Number Theory Online Course for Academic Credit
Number Theory is an introduction to one of the oldest and most beautiful branches of mathematics, covering divisibility, prime numbers, congruences, and applications to modern cryptography.
Course
DMAT 283 - Introduction to Number Theory
Credits
4 Semester Credit Hours
Delivery
Fully Online, Asynchronous, Self-Paced
Syllabus
RWU Course Catalog - DMAT 283 • Introduction to Number Theory
Course
DMAT 283
Course Title
Introduction to Number Theory
Transcript Title
Number Theory
Credits
4 Semester Credit Hours
Description
An introductory course in Number Theory, emphasizing computational aspects as well as a historical perspective. Topics include a study of the integers, induction, divisibility, primes, Euclidean Algorithm, Diophantine equations, congruences, Chinese Remainder Theorem, cryptography, primitive roots, quadratic residues, continued fractions, cubic and elliptic curves, Fermat's Last Theorem, and Gaussian Integers.
Prerequisite
Successful completion with grade C or higher in Precalculus or equivalent, or consent of instructor.
E-Textbook
Number Theory with Computer Applications by Kumanduri & Romero
Software
Mathematica and LiveMath
Syllabus PDF
DMAT 283 - Learning Outcomes
- To understand the general topic of Number Theory from first principles and examples
- To understand the historical aspect of Number Theory
- To understand divisibility, primes, and modular arithmetic
- To understand the basic concepts of cryptography and how Number Theory is used
- To understand the basic concepts of quadratic residues
- To understand the basic concepts of continued fractions
- To understand the basic concepts of Diophantine Equations and their approximate solutions
- To understand the basic concepts of Elliptic Curves
- To understand and utilize visualization tools such as computer algebra systems
DMAT 283 - Syllabus of Topics
1. Getting Started
1.1 Email and Chat
1.2 Learning About the Course
1.3 Required Hardware
1.4 Software Fundamentals
2. Divisibility and Primes
2.1 Divisibility
2.2 Primes
2.3 Unique Factorization
2.4 Elementary Factoring Methods
2.5 GCD and LCM
2.6 Linear Diophantine Equations
3. Modular Arithmetic
3.1 Congruences
3.2 Inverses Modulo m and Linear Congruences
3.3 Chinese Remainder Theorem
3.4 Polynomial Congruences
3.5 Magic Squares
4. Fundamental Theorems of Modular Arithmetic
4.1 Fermat Theorem
4.2 Euler Phi Function
4.3 Euler Theorem
4.4 Lagrange Theorem
5. Cryptography
5.1 Classical Cryptosystems
5.2 Public-Key Cryptography
5.3 The RSA Scheme
6. Cryptography
6.1 Classical Cryptosystems
6.2 Public-Key Cryptography
6.3 The RSA Scheme
7. Primality Testing and Factoring
7.1 Pseudoprimes and Carmichael Numbers
7.2 Strong Pseudoprimes and Probabilistic Primality Testing
7.3 Pollard (p-1)-method
8. Primitive Roots
8.1 The Concept of Order
8.2 The Primitive Root Theorem
8.3 The Discrete Logarithm
8.4 Primality Testing
9. Quadratic Congruences
9.1 Quadratic Residues
9.2 Computing Square Roots mod p
10. Continued Fractions
10.1 Introduction
10.2 Convergents
10.3 Infinite Continued Fractions
10.4 Quadratic Irrationals
10.5 Purely Periodic Continued Fractions
10.6 Classical Continued Fraction Expansions
11. Continued Fractions
11.1 Introduction
11.2 Convergents
11.3 Infinite Continued Fractions
11.4 Quadratic Irrationals
11.5 Purely Periodic Continued Fractions
11.6 Classical Continued Fraction Expansions
12. Diophantine Approximations
12.1 Best Approximations
12.2 Intermediate Convergents and Good Approximations
12.3 Algebraic and Transcendental Numbers
13. Diophantine Equations
13.1 Introduction
13.2 Congruence Methods
13.3 Pythagorean Triples
13.4 Sums of Two Squares
13.5 Fermat Last Theorem
14. Elliptic Curves
14.1 Introduction
14.2 Projective Spaces
14.3 The Group Law on Elliptic Curves
14.4 Elliptic Curves Modulo Primes
14.5 Rational Points on Elliptic Curves
Distance Calculus Referenced Colleges & Universities (29 Years - 393+ Institutions)
Distance Calculus students have transferred course credits to these colleges and universities:
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Distance Calculus - Student Reviews
Posted: May 18, 2025
Courses Completed: Probability Theory
A great way to learn probability theory through visualizations, code, and math. Rather than just solving equations through pencil and paper, this course helped me to see how how probability distributions form and behavior through simulations and visuals. I would recommend this course to anyone looking for a way a more interactive way to learn mathematics and at their own pace.
Transferred Credits To: none yet
Posted: Jun 6, 2020
Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory
I loved these courses. So in depth and comprehensive. The mix of software and math curriculum was tremendously helpful to my future studies and career in engineering. I highly recommend these courses if you are bored of textbook courses.
Transferred Credits To: University of Massachusetts, Amherst
Posted: Apr 13, 2020
Courses Completed: Calculus I
I really enjoyed this course, much more than I thought I would. I needed to finish this course very fast before starting my graduate degree program @ Kellogg. I was able to finish in 3 weeks. I liked the video lectures and the homework process. I highly recommend this course.
Transferred Credits To: Kellogg School of Business, Northwestern Univ
Posted: Feb 8, 2026
Courses Completed: Precalculus, Calculus I
The courses were excellent. Very flexible and engaging and the platform offers a lot of upper-level courses. Dr. Curtis is an outstanding professor and very responsive. I would take again.
Transferred Credits To: None yet
Posted: Jan 28, 2026
Courses Completed: Calculus I
After two failed attempts at my university, this course helped me understand Calculus. The live maths tool along with Dr. Curtis were especially helpful, allowing me to visualize concepts and expand my understanding. The explanations were clear, the examples practical, and I could learn at my own pace, which built my confidence. Thank you.
Transferred Credits To: University of Namibia
Posted: Dec 18, 2025
Courses Completed: Differential Equations
Transferred Credits To: Saint Joseph High School
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