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MATHS 498 Senior Seminar, Fall 2009

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Syllabus

Course Project

Project Topics

ETS Major Field Exam Information

Course Schedule

Mathematica Tutorial

Saint Andrews’ University History of Mathematics

Math World Mathematics and Science Reference

Peer Review Form

Week 1

• Modeling Heat Flow in a Thermos Talk
• Thermos Paper
• Beer Paper
• Homework 1

Week 2

• Outline of Ehrismann’s paper
• A Brief Introduction to Differential Equations Talk
• NOVA’s companion website to “Trillion Dollar Bet”
• Homework 2

Week 3

• Discuss Chapter 1 of Fermat’s Enigma
• BeerTestSample Mathematica Notebook
• Washington Post article
• John Lorch’s paper
• Homework 3

Week 4

• How to be a Mathematics Professor
• Discuss Washington Post article and John Lorch’s paper
• Discuss Chapter 2 of Fermat’s Enigma
• The Falling Ladder Paradox paper
• Homework 4

Week 5

• Discuss Chapter 3 of Fermat’s Enigma
• Fermat’s Method of Infinite Descent
• Falling Ladder Problem
• Discuss The Falling Ladder Paradox paper.
• How to use Mathematica to solve or check math problems!
• Ladder Plot Hints (PDF) (Mathematica)
• Do Dogs Know Calculus?
• Homework 5

Week 6

• Discuss Chapter 4 of Fermat’s Enigma
• Sam Lloyd’s 15 Puzzle
• Introduction to Cryptography
• Virtual Enigma Machine
• RSA on Mathematica
• Homework 6

Week 7

• The Geometry Junkyard (Escher) (Hyperbolic Geometry)
• Mathematics in Industry – Irene Livshits (postponed)
• Wavelets and Data Compression

• CNN Article on Mathematics Careers
• MAA Career Profiles
• Homework 7

Week 8

• ETS Major Field Exam – RB 118 (3:20 – 5:30 pm)

Week 9

• Discuss Chapter 5 of Fermat’s Enigma
• Student Research at National Laboratories
• Complex Function Plotting Tool
• Complex Tool Intro Sheet
• Homework 8

Week 10

• What is Actuarial Science? – Bart Frye
• http://www.beanactuary.com/
• Discuss Chapter 6 of Fermat’s Enigma
• Modulo Arithmetic and Additive Ciphers
• Homework 9

Week 11

• Discuss Chapter 7 and Epilogue of Fermat’s Enigma  
• Watch “The Proof” Video
• Wiles’ Paper (PDF)
• Wiles and Taylor’s paper (PDF)
• The Mathematics Genealogy Project
• Homework 10

Week 12

• What is Mathematics Education? – guest speaker Kathryn Shafer

• Papers to read for Week 12 (Please read in the order listed!)

• “Teaching Mathematics in the United States” by Al Cuoco (PDF)
• “E.H. Moore’s Early Twentieth-Century Program for Reform in Mathematics Education” by David Lindsay Roberts (PDF)
• “The Mathematics Education Reform:  Why You Should be Concerned and What You Can Do” by H. Wu (PDF)
• “Beyond the Math Wars” by Judith Roitman (PDF)

• National Council of Teachers of Mathematics (NCTM) Web Page (Includes latest version of NCTM Standards) http://www.nctm.org/

Week 13

• Elliptic Curves and Elliptic Curve Cryptography
• Certicom’s Website www.certicom.com
• Certicom’s Geometric Elliptic Curve Model
• Certicom’s Finite Geometric Elliptic Curve Model
• Diffie-Hellman Key Exchange Example (Mathematica Notebook) (PDF Version)
• Homework 11

Week 14 – Fruesday (Friday classes meet!)

• Here are some papers to read over Thanksgiving Break!
• Modular Forms Associated with the Full Modular Group
• Three Fermat Trails to Elliptic Curves
• Fun with Elliptic Curves! (Mathematica Notebook) (PDF)
• Fermat:  The Founder of Modern Number Theory

Week 15 – Topic Presentations

Week 16 – Topic Presentations

Week 17 (Final Exam Period) – Topic Presentations