Number Theory – Mathematics 0420
Brown University – Spring, 2018
Professor Joseph Silverman
Text 
A Friendly Introduction to Number Theory (4th edition, 2012)
by Joseph H. Silverman, Pearson, ISBN: 9780321816191 You may freely download Chapters 1–6 and other material on the FRINT home page . 

Office  Mathematics Department, Kassar House, Room 202 
Phone  8631124 
jhs@math.brown.edu  
Web Site  www.math.brown.edu/~jhs/MA0042/MA0042HomePage.html 
Office Hours 
Monday 2:00–2:45pm and Tuesday 10:00–11:00am
The last regularly scheduled office hour will be Tuesday, May 8, 10:00–11:00am. There will be one additional extra office hour on Tuesday, May 15, 3:00–4:00pm. Click here for Information about Office Hours and Other Academic Resources 
Course Time  TuTh 2:30–3:50 PM (K Hour) 
Course Location  Barus Holley 161 
Homework 
I will keep a list of reading and homework assignments on
the following web page:
Click here to go to the Math 0420 Homework Page. 
Problem Sets 
NOTE:
The problem sets are challenging. Don't leave them until
the last minute! We will be moving rapidly. In order to learn the
material, it is very important to
DO THE HOMEWORK WHEN IT IS ASSIGNED.
RULES: Homework must be stapled. All problems must be clearly labeled. Late homework will not be accepted under any circumstances. (If you haven't finished the HW, just hand in what you've done. A few missing problems during the semester are unlikely to affect your grade, and it's an imposition on the grader to have to go back and grade late homeworks.) 
Note on Using Computers in Math 0420  Computers are a useful tool that can be used to generate data for making conjectures and to perform computations that would be tedious to do by hand. However, they are not a replacement for understanding. So for example, you might use a computer to compute the greatest common divisor of two large numbers, but you should be sure that you understand how the computer is doing the computation. 
Computer Package for Math 0420 
I tend to use a computer program called PARIGP to do
number theory calculations. The good news about PARI is that it is free
and very fast and powerful at doing number theoretic computations.
The bad news is that it's not tremendouly user friendly.
If you're computer savvy, you can download PARI here:
Click here to go to the PARI home page. Another way to use PARI to do short calculations is to use the SAGE web site. Or you can use SAGE itself, which is another computer algebra package that can be used for number theory computations.
As an alternative, I have written a web page number theory calculator
that you can use for Math 0420. It is not as versatile as PARI or SAGE and
it can only handle numbers up to about 16 digits, (and it does not
warn you when the numbers get too big, it just gives the wrong answer).
However, it it is very easy to use.

Dates to Remember: There will be two inclass hour exams and a final exam.
Hour Exam #1 
Tuesday February 27 
Covers Ch. 1, 2, 4–10 
Exam 1 Solutions 
Hour Exam #2 
Tuesday April 10 
Covers Ch. 11–12, 14–18, 20–22 
Exam 2 Solutions 
Final Exam 
Wednesday May 16 
Time 2:004:00pm 
The final exam is cumulative. It covers Chapters 12, 412, 1418, 2022, 2425, 3134, 3739 Final Exam Solutions 
Grading: The course grade will be determined on the following basis:
Problem Sets 
20% 
Hour Exams (22.5% each) 
45% 
Final Exam 
35% 
Syllabus