James Cook's Number Theory Homepage

Material from my 2015 Number Theory Course:
For a day by day overview of our course see:

• Spring 2015 Number Theory Course Planner

Basically, our plan is to work our way through Stillwell's Elements of Number Theory .
We decided to tape a few lectures, the evidence is found here:

Number Theory 2015 playlist on YouTube

Missions:
These are the required homeworks for this course. The problems are mainly taken from Stillwell's text, enjoy.

• Mission 1
• Mission 2
• Mission 3
• Mission 4
• Mission 5
• Mission 6
• Mission 7
• Mission 8
• Mission 9
• Mission 10

Lecture Notes:
I hope to add some resources here as the course continues. We did cover a bit more than is posted here, but, these are a nearly complete account of the content of the Spring 2015 offering of Math 307.

• Lecture 1 (from chapter 1)
• Lecture 2 (from chapter 2)
• Lecture 3 (congruence modulo an integer)
• Lecture 4 (Lagrange's Theorem, Wilson's Theorem, Euler's Theorem; group theoretic arguments in Chapter 3)
• Chinese Remainder Examples (supplementary handout)
• Modular Arithmetic (supplement to add depth to treatment of modular arithmetic)
• Summary of Topics for Test 1
• Lecture 7 (RSA cryptosystems and a cautionary tale on why we should learn more group theory)
• Lecture 8 (from chapter 5, Pell's Equation)
• Lecture 10 (chapter 6, Gaussian Integers)
• Lecture 11 (chapter 6, application of Gaussian integers to two-square theorem)
• Lecture 12 (chapter 7, quadratic integers)
• Lecture 14 (chapter 8, quaternions and the 4-square identity)
• Lecture 15 (chapter 8, Hurwitz integers)
• Lecture 16 (chapter 9, quadratic reciprocity)
• Lecture 19 (chapter 10, rings of algebraic numbers)
• Lecture 21 (chapter 11, ideals)
• Lecture 22 (chapter 11, ideal calculations)
• Lecture 24 (chapter 12, prime and maximal ideal theorems)
• Lecture 25 (chapter 12, conjugate ideals and divisibility as containment)
• the whole course on a page front (thanks to Erica for this)
• the whole course on a page back (thanks to Erica for this)

Exams and Solutions From Spring 2015:
Beware the errors.

• Test 1 and my Solution to Test 1
• Test 2 and my Solution to Test 2
• Test 3 and my Solution to Test 3

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Last Modified: 8-13-2015