Customer Reviews

Master Math: Pre-Calculus and Geometry

5 star:		(3)
4 star:		(1)
3 star:		(2)
2 star:		(0)
1 star:		(0)

 

 

This book is pretty small but it gives great explanations of geometric shapes, angles, and trig functions like tan, sin, cos, and others. It's straight to the point and I learned from it very quickly. I highly suggest getting this book before moving on to a more advanced, or even just a regular geometry or trig book.

Master Math: Pre-Calculus Table of Contents

Introduction

Chapter 1 Geometry

1.1. Lines and angles 1.2. Polygons 1.3. Triangles 1.4. Quadrilaterals (four sided polygons) 1.5. Circles 1.6. Perimeter and area of planar two-dimensional shapes 1.7. Volume and surface area of three-dimensional objects 1.8. Vectors

Chapter 2 Trigonometry

2.1. Introduction 2.2. General trigonometric functions 2.3. Addition, subtraction and multiplication of two angles 2.4. Oblique triangles 2.5. Graphs of cosine, sine, tangent, secant, cosecant and cotangent 2.6. Relationship between trigonometric and exponential functions 2.7. Hyperbolic functions

Chapter 3 Sets and Functions 3.1. Sets 3.2. Functions

Chapter 4 Sequences, Progressions and Series

4.1. Sequences 4.2. Arithmetic progressions 4.3. Geometric progressions 4.4. Series 4.5. Infinite series: convergence and divergence 4.6. Tests for convergence of infinite series 4.7. The power series 4.8. Expanding functions into series 4.9. The binomial expansion

Chapter 5 Limits

5.1. Introduction to limits 5.2. Limits and continuity

Chapter 6 Introduction to the Derivative

6.1. Definition 6.2. Evaluating derivatives 6.3. Differentiating multivariable functions 6.4. Differentiating polynomials 6.5. Derivatives and graphs of functions 6.6. Adding and subtracting derivatives of functions 6.7. Multiple or repeated derivatives of a function 6.8. Derivatives of products and powers of functions 6.9. Derivatives of quotients of functions 6.10. The chain rule for differentiating complicated functions 6.11. Differentiation of implicit vs. explicit functions 6.12. Using derivatives to determine the shape of the graph of a function (minimum and maximum points) 6.13. Other rules of differentiation 6.14. An application of differentiation: curvilinear motion

Chapter 7 Introduction to the Integral

7.1. Definition of the antiderivative or indefinite integral 7.2. Properties of the antiderivative or indefinite integral 7.3. Examples of common indefinite integrals 7.4. Definition and evaluation of the definite integral 7.5. The integral and the area under the curve in graphs of functions 7.6. Integrals and volume 7.7. Even functions, odd functions and symmetry 7.8. Properties of the definite integral 7.9. Methods for evaluating complex integrals; integration by parts, substitution and tables

Index

Appendix Tables of Contents of First and Second Books in the Master Math Series

Joining others in the 'Master Math' series is this fine introduction on calculus, covering the basics of sets, functions and integrals. Basic formulas, principals, discussions of sequences and progressions, and step-by-step directions link formulas to everyday life and provide calculus students with an excellent foundation for progressing to the next step. The result is a 'must' for any high school or college collection where calculus is an introductory course, and for any student taking it.

This is a nicely written and well-organized book. While not error-free, the relative number of mathematical errors seems similar to review books from competitors.

The text's main flaw is its breadth of coverage. It's really closer in size to a pamphlet than a book. Particularly as the font appears to have been "artificially" enlarged to make this short work appear even longer. You can confirm this yourself by using Amazon helpful, "Look inside this book" feature. Compared to, for example, the author's "Master Math: Calculus" in this same series, the font here appears to be about 40% larger. In addition, sections often end with considerable white space remaining before the end of the page.

Even with its larger font, this is quite a small-sized text, excluding the index, of less than 170 pages. Using a more typical font size, this text would probably be around 100 pages long. Of the 170 pages. about 90 pages are actually devoted to pre-calculus and geometry. The remainder, almost one-half the book, covers calculus topics: limits, derivatives, and integrals. Thus, the breadth of coverage of both pre-calculus and geometry is quite limited. This allows the author to concentrate on some key topics in both areas, but a consequence is that breadth of coverage is relatively minimal.

One of the earlier reviewers said, "Lots of good trig". While what's presented is nicely done, the chapter on trigonometry is less than 20 pages, and there are some presentation problems. For example, the graphs for the sine and cosine appear to have been constructed from joined semicircles rather than displaying actual sine and cosine functions.

Although mathematical plotting software was widely when this work was published, the author did not include output from such software in this book. This has resulted in many inappropriately drawn curves not only in the trigonometry section, as mentioned above, but in the sections on derivatives and integrals.

This book is more a sampler of many interesting topics in its title, but it cannot be recommended if a relatively comprehensive coverage of pre-calculus, geometry, or introductory calculus is needed.

This is the third one in the `Master Math' series. Like the earlier ones, this too follows the same style. Simple, but effective. As I told in the review for the first two books, I was looking for a book to brush up my math after 22 years. I am repeating the same stuff, just keep one thing in mind; this is neither a text book nor a replacement for it. Written in a very simple and clear language and it is not just a collection of formulas and definitions. If you are starting after a long break, it is better you follow the reading order, go through the first and second books first. I agree with one of the reviewer with respect to the value of `Pi'; it is written clearly as "The value of Pi is 22/7 or approximately 3.141592654" but when we divide 22 by 7, what we get is 3.14285714 `. About the confusion regarding the relationship of pi, circumference and diameter, the book clearly says that "More specifically, Pi is equivalent to the circumference divided by the diameter of a circle". This book won't disappoint you. If all you want is to brush up or learn the basics or a fast reference, this is the book for you. If you are serious about the subject, add one more book and don't minus this.

This is a decent book if you want to review this material. However, when I read a math book and there are basic facts that are just plain wrong I get worried. In chapter 1, page 23, the author begins to discuss Pi. In just two bullet points the author makes several incorrect or incomplete statements.

1) "Pi defines the ratio between the circumference and the diameter of a circle." CORRECT, the author should have stopped here.

2) "More specifically, Pi is the equivalent to the circumference divided by the radius of a circle." WRONG. The formula for circumference is: Circumference = Pi * Diameter. Therefore Pi = Circumference / Diameter.

NOTE: Another reviewer has stated that the above statement is wrong. I stand by my statement. Either he has a different version of the book or he read it wrong. The version that I have was published in 1996 and the full paragraph says the following:
"Pi, or (symbol for Pi here), defines the ratio between the circumference and the diameter of a circle. More specifically, Pi is equivalent to the circumference divided by the radius of a circle."
The author starts off correctly but makes the error in the second sentence which is the statement I originally quoted.

3) "The value of Pi is 22/7 or approximately 3.141592654." Absolutely WRONG and Partially WRONG. You can NOT say that Pi IS 22/7. This is so commonly used. In fact, I learned the same thing in grade school. However, if we divide 22 by 7 it is not equal to Pi by the third decimal place. 22/7 = 3.142... and Pi = 3.141... which leads me to the partially wrong portion of the statement. Whenever giving an approximate value of Pi it should be followed by ...

So, while the book can be a good review, be careful.