Table of Contents
For my wife, Lisa, who makes my life worth living, and my son, Nicholas, who taught me that waking up in the morning with the people you love is just the best thing in the world.
Introduction
Picture this scene in your mind. I am a high school student, chock-full of hormones and sugary snack cakes, thanks to puberty and the fact that I just spent the $3 my mom gave me for a healthy lunch on Twinkies and doughnuts in the cafeteria. I am young enough that I still like school, but old enough to understand that Im not supposed to act like it, and my mind is active, alert, and tuned in. There are only two more classes to go and my day is over, and with that in mind, I head for algebra class.
In retrospect, I think the teacher must have had some sort of diabolical fun-sucking and joy-destroying laser ray gun hidden in the drop-down ceiling of that classroom, because just walking into algebra class put me in a bad mood. Its as hot as a varsity football players armpit in that windowless, dank dungeon, and strangely enough, it always smells like a roomful of people just finished jogging in place. Vague yet acrid sweat and body odor attack my senses, and I slink down into my chair.
I have to stay awake today, I tell myself. I am on the brink of getting hopelessly lost, so if I drift off again, I wont understand anything, and we have a big test in a few days. However, no matter how I chide and cajole myself into paying attention, it is utterly impossible.
The teacher walks in and turns on a small oscillating fan in a vain effort to move the stinky air around and revive her class. Immediately she begins, in a soft, soothing voice, and the world in my peripheral vision begins to blur. Uh oh, soft monotonous vocal delivery, the droning white noise of a fan, the compelling malodorous warmth that only occupies rooms built out of brightly painted cinderblock all elements that have thwarted my efforts to stay awake in class before.
I look around the room, and within 10 minutes most of the students are asleep. The few that are still conscious are writing notes to boyfriends or girlfriends. The schools star soccer player sits next to me, eyes wide and staring at his Trapper Keeper notebook, having regressed into a vegetative state as soon as class began. I begin to chant my daily mantra to myself, I hate this class, I hate this class, I hate this class and I really mean it. As far as I am concerned, algebra is the most boring thing that was ever created, and it exists solely to destroy my happiness.
Can you relate to that story? Even though the individual details may not match your experience, did you have a similar mantra? Some people have a hard time believing that a math major really hated math during his formative years. I guess the math after algebra got more interesting, or my attention span widened a little bit. However, thats not the normal course of events. Luckily, my extremely bad experience with math didnt prevent me from taking more classes, and eventually my opinion changed, but most people hit the brick wall of algebra and give up on math forever in hopeless despair.
That was when I decided to go back and revisit the horribly boring and difficult mathematics classes I took, and write books that would not only explain things more clearly, but make a point of speaking in everyday language. Besides, I have always thought learning was much more fun when you could laugh along the way, but thats not necessarily the opinion of most math people. In fact, one of the mathematicians who reviewed my book The Complete Idiots Guide to Calculus before it was released told me, I dont think your jokes are appropriate. Math books shouldnt contain humor, because the math inside is already fun enough.
I believe that logic is insane. In this book, Ive tried to present algebra in an interesting and relevant way, and attempted to make you smile a few times in spite of the pain. I didnt want to write a boring textbook, but at the same time, I didnt want to write an algebra joke book so ridiculously crammed with corny jokes that it insults your intelligence.
I also tried to include as much practice as humanly possible without making this book a million pages long. (Such books are hard to carry and tend to cost too much; besides, you wouldnt believe how expensive the shipping costs are if you buy them online!) Each section contains fully explained examples and practice problems to try on your own in little sidebars labeled Youve Got Problems. Additionally, Chapter 20 is jam-packed with practice problems based on the examples throughout the book, to help you identify your weaknesses if youve taken algebra before, or to test your overall knowledge once youve worked your way through the book. Remember, it doesnt hurt to go back to your algebra textbook and work out even more problems to hone your skills once youve exhausted the practice problems in this book, because repetition and practice transforms novices into experts.
Algebra is not something that can only be understood by a few select people. You can understand it and excel in your algebra class. Think of this book as a personal tutor, available to you 24 hours a day, 7 days a week, always ready to explain the mysteries of math to you, even when the going gets rough.
How This Book Is Organized
This book is presented in seven sections:
In Part 1, A Final Farewell to Numbers, youll firm up all of your basic arithmetic skills to make sure they are finely tuned and ready to face the challenges of algebra. Youll calculate greatest common factors and least common multiples, review exponential rules, tour the major algebraic properties, and explore the correct order of operations.
In Part 2, Equations and Inequalities, the preparation is over, and its time for full-blown algebra. Youll solve equations, draw graphs, create equations of lines, and investigate inequality statements with one and two variables.
In Part 3, Systems of Equations and Matrix Algebra, youll find the shared solutions of multiple equations and learn the basics of matrix algebra, a comparatively new branch of algebra thats really caught on since the dawn of the computer age.
Things get a little more intense in Part 4, Now Youre Playing with (Exponential) Power! because the exponents are no longer content to stay small. Youll learn to cope with polynomials and radicals, and how to solve equations that contain variables raised to the second, third, and fourth powers.
Part 5, The Function Junction, introduces you to the mathematical function, which takes center stage as you advance in your mathematical career. Youll learn how to calculate a functions domain and range, find its inverse, and graph it without having to resort to a monotonous and repetitive table of values.
Fractions are back in the spotlight in Part 6, Please, Be Rational! Youll learn how to do all the things you used to do with simple fractions (like add, subtract, multiply, and divide them) when the contents of the fractions get more complicated.
Finally, in Part 7, Wrapping Things Up, youll face algebras playground bully, the word problem. However, once you learn a few approaches for attacking word problems head on, you wont fear them anymore. Youll also get a chance to practice all of your skills in the Final Exam; dont worry, it wont be graded.
![W. Michael Kelley [W. Michael Kelley] - Calculus I](/uploads/posts/book/119087/thumbs/w-michael-kelley-w-michael-kelley-calculus-i.jpg)
