**
MATH 680 Fall 2017
**

# Basic Information

**Instructor**: Jeff Thunder**Office**: WH 362**Phone**: 753-6761**e-mail**: jthunder@math.niu.edu**Office Hours**: Monday, Wednesday, Friday, 11:00-11:50 a.m. or by appointment.

# Homework

Homework will be assigned somewhat irregularly. I'll announce assignments (and due dates) in class and also post them to this webpage. You are free to work with other students on the homework; in fact, this is encouraged. Sloppy and/or illegible work will be returned back with no credit! Your homework is something of which you should be proud (notice how I didn't end with a preposition there). Expect to spend lots of time on it.

# Homework Assignments

- First homework assignment (Due 9/8)
- Second homework assignment (Due 9/15)
- Third homework assignment (Due 9/22)
- Fourth homework assignment (Due 10/4)
- Fifth homework assignment (Due 11/1)
- Sixth homework assignment (Due 11/8)
- Seventh homework assignment (Due 11/17)
- Eighth homework assignment (Due 11/27)
- Assignment 8 1/2:
**carefully**(re)do the estimates for exercise 23 (Due 12/4) - Ninth homework assignment (Due 12/11)

# Final Exam

The final exam will be held Monday, December 11 from 10:00-11:50 in our usual classroom. You will be asked to present a solution to (one part of) one of the following exercises: final exam questions.

# Text and Syllabus

Rather than a formal textbook, I'll be making available written up lecture notes. These will be made available in a timely fashion.

We will begin the course with a survey of some important arithmetic functions. We'll study some early, more elementary estimates involving primes, then proceed with a proof of the prime number theorem. We'll also study Dirichlet's result on primes in arithmetic progression. We'll finish with more quantitative results concerning the prime number theorem as time allows.

# Handouts

- Arithmetic Functions
- Chebyshev's Estimates
- Bertrand's Postulate
- The Riemann Zeta Function
- generic results on infinite products
- A Particular Infinite Product
- Dirichlet Series
- Primes in an Arithmetic Progression
- The Prime Number Theorem
- The Functional Equation
- A Quantitative Prime Number Theorem I: Zero-Free Regions
- A Quantitative Prime Number Theorem II: The Inverse Mellin Transform
- Hardy's Theorem (zeros along the critical line)
- Stirling's Formula
- Properties of the xi Function
- Classical Estimates for the Psi Function
- The Distribution of the Zeros

## Homer does math!

Yes indeed, there's plenty of math humor to be found in the Simpsons. Just look and see!

Last update: Dec. 6, 2017