Math Chat: Algebra, Voting Systems, Logarithms, and why .999... = 1

Math Chat is a potpourri of diverse mathematical topics to discuss. This month we are highlighting three videos that focus on the nature and history of algebra, voting systems, logarithms, and why .999... = 1. If you have a favorite math topic or a math question, bring it and we can chat about it too!

To start the discussion, here are three videos that explore algebra, voting, logarithms, and the fact that .999... = 1.

• This 1¾ hour video of Keith Devlin (http://www.youtube.com/watch?v=FME9avU3u2Y) discusses the nature and history of algebra and ends with a survey of the mathematical paradoxes of voting systems. In addition, the last 18 minutes is a general Q&A on the Nobel Prize in economics, math education, and game theory which we can also discuss. Read my notes on Devlin's lecture (https://plus.google.com/104222466367230914966/posts/Xteeo2w4d39).

http://www.youtube.com/watch?v=FME9avU3u2Y

Note: Keith Devlin's MOOC "Introduction to Mathematical Thinking" begins on Feb 3rd (10 weeks long deadline-driven course): https://www.coursera.org/course/maththink

• Vi Hart's video of 9.999... reasons that .999... = 1 (http://www.youtube.com/watch?v=TINfzxSnnIE)

http://www.youtube.com/watch?v=TINfzxSnnIE

• Vi Hart's video on logarithms (http://www.youtube.com/watch?v=N-7tcTIrers)

http://www.youtube.com/watch?v=N-7tcTIrers

Discussion topics and some questions:

• The Nature and history of algebra

• How does algebra differ from arithmetic and algorithm?

• How did algebra develop historically?

• What is the difference between algebraic expression, algorithm, and a model?

• What are the differences between plurality voting, single transferable vote (STV), and approval voting? Which method do you think is most fair?

• Devlin asserts "you tell me who you want to win, and I can give you a fair way to count the votes so that person will win": do you believe it?

• In single transferable vote (STV), is it possible that by adding support to a candidate they could shift from winning to losing? Is it fair that the order in which candidates are eliminated can make that much difference (in STV)?

• Is the expression "the will of the people" meaningful?

• What are the implications of Arrow's Impossibility Theorem to democracy?

• Does .999... = 1?

• Which of Vi Hart's reason's most appeals to you?

• Are there any of her reasons that you do not understand?

• Does Vi Hart's video on logarithm's give a good picture of how they work?

• Do you have any questions about logarithms?