Grading: 30% homework, 25% midterm, 45% final exam

Homework: Assigned weekly, due each Wednesday in class

Welcome to Math 115A: Number Theory

Number theory is a very classical branch of mathematics, going back as
far as ancient Greece and China. For most of its history, it was viewed
as the sort of mathematics one does purely for fun, with no interest in
or prospect of applications, but since the development of
number-theory-based codes in the 1970's, it has become a crucial component
of modern cryptography. Part of the appeal of number theory is its
elementary nature; while a certain amount of mathematical maturity is
necessary for this course, it will not directly use anything beyond
basic high school algebra, and lacks the abstraction of abstract (or even
linear) algebra.

Lecture notes

I will post notes here to supplement the textbook as seems appropriate.

Axioms for the integers:
This gives a list of axioms for the integers, and some proofs of very
basic properties.

Z/mZ as
a number system: This note introduces the idea of thinking of
congruence classes modulo m as an alternative number system.

For those who are following in the book, here is a summary of which
book sections were involved in which lectures. However, I typically do not
cover everything in a given section, and there may be some material not
included in the book.

10/3: introductory, no specific material.

10/6: Appendix A (see also axioms handout above), parts of
sections 1.3 and 1.5.

10/8: Parts of sections 1.5, 3.1 and 3.5.

10/10: Parts of sections 3.3 and 3.4.

10/13: Parts of sections 3.4 and 3.5.

10/15: Parts of sections 3.5 and 3.1.

10/17: Parts of sections 3.1, 3.6 and 3.7.

10/20: Rest of section 3.7.

10/22: Examples relating to section 3.7, beginning of 4.1.

12/8: Example of Dixon's algorithm, the quadratic sieve.

12/10: More on the quadratic sieve, further developments.

12/12: Review.

Problem sets

Problem sets will be posted here each Wednesday, due the following Wednesday
in class. You are encouraged to collaborate with other students, as
long as you make sure you understand your answers and they are in your own
words. You are not, under any circumstances, allowed to get answers to
problems from any outside sources.

Some points will be awarded for the total number of completed problems, but
only a selection of problems will be fully graded from each problem set.
To minimize
resulting randomness of scores, your lowest problem set score will be
dropped when calculating your grade.

Problem set #1, due 10/15: do the following exercises from the
book: 6 of Appendix A; 20 and 24 of 1.3; 14, 16 and 26 of 1.5; 10 and 14
of 3.3; and 2 of 3.4.

There will be one in-class midterm exam, on Wednesday, November 5. It
will cover all material up through and including the lecture on Wednesday,
October 29, corresponding to the first four homeworks. See above for the
corresponding sections from the textbook.

The final exam is scheduled for Tuesday, December 16, 1:00-3:00 PM, in
Art 217.
It will cover all material from all 9 homework assignments, corresponding
to all lecture material up through the discussion of the Fermat factorization
method on 12/5.

The median on the midterm was 57.5%, and the mean was 54%. The letter grade
ranges corresponding to the raw scores are as follows:
70-100%: A range
60-70%: B range
40-60%: C range
30-40%: D range
0-30%: F

The median on the final was 54.5%, and the mean was 58%. The letter grade
ranges corresponding to the raw scores are as follows:
75-100%: A range
55-75%: B range
40-55%: C range
30-40%: D range
0-30%: F

Students with Disabilities

Any student with a documented disability (e.g. physical, learning,
psychiatric, vision, hearing, etc.) who needs to arrange reasonable
accommodations must contact the Student Disability Center (SDC). Faculty
are authorized to provide only the accommodations requested by the SDC. If
you have any questions, please contact the SDC at (530)752-3184 or
sdc@ucdavis.edu.

Math Cafe

The Math Cafe is organized by the Women's
Resources and Research Center, and offers a place to meet and discuss
math, and has tutoring available even for upper-division classes.

Anonymous Feedback

If you have any feedback on the course, regarding lecture, discussion
section, homework, or any other topic, you can provide it anonymously
with the below form. Because of the anonymity, I cannot reply to
emails from this form, so if you have a question, please just use
regular email.