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College Algebra: An Introduction to Algebra


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About this Lesson

  • Type: Video Tutorial
  • Length: 5:50
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 62 MB
  • Posted: 06/26/2009

This lesson is part of the following series:

College Algebra: Full Course (258 lessons, $198.00)
College Algebra: Basics & Prerequisites (37 lessons, $52.47)

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.

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 UT-Austin 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, p-adic 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

2174 lessons

Founded in 1997, Thinkwell has succeeded in creating "next-generation" 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 technology-based textbooks. For more information about Thinkwell, please visit or visit Thinkwell's Video Lesson Store at

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...


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Hey, welcome to algebra. My name is Professor Edward Burger, and I am looking forward to sharing with you all that I know about algebra, which will take about five minutes. No, but really... We're going to take a look at algebra from the very beginning through sort of the entire course, and see what's at the heart of algebra. Now, you know what makes the subject hard? It's the fact that it's a whole bunch of different topics and different techniques that are sort of pulled together. And if you think of them as different topics and different techniques, then it's like a ton of stuff you have to memorize and you've got to remember all this stuff--the formulas, the lines, the slopes... And after a while you have blurry vision.
The real key is to sort of see the basic ideas behind all these techniques. And the power of seeing the ideas behind the techniques is that way we can actually see sort of the major themes and the major paradigms, and then we can actually understand what's going on more effectively, we can actually solve the questions and answer the questions we're asked, solved the problems that we face more accurately and more correctly, not by sort of picking and choosing things sort of randomly and saying, "Well, I'll just try this and hope it works," but really having a concrete an firm understanding about what's going on.
Now, that path, by the way, is going to be bumpy. There's a lot of stuff up there that requires sort of a lot of work and is technical stuff and so forth, and so what we're going to do together is work through that, and you're going to see sort of the classic mistakes that people make, and I will make those mistakes and you'll see what it looks like, and so that way you hopefully won't make them yourself. And you'll see sort of the tricks of the trade and you'll see sort of how to do things, and you'll have an opportunity to try. The important thing, and the only way to really learn how to do math at all is to do it. It's really not a spectator sport, it's a sport that you have to sort of delve into and just do, and I know you can do it.
So I hope that you're going to join me in this course on algebra to really nail it for sure and just conquer it. Now, in fact, we're going to have some fun, too. There are deep ideas, there are hard ideas, but we're also going to try to do it in sort of a fun way. For example, we're going to see how algebra will allow us to make lots of money. This is pretty cool. If you had a lot of money, maybe you wouldn't even take algebra. In fact, if you had all the money in the world, would you take algebra? I don't know? Anyway, we'll see. Also, we'll see that it's hip to be square.
We'll play all sorts of games, like "Match Game," whatever that means right now. It's not clear. We'll play "What's My Curve." That's going to be sort of fun. You're going to learn about that. And, of course, "Can They Multiply?" That's right, there's even a little bit of nuance and romance here in algebra, even though you'd say, "God, romance in algebra? Not possible." And we'll see waves and fish and so forth. We'll learn about rolling dice and seeing the probability of winning at dice and card games. That's sort of a fun thing to do. We'll learn about things like spring motion and see how well that works and see that really, it's algebra. In fact, when you think about the whole world, the truth is that Algebra is all around us. Algebra is just all around us all the time. And so to sort of capture this and really understand this, is a great thing to do. It's really fun.
How's this going to work? Well, basically, I'll talk for a little bit and give sort of a little bit of a lecture or whatever you want to call it, or just commentary or thoughts or random thoughts, or whatever I'm thinking at the moment, and over here on the side board here, on this white board, what you're going to see there are some really pretty prose written out really pretty with figures and so forth. Boy, it's really cool. For example, I might want to say, "You can nail algebra." See, there it is. So I can use that. And also, it's an opportunity or interface for us to communicate. For example, suppose I want your input on something. Well, I can actually have your input by just asking a question and having you sort of input the answer. For example, suppose I want to ask you what you think your grade is going to be in this course, and here are three possibilities. Okay, here we go. Possibility number one, you get an A; possibility number two, you get an A; possibility number three, you get an A. All right. Vote now for which grade you think you're going to get in this course.
Introduction to Algebra Page [1 of 1]

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