these questions, and work out details which are omitted.
2. If, during the course of your study, you cannot understand some point or cannot complete missing details, make a note of this immediately and ask your teacher to explain it to you or to the class.
3. In your study of mathematics, form the habit of studying at a regular time and at a regular place.
4. Be certain that you understand a problem before you attempt to work it. In other words, have a plan of attack as you begin to work. Have some idea of where you are going and how you intend to get there.
5. If you cannot formulate a plan of attack, study the preceding discussion and the examples. Use the index freely to find topics that may help you plan an attack.
6. Definitions, postulates, and theorems should be understood and remembered. If you do not understand them, you probably cannot use them.
7. Whenever possible, draw diagrams sketches, and graphs which are related to the data of the problem.
8. Write neatly and organize your work in a logical fashion. Many mistakes in mathematics result from bad writing habits.
9. Rapidly check each step of a computation as you complete it. To believe that you have completed a problem and then discover that a simple error was made in the first step is disheartening.
10. After you have completed a problem, ask yourself if the answer is reasonable. Intuition plays an important part in mathematics.
11. Finally, don't give up to readily! Learning is a result of interest and effort."
[2] Mary P. Dolciani et al., Modern Introductory Analysis, Houghton Mifflin (1964) 651p. The first 70 pages of which consist of the following quagmire.
1-1 Logical Statement; Sets
1-2 Variables and Quantifiers
1-3 Operations on Sets and Statements
1-4 Conditional Statements and Converses
1-5 Negations
1-6 Complements
1-7 Evaluating Compound Statements; Truth Tables
1-8 Patterns of Inference
2-1 Axioms of Fields
2-2 Proving Theorems
2-3 Indirect Proof
2-4 Axioms of Order
2-5 Absolute Value
2-6 Subsets of R
If my Advanced Mathematics textbook had started out with this material, most of my classmates and I would have been as completely turned off as most students have been during the past 45+ years.
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