Number Theory for Beginners

Course Description and Grading Breakdown

This course is an introduction to number theory. No background in the topic is required, and all are welcome.

Number theory is the study of the natural numbers. Although its ultimate scope is vast, in this course we will start at the very beginning. The topics covered will include:

Primes and divisibility, Diophantine equations and Pythagorean triples, modular arithmetic, Euler's phi-function, solutions of congruence equations, Fermat and Mersenne primes, RSA encryption, Quadratic reciprocity, sums of squares, Gaussian integers, diophantine approximations, continued fractions, and binary quadratic forms.

The final project will be a programming assignment. Students are encouraged to learn to use PARI, which is designed for number theoretic calculations. It is now incorporated into Sage, which is also very useful. See the notes section below for links to introductory guides.


Course Meeting Time and Location
Monday, Wednesday and Friday
1:00 - 1:55 pm
B111 Downs Laboratory of Physics (DWN)

Course Instructor Contact Information and Office Hours
221 Math Department (Building #15)
Office Hours: Mondays 2-3pm

TA Contact Information and Office Hours
2-J Math Building
Office Hours: Wednesdays 4-5pm, Common Room in the Math Department.

Course Schedule and Textbook

 DateTopic 
  
  

Lecture Notes



 Current     (pdf)
 2017(pdf)
 Sage Intro    (pdf)




Course Policies

Grade will be based on six assignments, plus one final project.


Assignments
 Date PostedAssignment Due Date  Solutions
 Friday, April 6HW1 Friday, April 13 (due in class)
 Thursday, April 12HW2 Friday, April 20    
 Friday, April 20HW3Friday, April 27            
 Friday, April 27 HW4Friday, May 4   
 Thursday, May 3 HW5 Friday, May 11        
 Friday, May 11 HW6 Friday, May 18            
 Friday, May 18 Final Project Friday, June 15
Midterm and Final Exam


Collaboration Table
 HomeworkExams
You may consult:  
Course textbook (including answers in the back)YESYES
Other booksYESNO
Solution manualsNONO
InternetYESNO
Your notes (taken in class)YESYES
Class notes of othersYESNO
Your hand copies of class notes of othersYESYES
Photocopies of class notes of othersYESNO
Electronic copies of class notes of othersYESNO
Course handoutsYESYES
Your returned homework / examsYESYES
Solutions to homework / exams (posted on webpage)YESYES
Homework / exams of previous yearsNONO
Solutions to homework / exams of previous yearsNONO
Emails from TAsYESNO
You may:

Discuss problems with othersYESNO
Look at communal materials while writing up solutionsYESNO
Look at individual written work of othersNONO
Post about problems onlineNONO
For computational aids, you may use:

CalculatorsYES*NO
ComputersYES*NO

* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work.  For example, "by Mathematica" is not an acceptable justification for deriving one equation from another.  Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them.

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Zavosh Amir-Khosravi,
Apr 12, 2018, 12:31 PM
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Zavosh Amir-Khosravi,
Apr 16, 2018, 12:20 PM
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fi.pdf
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Zavosh Amir-Khosravi,
May 18, 2018, 4:59 PM
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hw1.pdf
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Zavosh Amir-Khosravi,
Apr 8, 2018, 10:49 PM
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hw2.pdf
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Zavosh Amir-Khosravi,
Apr 12, 2018, 6:02 PM
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hw3.pdf
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Zavosh Amir-Khosravi,
Apr 20, 2018, 6:52 PM
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hw4.pdf
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Zavosh Amir-Khosravi,
Apr 27, 2018, 2:03 PM
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hw5.pdf
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Zavosh Amir-Khosravi,
May 7, 2018, 9:43 PM
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hw6.pdf
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Zavosh Amir-Khosravi,
May 11, 2018, 6:29 PM
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Zavosh Amir-Khosravi,
Apr 12, 2018, 12:36 PM