Applied Number Theory: CSC 4110/5110 (Spring 2022, Online Course)

Professor Ellen Gethner

Syllabus

automatically updated on 9 January 2022

[ Instructor and Office Hours | Class Time and Room | Textbook and Software | Prerequisites | Objectives | Grades and Policies | Schedule| Academic Deadlines | Mental Health Resources | ]

Instructor

Dr. Ellen Gethner
Email: ellen dot gethner at ucdenver dot edu
Office: Lawrence Street Center LW 817 (not on campus due to pandemic)
Phone: Not on campus due to pandemic for now
Office hours are on zoom until further notice: Make an appointment with the CS office at 303-315-1408 to obtain a time and a zoom link.

Class Time and Room

This is an online self-paced course; all material is on canvas. Relevant details about assignments, quizzes, and tests and their respective due dates are on canvas and on this page.
Click on the Schedule link for all reading material and due dates.

Required Textbook and Software and Laptop

  1. Textbook: Elementary Number Theory, 6th edition by Kenneth Rosen, published by Pearson. Available at the Auraria book store and many other places.
  2. Software Requirement: All class notes and homework assignments are given as Mathematica notebooks; you can get Mathematica free through the University of Colorado HERE. You must VPN into campus before gaining access to the site. To activate the software be sure to use your official university email address when you work through the steps/instructions on the website.

Other Resources (send interesting links and I'll add them)

  1. introductory prime number theory resources
  2. Riemann Hypothesis
  3. A page with free number theory textbook downloads
  4. RSA Challenge (archived)
  5. The Number Theory Web
  6. Number Theory Visualizatons
  7. Gaussian Primes What does the graphic at the top of this page mean?

Prerequisites

CSCI 2411 (Discrete Structures)

Course Objectives

Grades and Policies

Suggested Self Paced Schedule (Due dates are firm)

Lecture Date Topic(s) Comments Reading Assignment, Quiz, and Exam Schedule
One 18 and 20 January Introduction to Number Theory Vocabulary and Definitions; Mathematica demo Chapter 1.1-1.5, 2.1-2.3 and class notes Homework problems are in this week's mathematica notebook
Two 25 and 27 January Vocabulary and Definitions, continued Primes and greatest common divisor Chapter 3.1 and 3.2. Class notes. For Undergraduates Only: Prerequisite Assessment Quiz Due on Monday by 11:59pm. The quiz is online and can be found on canvas under Course Summary.
Three 1 and 3 February GCD, Euclidean Algorithm, Fundamental Theorem of Arithmetic Chapter 3.3, 3.4, and 3.5 and class notes Quiz 1 due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one quiz for the entire team. Homework problems are contained in the mathematica notebook
Four 8 and 10 February Fermat Numbers, Congruences, Chinese Remainder Theorem Homework problems are contained in the mathematica notebook 3.6, 4.1, 4.2, 4.3 and class notes
Five 15 and 17 Feb Wilson's Theorem, Fermat's Little Theorem, Pollard Factoring Method 6.1 and class notes Quiz 2 due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one quiz for the entire team. Homework problems are in this week's mathematica notebook
Six 22 and 24 Feb Pseudoprimes, Euler's Theorem (generalizes Fermat's Little Theorem), Euler's phi function 6.2, 6.3, 7.1 through example 7.4 Quiz 3 is due on Tuesday at 12:30pm and covers material through 6.1; Uplaod on canvas with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one quiz for the entire team. The next batch of homework problems are in this week's mathematica notebook
Seven 1 and 3 March Perfect Numbers, Mersenne Primes, Cryptography Main topic is public key cryptography, particularly RSA 8.1, 8.3 (not covered in class, but useful to know), 8.4 (RSA) and class notes
Eight 8 and 10 March Midterm (Tuesday) plus the Diffie-Hellman Key Exchange, Playing Poker over the phone, Secret Sharing Schemes (Tuesday) read 8.6 for Tuesday and the midterm exam will be due on Tuesday 8th March The midterm will cover material up through 7.3 in the Mathematica notebook "NumberTheoryWeek7_Part1" The Midterm Exam is due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one exam for the entire team.
Nine 15 and 17 March Another Threshold Scheme, Primitive Roots, Discrete Log Problem, and ElGammal Encryption Alternative approaches to these topics are given in this week's Mathematica notebook 9.1-9.4 and class notes
null 20-26 March Spring Break: no classes, no office hours
Ten 29 and 31 March Topic Special Topic TBA Quiz 4 is due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one quiz for the entire team. The next batch of homework problems are in this week's mathematica notebook.
Eleven 5 and 7 April Elliptic Curve Cryptography Class notes
Twelve 12 and 14 April Quadratic reciprocity 9.4 (again), 11.2, 11.2, and class notes Quiz 5 is due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one quiz for the entire team.
Thirteen 19 and 21 April TBA Grad student video presentations Lecture slides and videos on canvas
Fourteen 26 and 28 April TBA Grad student video presentations Lecture slides and videos on canvas
Fifteen 3 and 5 May Tuesday FINAL EXAM Tuesday 3rd May, Exam 2. The Final Exam is comprehensive and will include material from the week 12 Mathematica notebook on quadratic reciprocity. The Final Exam is due on Tuesday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up should write up solutions together (your own work!) and hand in one exam for the entire team.
Sixteen Week of 10 May Monday office hours to be determined.

Mental Health Resources

CU Denver faculty and staff understand the stress and pressure of college life. Students experiencing symptoms of anxiety, depression, substance use, loneliness or other issues affecting their mental well-being, have access to campus support services such as the Student and Community Counseling Center, the Wellness Center and the Office of Case Management. Students also have access to the You@CUDenver on-line well-being platform available 24/7. More information about mental health education and resources can be found at Lynx Central and CU Denver’s Health & Wellness page. Students in imminent crisis can contact Colorado Crisis Services for immediate assistance 24/7 or walk-in to the counseling center during regular business hours.