Applied Number Theory: CSC 4110/5110 (Spring 2023, Online Course)

Professor Ellen Gethner

Syllabus

automatically updated on 3 January 2023

[ 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 at present)
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

With the exception of the midterm and final examinations, which are in person without your team (Tuesday, 7 March 2023 and Tuesday 2 May 2023-- plan your travel accordingly), the rest of this course is completely online. This course is online and 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

ABET Assessment Criteria

1. Analyze a complex computing problem and to apply principles of computing and other relevant disciplines to identify solutions.

Grades and Policies

Suggested Self Paced Schedule (Due dates are firm)

Lecture Date Topic(s) Comments/ABET Reading Assignment, Quiz, and Exam Schedule
One 17 and 19 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 24 and 26 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 31 January and 2 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 upload one quiz for the entire team. Homework problems are contained in the mathematica notebook
Four 7 and 9 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 14 and 16 Feb Wilson's Theorem, Fermat's Little Theorem, Pollard Factoring Method ABET: Problem 2 on quiz 2--last digit of expansion + induction 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 upload one quiz for the entire team. Homework problems are in this week's Mathematica notebook
Six 21 and 23 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; Upload 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 upload one quiz for the entire team. The next batch of homework problems are in this week's mathematica notebook
Seven 28 Feb and 2 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 Grad Student Team Project Proposal Due as an Upload on Canvas on Tuesday
Eight 7 and 9 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 is on 7th March in North classroom 1202 from 3:30-4:45pm. The midterm will cover material up through 7.3 in the Mathematica notebook "NumberTheoryWeek7_Part1" The Midterm Exam is in class, in person, without your team, on Tuesday 7 March 3:30-4:45pm in North Classroom 1202. You may bring two pages of notes (8.5" x 11") on both sides and calculators are allowed. Do not hand in the notes.
Nine 14 and 16 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 19-25 March Spring Break: no classes, no office hours
Ten 28 and 30 March Topic ABET: Quiz 4 problem 3 (RSA computation) 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 upload one quiz for the entire team. The next batch of homework problems are in this week's mathematica notebook.
Eleven 4 and 6 April Elliptic Curve Cryptography Class notes
Twelve 11 and 13 April Quadratic reciprocity ABET: Quiz 5 problem 2 (elliptic curve cryptography) 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 upload one quiz for the entire team.
Thirteen 18 and 20 April Lecture slides and videos on canvas
Fourteen 25 and 27 April Grad student video presentations to be uploaded on canvas on Tuesday. Grad student video presentations Lecture slides and videos on canvas
Fifteen 2 and 4 May Tuesday FINAL EXAM Tuesday 2nd 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 in person without your team on Tuesday 2 May from 3:30-4:45 in North Classroom 1202. Calculators and two sheets (8.5x11 inches, both sides) of notes allowed. Do not hand in the notes.
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.