Math 312: Introduction to Number Theory
UBC, Winter 2016 Term 1: Sep 06 to Dec 02
- NEW: Practice midterms with solutions are available.
- NEW: The 2nd midterm covers the topics up to the lecture on Mon 24th Oct (inclusive).
This corresponds to topics up to section 7.3 of the textbook.
- NEW: Lecture notes relevant for the second midterm here and here.
- NEW: Office hours on Friday Oct 28th and Tuesday 1st November are cancelled.
- Solutions to Problem Set 4 are available.
- Lecture notes from week 7 available here.
- Problem Set 4 is available.
- Solutions to Problem Set 3 are available.
- Lecture notes from week 6 available here.
- Problem Set 3 is available.
- Lecture notes from week 5 available here.
- Solutions to the 1st midterm available.
- Lecture notes from week 4 available here.
- Practice midterms with solutions are available.
- The 1st midterm covers the topics up to the lecture on Mon 26th Sep (inclusive).
This corresponds to topics up to section 4.1 and part of 4.2 of the textbook.
- Lecture notes relevant for the first midterm here.
- Lecture notes from week 3 available here.
- Solutions to Problem Set 2 are available.
- Problem Set 2 is available.
- Lecture notes from week 2 available here.
- Solutions to Problem Set 1 are available.
- Extra sessions for office hours start next week (see details below).
- Problem Set 1 is available.
- Lecture notes from week 1 available here.
- The first class is on Wednesday 7th of September, room 460 LSK, 11:00-12:00.
Instructor: Nuno Freitas
Office: Mathematics Building, room 209
Office hours: Mon Wed 12:30-14:00, room 300B LSK building
e-mail: (My first name)@math.ubc.ca
TA: Adela Gherga
Office hours: Tue 9:30-11:00 and Fri 15:30-17:00, room 300B LSK building
Lecture room: Leonard S. Klinck building, room 460
Lecture time: Mon Wed Fri: 11:00 AM to 12:00 PM
Textbook: K. Rosen, Elementary Number Theory, 6th edition.
This is a first course in number theory, aimed at students who have some (but not necessarily much) experience with reading and writing proofs. Specifically, it will be assumed that students are familiar with basic techniques of mathematical proof and reasoning such as induction and proof by contradiction.
We will introduce basic concepts of number theory, such as prime numbers, factorization, and congruences, as well as some of their applications, particularly to cryptography.
You can find a detailed syllabus here.
You can have an idea of what was done in the past by looking into the following websites:
- Math 312 during Summer 2016 can be found here.
- Math 312 during Fall 2015 can be found here.
Grading Scheme: There will be 3 midterms from which the least score will be automatically discarded.
The two top scores in the midterms will count for 20% + 20% = 40% of the final grade.
The final exam will correspond to the remaining 60% of the final grade.
Homework: Lists of suggested problems from the textbook
will be made available regularly. 20% of each midterm and final exam will
constitute of listed problems.
Exams: All exams will be closed-book, closed-note, no calculators. You are required to
be present at all examinations. Non-attendance will result in a mark of zero
being recorded. No make up midterms will be given.
Midterm: All the midterms will take place during class. Probable dates are
- 1st midterm: 30th of September
- 2nd midterm: 28th of October
- 3rd midterm: 18th of November.
Homework problems and other things you should do
- Review sections 1.1, 1.2, 1.3, 1.4 and Appendix A of the Textbook.
- Solve as much exercises from the book as you can. There is no better way of learning the material.
- Discuss the material and exercises with your colleagues, but make sure you are
able to write down the details in your own words. You will have to do it during the midterms and final.
- When writing your answers justify every step.
In particular, always mention which theorems your are using, even when it is obvious or a repetition.
There is no such thing as too much detail.
- PROBLEM SET 1:
Section 1.3: 4, 14, 22, 24
Section 1.5: 26, 36
Section 2.1: 12, 13, 17
Section 3.1: 6, 8
Section 3.3: 6, 10, 12, 24
Section 3.4: 2a, 2b, 2c, 6a, 6b
Section 3.5: 10, 30, 34, 56
Section 3.7: 2, 6
- Solutions to Problem Set 1 here.
- PROBLEM SET 2:
Section 4.1: 4, 30, 36
Section 4.2: 2a, 2b, 2c, 2d, 6, 8, 10
Section 4.3: 2, 4a, 4b, 4c, 22
Section 5.1: 2, 4, 22
Section 5.5: 12, 13
- Solutions to Problem Set 2 here.
- Practicing with previous midterms and exams is very helpful.
A past midterm with solutions is here
Another past midterm with solutions is here
- The 1st midterm with solutions is here: Version A, Version B.
- PROBLEM SET 3:
Section 6.1: 4, 10, 12, 24, 26
Section 6.2: 2, 8, 12, 18
Section 6.3: 6, 8, 10, 14
Section 7.1: 4, 8, 18
- Solutions to Problem Set 3 here.
- PROBLEM SET 4:
Section 7.2: 4, 10, 12
Section 7.3: 14
- Solutions to Problem Set 4 here.
- Practice with the previous midterm available above.
- Another past midterm with solutions is here