Math 104A General Information
Fall 2006
Course Information
This is a first course in elementary number theory. Topics include: properties of integers, prime numbers,
Diophantine equations, congruences and quadratic reciprocity. An important emphasis of the course is the
coherent writing of mathematical proofs.
Class time and Location: MWF 11:50 pm at Warren Lecture Hall 2207.
Textbook: An Introduction to Number Theory, by Harold Stark.
Homework and Exams: see below
Instructor: Wee Teck Gan, Office: AP&M 5808, Tel :5340997, email: wgan@math.ucsd.edu
Office Hourse: Wed 11am12pm. (Office Hours during Final Exam Week:
Wed 11am12pm, Thurs 24pm)
Sections: A01 Tues 11:50pm, A02 Tues 22:50pm, HSS 2152
Teaching Assistant: Aaron Wong, Office Hrs: Tues: 34pm and Fri:
10:3011:30am at AP&M 6311, email: awong@math.ucsd.edu
(Office Hours during Final Exam Week: By Appointments during the priod Wed
and Thurs: 14pm).
Exams
There will be 3 midterms and a final exam.
All exams are closebook, closenotes. No calculator is allowed.
Final Exam: The final exam will be on Fri 12/8,
11:30am2:30pm. Here is a
Sample Final . (Question 5 is not in our syllabus, so dont worry about it).
And here is the solution .
Midterms: Will be held during the lecture hour on the following
dates. I will take your 2 best midterm scores for the computation of the
final grade, so you are allowed to drop one of your midterm scores.
Here are the midterm dates and the chapters of the book they cover:
(i) Oct 18 (Wed): covers Chapter 1 and 2, but excluding Sect 2.4. Here is a
Sample Midterm ;
(ii) Nov 8 (Wed): covers Section 3.13.4.
(iii) Nov 29 (Wed): covers Section 2.4, 3.5, 3.6 and stuff on quadratic
recoprocity (which is not in the textbook).
Student ID is required to take the exams. Students without ID will
not be allowed to take the exams.
(Absolutely) NO makeup exams.
Homework
There will be weekly homework
assignments, which you can find below. Homework is due in class on
Wednesdays.
Late homework will not be accepted.
I will pick your 5 best homework scores for the computation of
your final grade.
It is very important that you attempt all the homework, since it is almost
impossible to learn the subject matter without doing many problems.
We encourage you to work together on the exercises. Any assignment,
though, should represent your own work (i.e. you should write it up yourself).
Here are the homeworks:
HW1 (Due 10/4):
Problems ;
Selected Solutions ;
HW2 (Due 10/11):
Problems ;
Selected Solutions ;
HW3 (Due 10/18):
Problems ;
Selected Solutions ;
HW4 (Due 10/25):
Problems ;
Selected Solutions ;
HW5 (Due 11/1):
Problems ;
Selected Solutions ;
HW6 (Due 11/8): Problems
Selected Solutions ;
HW7 (Due 11/15):
Problems ;
Selected Solutions ;
HW8 (Due 11/27, Mon):
Problems ;
Selected Solutions ;
Rough Schedule
Here's an approximate weekbyweek schedule:
Week 1: Divisibility and prime numbers
Week 2: Greatest common divisor and Euclid's algorithm, Fundamental
theorem of arithmetic (unique factorization)
Week 3: Irrationality, Linear Diophantine equations, Pythagorean triples
Week 4: Fermat's infinite descent, Midterm I, Multiplicative functions
Week 5: Introduction to Congruences: basic properties, linear congruence
equations
Week 6: Chinese remainder theorem, Fermat's little theorem, Wilson's
theorem
Week 7: Reduced residue system and Euler's theorem, Midterm II
Week 8: Orders and Primitive roots
Week 910: Legendre symbols and Quadratic reciprocity, Midterm III
Grades
Grades will be based on the following percentages.
Homework 
20% 
Midterms 
30% 
Final 
50% 
