USA 13,509MGF 1107H

Liberal Arts Mathematics II for Honors

 

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Course Handouts

     Course Outline: This document will give you a good idea of what the course will be like.

     Schedule: This document gives a tentative schedule for the entire term.

     Assignment Sheet: This document contains a partial list of assignments for the course. The warm ups should be emailed to me, while the other assignments should be completed on paper and turned in at the beginning of the class on the day they are due.

     Homework Sheet: This document contains a list of problems to complete in order learn the material.

     Course Objectives: This is the list of course of objectives established by the HCC mathematics cluster.


Reviews

      Review for Test 1

      Review for Test 2

     Review for Test 3

      Review for Test 4

      Review for Test 5

      Review for Final

 


Computer Projects

 

      Borda Count Project

      Hamilton Method Apportionment Project

      Congressional Apportionment Project

      Financial Mathematics Project

      Computer Algebra System Project

      HMTL Version of Computer Algebra System Project

      Number Theory Project

     HTML Version of Number Theory Project

 


TOPICS LINKS

The following is a list of links for each of the topics in my Liberal Arts Mathematics II course.

Voting Methods

     Example Problems on Voting Methods:  This site contains notes for a mathematics course at Princeton University.   There are good example problems for each of the voting methods we will study in our course.

     Voting Methods Lectures: A nice set of lesson on voting method courtesy of Washington State Universitys Department of Mathematics.

     2005 Heisman Trophy Voting: The Heisman Trophy in college football is decided by a Borda count.  Try working out the points for each player as given in at the bottom of this article. The article comes from the website devoted to the Heisman TrophyHeisman.com - Heisman Trophy.

     Solution to #15 in 1.1: This problem is a good example of a strategic voting question.

     Three Proofs of Arrows Impossibility Theorem: Although these proofs by John Geanakoplos are beyond the level of the course, I have included this link here for any interested students. It is a pdf file and requires acrobat reader to open it.

     Instant Runoff Voting: In some parts of the country voters are advocating the use of Instant Runoff Voting as a fairer way to resolve local elections. This is a practical implementation of the Hare method we discuss in class. My thanks to James Moore for bringing the issue to my attention.

     Online Voter Registration: A link to the voter registration site maintained by the Florida Department of State Division of Elections.

Apportionment

     Congressional Apportionment:  This site contains information on apportionment from the U. S. Census Bureau.  It includes information on the history of apportionment in the U.S. and how the apportionments are calculated.

     United States House of Representatives: This page contains a list of the all the members of the United States House of Representatives. The link takes you to the section on the list with the members from Florida.

Financial Mathematics

      Formulas for the Financial Mathematics:  These are the formula we will learn about


Graph Theory

     Graph Theory -- from MathWorld: A short description of Graph Theory.

     The Konigsberg Bridge Problem:  This site contains information about Eulers well-known problem and the origins of Graph Theory.

     History of the TSP: A great site on the history of the traveling salesman problem.

     William Hamilton: A short biography of the mathematician for whom the hamiltonian circuit is named.

     Julia Robinson: A short biography of the mathematician believed to have coined the term traveling salesman problem. She is also the first women to be elected to the National Academy of Sciences.


Number Theory

      Number Theory -- from MathWorld: A short description of Number Theory.

      An Example of Modular Arithmetic: This example shows how modular arithmetic can simplify some kinds of computations. 

     Information Sheet for Cryptology:  Formulas and other information for doing affine ciphers.

     Euclid's Elements:  A wonderful HTML version of Euclid's Elements.  It contains lots of explanatory text and diagrams. Many of the diagrams are java applets that can be manipulated to help in understanding the theorems.

     Fermat: Fermat was an amateur mathematician who corresponded with the best mathematicians of his day in his effort to solve mathematical problems. He proposed, and claimed to prove, Fermats Last Theorem.

     Euclid: The author of the Elementsa work which collected and expanded on the Geometry and Number Theory known to the ancient Greeks.

     Eratosthenes: Two hundred fifty years before the birth of Christ this African-born mathematician use Geometry to accurately calculate the circumference of the Earth.

     Andrew Wiles: In 1993, he proved Fermat Last Theorem a 300-year old unsolved mathematics problem in Number Theory.

Ambrioso Fall 2006