In reminiscing of my teaching career, I am frequently reminded of how unwillingly many of my students were to listen to me during the first few class lectures. The lack of interest and frankly not knowing how to study was very evident. I could only hope to keep them interested enough to stay in the course. My approach in teaching mathematics and other technical subjects has always been in the form of trying to present any topic in the simplest way possible. I have always believed that many of our academic texts, particularly those that lay the foundation for learning math and science, are either written in an abstract and difficult to follow language, lack sufficient number of detailed sample problems, or are not explained adequately for a student to become interested in the subject.
It is my belief that the key to learning mathematics is through positive motivation. Students can be greatly motivated if subjects are presented concisely and the problems are solved in a detailed step by step approach. This keeps the student motivated and provides a great deal of encouragement in them wanting to learn the next subject or to solve the next problem. During my teaching career, I found this method to be an effective way of teaching. I have never forgotten the expressions of gratitude that I have received from students for helping them realize mathematics is indeed an interesting subject to pursue. The fact that they could truly learn math and develop a positive interest in taking the next math course was gratifying for me. I hope by presenting subjects with the methods used in this book, more students will become interested in the subject of mathematics and can carry this approach and philosophy to future generations.
The scope of this book is intended for educational levels ranging from the 8th grade to adult. The book can also be used by students in home study programs, parents, teachers, special education programs, preparatory schools, and adult educational programs including colleges and universities as a main text, a thorough reference, or a supplementary book. A fundamental understanding of basic mathematical operations such as addition, subtraction, multiplication, and division is required.
“Mastering Algebra: An Introduction” is the first in a series of three books on algebra. It addresses the basics of algebra by introducing the student to topics such as integer fractions, exponents, radicals, fractional exponents, and polynomials. The second book, “Mastering Algebra: Intermediate Level” addresses topics such as factoring, algebraic fractions, functions of variables, and graphing. The third book, “Mastering Algebra: Advanced Level” addresses areas such as solving and graphing quadratic equations, parabolas, circles, ellipses, hyperbolas, and vectors.
This book is divided into six chapters. Chapter 1 introduces the student to the concept and use of signed numbers, parentheses, and brackets as math expressions in solving mathematical operations. How integer fractions are simplified, added, subtracted, multiplied, and divided are described in Chapter 2. (It is essential that students be thoroughly familiar with sign numbers, the use of parentheses, brackets, and fractional operations before proceeding with other chapters.) The subject of exponents is addressed in Chapter 3. Students learn how to solve and simplify numbers and variables that are raised to integer exponents. Radical expressions and how they are simplified and mathematically operated on are addressed in Chapter 4. In this section students learn how to add, subtract, multiply, divide, and rationalize radical expressions. Chapter 5 addresses a more difficult class of exponents by showing how to simplify and solve fractional exponents. The subject of polynomials and how different types of polynomials are added, subtracted, multiplied, and divided are addressed in Chapter 6. Finally, detailed solutions to the exercises are provided in the Appendix. Students are encouraged to solve each problem in the same detail and step by step format as shown in the text.
It is my hope that all the Hamilton Education Guides stand apart in their understandable treatment of the presented subjects and for their clarity and special attention to detail. I hope readers of these books will find them useful. Any comments and suggestions for improvement of this book will be appreciated.
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Dan Hamilton received his B.S. degree in Electrical Engineering from Oklahoma State University and Master’s degree, also in Electrical Engineering, from the University of Texas at Austin. He has taught a number of math and engineering courses as a visiting lecturer at the University of Oklahoma, Department of Mathematics, and as a faculty member at Rose State College, Department of Engineering Technology, at Midwest City, Oklahoma. He is currently working in the field of aerospace technology and has published numerous technical papers.