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About this Lesson
 Type: Video Tutorial
 Length: 4:16
 Media: Video/mp4
 Use: Watch Online & Download
 Access Period: Unrestricted
 Download: MP4 (iPod compatible)
 Size: 45 MB
 Posted: 06/26/2009
This lesson is part of the following series:
Beg Algebra: Introduction (4 lessons, $5.94)
Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Beginning Algebra. This course and others are available from Thinkwell, Inc. The full course can be found athttp://www.thinkwell.com/student/product/beginningalgebra. The full course covers linear equations, inequalities, polynomials, rational expressions, relations and functions, roots and radicals, quadratic equations and systems of equations.
Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.
He has also taught at UTAustin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest named him in the "100 Best of America".
Prof. Burger is the author of over 50 articles, videos, and books, including the trade book, Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and of the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, padic analysis, the geometry of numbers, and the theory of continued fractions.
Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.
About this Author
 Thinkwell
 2174 lessons
 Joined:
11/13/2008
Founded in 1997, Thinkwell has succeeded in creating "nextgeneration" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technologybased textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.
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Beginning Algebra
Welcome to algebra. I am professor Burger and I am so excited to be with you on this journey through interesting and challenging mathematical vistas. When I think of algebra I have all sorts of ideas, and probably you have your own feelings and emotions, and I hope some of them are positive. Together we are going to have some fun while we think about some really abstract and interesting ideas. Ideas that actually are applicable to our everyday world, not only in our everyday lives, but also to described phenomenon around us. In this opening lecture I just want to share with you a couple of thoughts about how I see mathematics in general, how I see algebra in specific, and then more generally how to look at issues when we face them.
First of all, what to me is mathematics? Mathematics is the act of thinking quantitatively. The key thing there is the word act. So, how do you actually do mathematics? The way to do mathematics is by doing it. You have to try, you have to get in there, and you have to try it on your own. It is so important to try things, make mistakes, and learn from those mistakes. It is by making mistakes that we understand the depth and the detail involved and realize that issues, that seem obvious at first, are actually deeper than we first thought.
With respect to this particular course, there are all sorts of wonderful lessons we are going to pick up here. I want to highlight a couple of them really fast for you. The first one is the fact that so many times when we are converting issues from the real world to the mathematical world, we almost need a lexicon to translate back and forth. One great thing we see all the time is that if we see the word "of", it just means multiplication. So, for example, if I say half of a number is six, what does that mean? It means half of some number, or half times some number is six, and so we would see 12. So, you will see this kind of thing recurring again and again. If you hear the word "and", that always means add. If I say seven and two, that just means add seven and two. So, you will see how the everyday words that we use actually have reflections mathematically. Once we embrace those meanings we can actually understand the math much better. Finally, one of the most important themes we will see in this class together again and again everywhere, not just in the applied issues, but even in the more abstract issues, is the notion of combining like terms. If things are alike we can put them together. If they are not, we can't put them together. So we will constantly struggle in this course to put things together that don't look the same. Our journey and challenge is to somehow massage them both so they in the end actually look the same and we can compare them, therefore only combining like terms.
How do you solve hard problems? The answer is, you can do it in three basic steps. The first thing to conquer the unknown is to first understand what you are asked. In fact, I will argue quite strongly that understanding is job one. In fact, if you just understand the question, you are 80% of the way to a solution. So where are we? We have a bunch of things that we know and we have this challenge that we face. What do we need? We need a bridge to take us from our known understanding into the realm we are trying to approach. In this course we are going to see that bridge usually takes on algebraic flavor. We will have some things that we know and there will be some unknowns. The link between the knowns and unknowns will be some sort of algebraic expression or some sort of algebraic equation. Once we put that together we can actually resolve the issue by solving it.
I hope you are going to be excited about the adventure ahead. There will be lots of x's, and lots of numbers, and lots of fractions, but always there will be great ideas and a lot of fun. I'll see you at the first lecture.
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