Math 312: Introduction to Number Theory
UBC, Winter 2017 Term 1: Sep 05 to Dec 01
Announcements
- NEW: Solutions to Pactice Set 7 available.
- You can find past final exams and solutions here.
- The final exam takes place on Friday Dec 15th at 8h30, in the room SWNG 222.
- Solutions to Pactice Set 6 available.
- Code for cryptography here and factorization methods here
- Demo done in class by Adela here
- Practice Set 7 available.
- Slides from the lectures about cryptography here.
- Solutions to the third midterm available here.
- Practice Set 6 available.
- Practice midterm available.
- Solutions to Pactice Set 5 available.
- Problem Set 7 available. Due Friday 10th Nov.
- Practice Set 5 available.
- Solutions to Pactice Set 4 available.
- Solutions to the second midterm available here.
- Problem Set 6 available. Due Friday 3rd Nov.
- Practice Set 4 available.
- Practice midterm available.
- Solutions to Pactice Set 3 available.
- Problem Set 5 available. Due Monday 23rd Oct.
- Solutions to the first midterm available here.
- Solutions to Pactice Set 2 available.
- Problem Set 4 available. Due Monday 16th Oct.
- Practice Set 3 available.
- Problem Set 3 available. Due Friday 6th Oct.
- Practice Set 2 is available.
- The 1st midterm covers up to section 12 (inclusive) of the lecture notes.
- Practice midterm available.
- Problem Set A available. Due Friday 17th Nov.
- Solutions to Pactice Set 1 available.
- Pactice Set 1 updated: exercises 42 and 42 in section 3.5 included.
- Problem Set 2 is available. Due Monday 25th Sep.
- The lecture room for Fridays lectures has CHANGED PERMANENTELY to the room BUCH A104.
- Practice Set 1 is available.
- Problem Set 1 is available. Due Friday 15th Sep.
- Office hours start on Monday 11th (inclusive).
- The first class is on Wednesday 6th of September, 11:00-12:00,
room D300 Chemistry bld.
General Information
Instructor: Nuno Freitas
Office: Mathematics Building, room 209
e-mail: (My first name)@math.ubc.ca
Lecture time: Mon Wed Fri 11:00-12:00
Lecture room: Mon, Wed: Chemistry building, room D300. Fri: Buchanan A, room 104.
Office hours: Mon 12:30-14:00 and Fri 9:00-10:30, room 300C LSK building.
TA: Adela Gherga
Office hours: Wed 12:30-14:00, room 300C LSK building.
e-mail: ghergaa@math.ubc.ca
Textbook: K. Rosen, Elementary Number Theory, 6th edition.
Lecture Notes: We will closely follow these notes. These are unrevised and work in progress so use them at your own risk!
Description
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.
Evaluation
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.
Grading homework will count for 10% of the grade. The final exam will correspond
to the remaining 50% of the final grade.
Attention: Independently of your term average, you need to obtain at least 40% on the final exam to pass the course.
Homework: A list of suggested problems
will be made available regularly. You will
be asked to solve and return some of them for grading.
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 midterm will be given.
If you must miss the midterm and you have a documented medical reason,
then you may request to have the weight of the midterm
transferred to the final exam.
Midterm: All the midterms will take place during class. Probable dates are:
1st midterm Friday 29th of Sep, 2nd midterm Friday 27th of Oct
and 3rd midterm Friday 17th of Nov.
Homework problems and other things you should do
- Review sections 1.1, 1.2, 1.3, 1.4 and Appendix A of the Textbook and sections 1 and 2 of the lecture notes.
- Solve as much exercises 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.
- Read the following
tips
on how to write your answers.
- PROBLEM SET 1: Solve the exercises in Sections 2, 3, 5, 6 of the lecture notes. You need to
give them back during class on Friday 15th September.
- Practice carefully also with the following exercises from the book.
- PRACTICE SET 1 (HERE):
Section 1.3: 4, 14, 22, 24
Section 1.5: 26, 36
Section 2.1: 12, 13, 17
Section 3.1: 6, 8, 9
Section 3.3: 6, 10, 12, 24
Section 3.4: 2a, 2b, 2c, 6a, 6b
Section 3.5: 10, 30, 34, 42, 45, 56
Section 3.7: 2, 6
- Solutions to Practice Set 1 here.
- PROBLEM SET 2: Solve the exercises in Sections 4, 7, 8, 9, 10, 11 of the lecture notes.
You need to give them back during class on Monday 25th of September.
- PROBLEM SET A here.
You need to give it back in class of the last midterm, Friday 17th of November.
- A past midterm for practice is here
- PRACTICE SET 2 (HERE):
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
- Solutions to Problem Set 2 here.
- PROBLEM SET 3: Solve the exercises in Sections 12, 13, 14, 15, 16 of the lecture notes.
You need to give them back during class on Friday 6th of October.
- PRACTICE SET 3 (HERE):
Section 6.1: 4, 10, 12, 24
Section 6.2: 2, 8, 12, 18
Section 6.3: 6, 8, 10, 14
Section 7.1: 4, 8, 18
- Solutions to Practice Set 3 here.
- PROBLEM SET 4: Solve the exercises in Sections 17, 18 (only exercise 18.3), 19, 20 in the lecture notes.
You need to give them back during class on Monday 16th of October.
- PROBLEM SET 5: Solve the exercises in Sections 21, 22 in the lecture notes.
You need to give them back during class on Monday 23rd of October.
- Another past midterm for practice is here
- PRACTICE SET 4 (HERE):
Section 7.2: 4, 7, 10, 12, 29
Section 7.3: 1, 8, 14
- Solutions to Practice Set 4 here.
- PROBLEM SET 6: Solve the exercises in Sections 23, 24, 25 in the lecture notes.
You need to give them back during class on Friday 3rd of November.
- PRACTICE SET 5 (HERE):
Section 9.1: 2, 6, 8, 12, 16
Section 9.2: 5, 8, 10, 16
Section 9.4: 2, 3, 4, 5, 8, 9, 18
- Solutions to Practice Set 5 here.
- PROBLEM SET 7: Solve the exercises in Sections 26, 27 in the lecture notes.
You need to give them back during class on Friday 10th of November.
- One more past midterm for practice is here
- PRACTICE SET 6 (HERE):
Section 3.6: 4a, 4b, 4c, 4d
Section 6.1: 26
Section 8.1: 2, 6, 8, 10, 12
Section 8.3: 6
Section 8.4: 2, 8, 14, 16
- Solutions to Practice Set 6 here.
- PRACTICE SET 7 (HERE):
Section 13.1: 2, 3, 4, 6, 13
Section 13.2: 3, 5
- Solutions to Practice Set 7 here.
- You can find past final exams and solutions here.