Applied Number Theory: CSC 4110/5110 (Spring 2024, Online Course)

Professor Ellen Gethner

Syllabus

automatically updated on 8 January 2024

[ 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: All office hours are on zoom
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 (Wednesday, 6 March 2024 and Wednesday 1 May 2024 in Student Commons Building 2500A from 12:30 to 1:45pm-- 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

  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 15 and 17 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 22 and 24 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 (almost midnight). The quiz is online and can be found on canvas under Course Summary.
Three 29 and 31 January GCD, Euclidean Algorithm, Fundamental Theorem of Arithmetic Chapter 3.3, 3.4, and 3.5 and class notes Quiz 1 due on Monday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up solutions together (your own work!) and upload one quiz for the entire team. Do not wait until the last minute to upload your quiz: no late quizzes will be accepted under any circumstances!!!!!!! Homework problems are contained in the mathematica notebook
Four 5 and 7 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 12 and 14 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 Monday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up solutions together (your own work!) and upload one quiz for the entire team. Do not wait until the last minute to upload your quiz: no late quizzes will be accepted under any circumstances!!!!!!! Homework problems are in this week's Mathematica notebook
Six 19 and 21 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 Monday 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 solutions together (your own work!) and upload one quiz for the entire team. Do not wait until the last minute to upload your quiz: no late quizzes will be accepted under any circumstances!!!!!!! The next batch of homework problems are in this week's mathematica notebook
Seven 26 and 28 Feb 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 Monday
Eight 4 and 6 March Midterm (Wednesday) plus the Diffie-Hellman Key Exchange, Playing Poker over the phone, Secret Sharing Schemes (Monday) read 8.6 for Wednesday and the midterm exam is on 6th March in Student Commons Building 2500A from 12:30-1:45pm. 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 Wednesday 6 March 12:30-1:45pm in Student Commons Building 2500A. 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 11 and 13 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 18-24 March Spring Break: no classes, no office hours
Ten 25 and 27 March Topic ABET: Quiz 4 problem 3 (RSA computation) TBA Quiz 4 is due on Monday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up solutions together (your own work!) and upload one quiz for the entire team. Do not wait until the last minute to upload your quiz: no late quizzes will be accepted under any circumstances!!!!!!! The next batch of homework problems are in this week's mathematica notebook.
Eleven 1 and 3 April Elliptic Curve Cryptography Class notes
Twelve 8 and 10 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 Monday by 12:30pm on canvas: with your team, open book, open notes, open internet, open friends. You and your team should write up solutions together (your own work!) and upload one quiz for the entire team. Do not wait until the last minute to upload your quiz: no late quizzes will be accepted under any circumstances!!!!!!!
Thirteen 15 and 17 April Lecture slides and videos on canvas
Fourteen 22 and 24 April Grad student video presentations to be uploaded on canvas on Monday. Grad student video presentations Lecture slides and videos on canvas
Fifteen 29 April and 1 May Wednesday FINAL EXAM (undergrads only) Wednesday 1 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 Wednesday 1 May from 12:30-1:45 in Student Commons Building 2500A. Calculators and two sheets (8.5x11 inches, both sides) of notes allowed. Do not hand in the notes.
Sixteen Week of 6 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.