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2. Algebra
3. Introduction

It is fairly common knowledge that geometry has its roots in Egypt and Greece. The Egyptians used geometry for practical purposes, and the Greeks formalized the study of geometry (and of most other subjects) through their use of logic. What we know as the Pythagorean Theorem, perhaps the most famous of all the formulas in geometry, was actually being used in Egypt well before Pythagoras was born and was being used in China centuries before Pythagoras. Much of what is studied in mathematics has a European slant to it because that is where the founders of the Western world originated. But algebra was developed and refined in India and along the sub-Asian continent as a problem-solving tool while Europe was living through the Dark Ages. Foremost in its development was the mathematician al-Kwarizimi, who lived 1,200 years ago in Baghdad.

During the European Renaissance and in the years that followed, mathematicians such as Cardano, Tartaglia, Fibonacci, Descartes, Leibnitz, Newton, Pascal, Euler, and the Bernoullis used algebra to solve more interesting and complex problems. Geometry, calculus, probability, and statistics are topics studied in today's high school mathematics classes. Each branch was developed to yield more information about the world—as it is, and as it might be. This may be the most important piece of information for you to keep in mind as you work through (note that we say, “work through,” not just “read”) this book. Mathematics has, for the most part, been developed to solve problems that have not been solved. Sometimes, the motivation is pride (as in the cases of Cardano and Tartaglia); sometimes it is financial, as in the case of Fibonacci. But very often physics is a major motivator.

The human drive to be more efficient in the workplace requires a better understanding of the forces that machines and nature exert. Leibnitz and Newton developed calculus on the basis of the analytic geometry created by Descartes, and their work was improved upon by Euler, the Bernoullis, and a host of other mathematicians, including many who are still continuing their investigations today. Pascal, who designed the first mechanical calculator (which was too complicated to be engineered with the technology of his day), is better remembered for formalizing the laws of probability. All of the work done by these men had its basis in algebra.

Just as the basic addition facts are the fundamental building blocks for elementary and middle school mathematics, algebra is the basic tool of high school mathematics, and calculus serves that purpose for higher-level mathematics. This book will serve as an extra resource for those who are currently studying elementary and intermediate algebra. It can also offer a review for those who need to refresh their skills.

Technology is a tool often applied in the study of algebra, and it is used in this text when appropriate. Appendix A gives a general overview of the topic, but the nuts and bolts of deriving the equations of best fit are included in the chapters themselves. The two tools used in writing this text are the TI 84 and TI Nspire calculators. An indispensable application of technology is its use to model behavior from a set of data with an equation of best fit. This, too, is included in the text, and it may be a new area of study for those using this book for review.

1. Home
2. Algebra
3. Introduction