arminstraub.com - Fall 2020: Intro to Number Theory (Math 311)

Overview

Instructor	Dr. Armin Straub MSPB 313 straub@southalabama.edu (251) 460-7262 (please use e-mail whenever possible)
Office hours	TR, 11am-1:15pm; TR 5:45-6:30pm Held virtually using Zoom; please make an appointment by email at least 2 hours in advance.
Class schedule	TR, 4:30-5:45pm, in MSPB 345 (Section 502) Due to COVID restrictions, you may only attend those meetings assigned to the cohort you signed up for.
Midterm exams	The tentative dates for our two midterm exams are: Thursday, October 1 (postponed from 9/29 due to Sally) Tuesday, November 3
Final exam	Thursday, November 19
Online grades	Homework Scores Exams: USAonline (Canvas)
Syllabus	syllabus.pdf

Assignments and course material

In order to be able to view the lecture recordings, you need to be logged into USAonline (Canvas). If you are still running into access issues, then please view the recordings through Panopto Video in our course page on Canvas.

	Dates	Assignments and course material
#1	08/18 08/20 08/25	Assignments: Homework Set 1 (due 9/1) Lecture notes: lectures-01-03.pdf Lecture recordings: lecture01-euclidean-algorithm.mp4 (corresponding PDF) lecture02-1-extended-euclidean-algorithm.mp4 (corresponding PDF) lecture02-2-extended-euclidean-algorithm.mp4 (corresponding PDF) lecture03-1-prime-factorizations.mp4 (corresponding PDF) lecture03-2-prime-number-theorem.mp4 (corresponding PDF) Class schedule: 08/18: online using pre-recorded lectures 08/20: in-person, Cohort R 08/25: in-person, Cohort T
#2	08/27 09/01 09/03	Assignments: Homework Set 2 (due 9/10) Lecture notes: lectures-04-06.pdf Lecture recordings: lecture04-diophantine-equations.mp4 (corresponding PDF) lecture05-congruences.mp4 (corresponding PDF) lecture06-modular-inverses.mp4 (corresponding PDF) Class schedule: 08/27: online using pre-recorded lectures 09/01: in-person, Cohort T 09/03: in-person, Cohort R
#3	09/08 09/10 09/15 ~~09/17~~	Assignments: Homework Set 3 (due 9/24; extended due to Sally) Lecture notes: lectures-07-09.pdf Lecture recordings: lecture07-1-residues-linear-congruences.mp4 (corresponding PDF) lecture07-2-systems-of-congruences.mp4 (corresponding PDF) lecture08-1-little-fermat.mp4 (corresponding PDF) lecture08-2-binary-exponentiation.mp4 (corresponding PDF) lecture09-different-bases.mp4 (corresponding PDF) Class schedule: 09/08: online using pre-recorded lectures 09/10: in-person, Cohort R 09/15: ~~in-person, Cohort T~~ (moved to 09/22 because of Sally)
#4	09/22 09/24 09/29	Assignments: Homework Set 4 (due 10/1) Lecture notes: lectures-10-12.pdf Lecture recordings: lecture10-1-chinese-remainder-theorem.mp4 (corresponding PDF) lecture10-2-quadratic-equations.mp4 (corresponding PDF) lecture11-1-quadratic-equations-part2.mp4 (corresponding PDF) lecture11-2-phi-function.mp4 (corresponding PDF) Class schedule: 09/22: in-person, Cohort T 09/24: in-person, Cohort T+R 09/29: online via Zoom zoom-notes-09-29.pdf
	10/01	Midterm Exam #1 practice material: midterm01-practice.pdf midterm01-practice-solution.pdf Midterm Exam #1 format: Not the real Midterm #1
#5	10/06 10/08	Assignments: Homework Set 5 (due 10/15) Lecture notes: lectures-13-14.pdf Lecture recordings: lecture13-1-eulers-theorem.mp4 (corresponding PDF) lecture13-2-multiplicative-order.mp4 (corresponding PDF) lecture14-primitive-roots.mp4 (corresponding PDF) Class schedule: 10/06: in-person, Cohort T+R 10/08: online using pre-recorded lectures
#6	10/13 10/15 10/20	Assignments: Homework Set 6 (due 10/27) Lecture notes: lectures-15-17.pdf Lecture recordings: lecture15-primitive-roots-part2.mp4 (corresponding PDF) lecture16-crt-and-powers.mp4 (corresponding PDF) lecture17-1-fermat-primality-test.mp4 (corresponding PDF) lecture17-2-absolute-pseudoprimes.mp4 (corresponding PDF) Class schedule: 10/13: in-person, Cohort T+R 10/15: online using pre-recorded lectures 10/20: in-person, Cohort T+R
#7	10/22 10/27 10/29	Assignments: Homework Set 7 (due 11/3) Lecture notes: lectures-18-19.pdf Lecture recordings: lecture18-1-quadratic-residues.mp4 (corresponding PDF) lecture18-2-wilsons-theorem.mp4 (corresponding PDF) lecture19-eulers-criterion.mp4 (corresponding PDF) Class schedule: 10/22: online using pre-recorded lectures 10/27: in-person, Cohort T+R 10/29: online via Zoom
	11/03	Midterm Exam #2 practice material: midterm02-practice.pdf midterm02-practice-solution.pdf
#8	11/05 11/10 11/12 11/17	Assignments: Homework Set 8 (due 11/19) Lecture notes: lectures-20-23.pdf Lecture recordings: lecture20-continued-fractions.mp4 (corresponding PDF) lecture21-1-real-numbers-as-cfs.mp4 (corresponding PDF) lecture21-2-more-on-cfs.mp4 (corresponding PDF) Class schedule: 11/05: online using pre-recorded lectures 11/10: in-person, Cohort T+R 11/12: online using pre-recorded lectures 11/17: online via Zoom zoom-notes-11-17.pdf
	11/19	Final Exam practice material: final-practice.pdf final-practice-solution.pdf

About the homework

Homework problems are posted for each unit. Homework is submitted online, and you have an unlimited number of attempts. Only the best score is used for your grade.
Most problems have a random component (which allows you to continue practicing throughout the semester without putting your scores at risk).
Aim to complete the problems well before the posted due date.
A 15% penalty applies if homework is submitted late.
Collect a bonus point for each mathematical typo you find in the lecture notes (that is not yet fixed online), or by reporting mistakes in the homework system. Each bonus point is worth 1% towards a midterm exam.
The homework system is written by myself in the hope that you find it beneficial. Please help make it as useful as possible by letting me know about any issues!

Exams and practice material

The following material will help you prepare for the exams.

Midterm Exam 1:
midterm01-practice.pdf, midterm01-practice-solution.pdf
Midterm Exam 2:
midterm02-practice.pdf, midterm02-practice-solution.pdf
Final Exam:
final-practice.pdf, final-practice-solution.pdf

Sage

For more involved calculations, we will explore the open-source free computer algebra system Sage.

If you just want to run a handful quick computations (without saving your work), you can use the text box below.

A convenient way to use Sage more seriously is https://cocalc.com. This free cloud service does not require you to install anything, and you can access your files and computations from any computer as long as you have internet. To do computations, once you are logged in and inside a project, you will need to create a "Sage notebook" as a new file.