Math 115
Introduction to Number Theory
MTuWTh 8-10 247 Cory
Dylan Yott
dyott@math.berkeley.edu
www.math.berkeley.edu/ dyott/Teaching.html
844 Evans
Office Hours: 10-11 MTuWTh
The details of this syllabus are subject to change.
Course Description: In this course we will study properties of the integers using the language
of divisibility and congruences. We will explore results about writing integers as sums of squares
and quadratic reciprocity, among other results. Then, we will study arithmetic functions and prove
certain analytic results about the distribution of primes. Finally, time permitted we will discuss
one of a few possible advanced topics such as: elliptic curves, p-adic numbers, quadratic number
fields, partitions
Prerequisite(s): 53, 54.
Credit Hours: 4
Text(s): The Theory of Numbers, 5th Edition
Author(s): Niven, Zuckerman, Montgomery; ISBN-13: 978-0471625469
Grade Distribution:
Homework
Take Home Exam 1
Take Home Exam 2
Midterm Exam
Final Exam
40%
10%
10%
20%
20%
Course Policies:
• Homework
– Homework is a crucial part of this course and as such students should expect to spend
significant time on it.
– Students are encouraged to work together on homework, but must write up solutions
individually.
– Homework is graded both for completeness, clarity, and style (important for proof writing).
• Take Home Exams and In-Class Exams
1
– Take Home Exams will be given on a Friday and collected on a Monday. All work on
take home exams should be worked on completely independently. Class notes and the
textbook can be used, but online resources are not allowed.
– No notes allowed on in-class exams.
• Attendance and Absences
– Attendance is crucial for success in the course and is where homework assignments will
be distributed and collected.
– Attendance will not directly factor into your grade.
Academic Integrity: The University defines academic misconduct as “any action or attempted
action that may result in creating an unfair academic advantage for oneself or an unfair academic
advantage or disadvantage for any other member or members of the academic community”. Any
acts of academic misconduct will be taken very seriously.
2
Tentative Course Outline:
The weekly coverage might change as it depends on the progress of the class. However, you must
keep up with the reading assignments.
Week
Content
Week 1
• Basic properties of integers, Divisibility and Congruences, Binomial Theorem
• Homework 1
Week 2
• Binomial Theorem (Cont’d), Chinese Remainder Theorem, Euler’s phi Function
• Homework 2, Take Home exam 1
Week 3
• Quadratic Residues, Hensel’s lemma, Sums of Squares
• Homework 3
Week 4
• Quadratic Reciprocity, Quadratic Forms
• Homework 4, Midterm
Week 5
• Arithmetic Functions, Distribution of Primes
• Homework 5
Week 6
• Distribution of Primes (Cont’d)
• Homework 6, Take Home Exam 2
Week 7
• Special Topics
• Homework 7
Week 8
• Special Topics
• Homework 8, Final
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