Teacher:Andy Engelward
Office:  51 Brattle Street, Cambridge, room 707

Phone: 781 676-0676
Email:engelward@math.harvard.edu

This course was created for middle school and high school mathematics teachers.  The aim of Math 301 is to give teachers a foundation in the basic working of the mathematics of number theory.  Prerequisites include a basic knowledge of number systems, artithmetic, algebra, and precalculus mathematics. Experience teaching these subjects is useful but not necessary.

In this course we will work through many proofs of basic number theory results.  One of the course goals will be to work through a proof of the fundamental theorem of arithmetic (that all positive integers can be uniquely factored as products of primes).  Some people consider this result to be a pretty obvious and perhaps even dull statement about the integer number system, but it turns out that the existence of such a theorem is not at all automatic.  In fact we might examine some other number systems in which such a statement is actually false, where numbers can be factored in two different ways.  If such a thing were to happen in our own beloved integers, then things would get pretty ugly pretty fast. 

 In our class we will also consider many other interesting topics from number theory as well, such as the Fibonacci sequence, decimal expansions, and public key cryptography – a system whose use has spread to the internet where it’s sometimes used to encrypt vital information conveyed over the web, such as credit card numbers.   If there are particular topics of interest to students in the class, we will try to incorporate them into the class as well.

In addition to studying number theory from a theoretical perspective, the class will also provide a variety of activities and games which teachers can bring to their classrooms to enhance their students' understanding and enjoyment of topics from number theory.

When accessing files from this website, if you need to read PDF files, you can download the Adobe Acrobat Reader for free.