**Liberal
Arts Mathematics II**

Click on image for source and a larger image.

**Course Handouts**

Ø **Syllabus**: This document will give you a good idea of
what the course will be like.

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

Ø Practice Problems: This document contains a list of problems to complete in order learn the material.

Ø Assignment Sheet: This document contains a list of homework problems to help students prepare for tests.

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

**Reviews**

Ø Review for Test 3

** **

**Computer Projects**

Ø Hamilton Method Apportionment Project

Ø Congressional Apportionment Project

Ø Financial Mathematics Project

Ø Computer Algebra System Project

Ø HMTL Version of Computer Algebra System Project

Ø 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**

Ø Example
Problems on Voting Methods: This site contains notes for a
mathematics course at

Ø Voting Methods
Lectures: A nice set of lesson on
voting method courtesy of

Ø 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 Trophy—Heisman.com - Heisman Trophy.

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

Ø Three Proofs of Arrow’s 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.

Ø 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. IRV is a practical implementation of the Hare method we discuss in class. My thanks to James Moore for bringing the issue to my attention.

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

**Apportionment**

Ø Congressional
Apportionment: This site contains information on apportionment from
the U. S. Census Bureau. It includes information on the history of
apportionment in the

Ø 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

**Financial
Mathematics**

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

Ø Populations
Projections: A web site devoted to
populations projections for the

Ø History of the Ben Franklin Institute: A wonderful real-life story of a founding father’s imaginative philanthropy and the power of compound interest.

**Graph Theory**** **

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

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

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

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

Ø 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**** **

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

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

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

Ø Cryptology Interactive Worksheet: This Excel worksheet allows the user to encode and decode messages using an affine cipher.

Ø Euclid's *Elements*: A wonderful HTML version of *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.

Ø 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, Fermat’s Last Theorem.

Ø Euclid: The author of the *Elements*—a work which collected and expanded on the Geometry and
Number Theory known to the ancient Greeks.

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

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

Ø The Ghost Whisperer Crystal Ball: An interesting application of Number Theory. How does it work?

**Ambrioso Summer
2009**