MATH 4900 - Senior Seminar

Class Information:

• class syllabus revision:
  
  As discussed via email, we will no longer have a final exam on perfect numbers.   Your grade will be based on the following scale:
  
  5% rough draft
  45% final paper
  50% presentation
   
• A youtube video that I made to show you how to use zoom for our class.
   
• The final exam study guide is here.
   
• The syllabus is here
• Information on the presentation and paper is here.
• Ideas for topics for your paper are here.
   
• Google slides
   
• Library math research guide
   
• The Great Internet Mersenne Prime Search
• The known Mersenne primes
• Some papers on Mersenne numbers and even perfect numbers

Example Latex template:

• You can replace the stuff in this template to write a paper with LaTeX if you want.   Note it also teaches you how to write in LaTeX at the same time.   Note: When you compile it, you may have to compile it twice to get the ?? to dissapear and the references / citations to appear.

LaTeX program download:

• Go here to get windows, mac, or linux versions of LaTeX.   I use the MacTex distribution on my mac.   I used the MikTex distribution when I was using a Windows PC.

Example powerpoint talks:

• Talk on Gaussian primes
• Talk on expander graphs

Mathematica programs:

• Lucas Lehmer test programs
   

Perfect numbers links:

• Solving the odd perfect number problem: some old and new approaches, by Jose Arnaldo Dris, Master's thesis, De La Salle University, 2008.
• Perfect Numbers and Mersenne Primes, by Barry Delello, Master's thesis, University of Central Florida, 1986.
• Euclid's proof on perfect numbers from Elements Book IX Prop 36
• Euler was working on this book on number theory.   See chapter 3 for the perfect number info.   The integral notation is the sigma function.   He loved calculations.   Take a look at notes 88, 89, and 100.
• Wiki page for Lucas-Lehmer test for the primality of Mersenne numbers.