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Re: Dolciani and SMSG
Posted:
Sep 18, 2011 6:08 PM


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 12thgrade 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.
11 Logical Statement; Sets 12 Variables and Quantifiers 13 Operations on Sets and Statements 14 Conditional Statements and Converses 15 Negations 16 Complements 17 Evaluating Compound Statements; Truth Tables 18 Patterns of Inference 21 Axioms of Fields 22 Proving Theorems 23 Indirect Proof 24 Axioms of Order 25 Absolute Value 26 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.



