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:
Agnes Scott College • Aiken Technical College • Albany College of Pharmacy and Health Science • Alma College • American Graduate University • American Public University • American University • Andrews University • Arizona State University • Armstrong Atlantic State Univeristy • Athens State University • Auburn University • Auburn University MBA Program • Augusta State University • Austin Peay State University • Azusa Pacific University • Babson College • Baruch College • Baylor University • Belmont University • Beloit College • Bentley University • Berklee College of Music • Berry College • Bethany College • Binghamton University • Bloomsburg University • Bluefield State College • Bluegrass Community and Technical College • Borough of Manhattan Community College • Boston Conservatory • Boston University • Bryant University • Buena Vista University • California Lutheran University • California Polytechnic State University, San Luis Obispo • California state University • California State 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Eastern Illinois University • Eastern Kentucky University • Eastern Mennonite University • Eastern Nazarene College • Elon University • Embry Riddle Aeronautical University • Embry Riddle University • Endicott College • Evangel University • Excelsior College • Fairifield University • Fairleigh Dickenson University • Ferris State University • Florida A & M University • Florida Agricultural and Mechanical University • Florida Atlantic University • Florida Institute of Technology • Florida International University • Florida State College, Jacksonville • Florida State University • Fordham University • Fox Valley Technical College • Franklin University • Freed-Hardamen University • Fresno State University • Friends University • Gannon University • George Mason university • George Washington University • George Washington University School of Business • Georgetown University • Georgia Institute of Technology • Georgia State • Georgia State University • Georgia Tech • Gordon College • Governor's State University • Green Mountain College • Griffith University • Grinnell College • Grove City College • Hamline University • Hampshire College • Hampton University • Harvard University, Kennedy School of Government • Harvard University: Kennedy School of Government, Medical Schools • Hillsdale College • Hillsdale University • Hiram College • Hofstra University • Howard University • Huntingdon College • Illinois Institute for Technology • Illinois Institute of Technology • Indiana University • Iowa State University • Jacksonville State University • James Madison University • Jeff State Community College • Johns Hopkins Univerisity • Johns Hopkins University • Kalamazoo College • Kansas State University • Kaplan University • Kennesaw State University • Kentucky State University • Kettering University • Kings College, University of London • La Sierra University • Lebanon Valley College • Lee University • LeTourneau University • Liberty University • Lincoln University of 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Distance Calculus - Student Reviews
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: Jan 12, 2020
Courses Completed: Calculus I, Calculus II, Multivariable Calculus
Curriculum was high quality and allowed student to experiment with concepts which resulted in an enjoyable experience. Assignment Feedback was timely and meaningful.
Posted: Jan 8, 2021
Courses Completed: Probability Theory
A fantastic course! I was able to complete it in about half a year (with a few gaps) alongside other coursework I was completing. There are no deadlines except the one-year mark after registering, so you work at your own rate and schedule.
Probability Theory is required for me to apply to Master's programs in Statistics, so I was glad when I found Distance Calculus. While the course was slightly less difficult than I originally expected, there were parts that definitely slowed me down and made me think. (Also, although calculus is not everywhere in the course, it is everywhere in normal and exponential variables and beyond, so make sure to review derivatives and integrals (single and double)!) I used Mathematica for my software, and it helped speed along calculations and proved to be the perfect stage and tool for this material. I think visual learners will absolutely revel in how the material is presented in this course. (I know I did!) As there is plenty of writing and calculation to do, you have many opportunities to develop and strengthen your voice as a mathematician. The modern format of 80% electronic notebook work and 20% handwritten work is an excellent mixture for studying probability theory and grasping its core ideas. Dr. Curtis is clear in his answers to any questions and concerns you may have and is highly responsive to email and chat, and to responses you leave in your notebooks. He truly wants to help you and to see you succeed, and he is always on your side.
I highly recommend Probability Theory with Distance Calculus!
Probability Theory is required for me to apply to Master's programs in Statistics, so I was glad when I found Distance Calculus. While the course was slightly less difficult than I originally expected, there were parts that definitely slowed me down and made me think. (Also, although calculus is not everywhere in the course, it is everywhere in normal and exponential variables and beyond, so make sure to review derivatives and integrals (single and double)!) I used Mathematica for my software, and it helped speed along calculations and proved to be the perfect stage and tool for this material. I think visual learners will absolutely revel in how the material is presented in this course. (I know I did!) As there is plenty of writing and calculation to do, you have many opportunities to develop and strengthen your voice as a mathematician. The modern format of 80% electronic notebook work and 20% handwritten work is an excellent mixture for studying probability theory and grasping its core ideas. Dr. Curtis is clear in his answers to any questions and concerns you may have and is highly responsive to email and chat, and to responses you leave in your notebooks. He truly wants to help you and to see you succeed, and he is always on your side.
I highly recommend Probability Theory with Distance Calculus!
Email: comojica@ucdavis.edu
Posted: Jun 25, 2026
Courses Completed: Multivariable Calculus
The professor as well as the TAs give great feedback when you need help with problems and the videos are great at explaining concepts. Return time on work is good and the work is not too much to handle.
Transferred Credits To: University of Wisconsin
Posted: Jun 24, 2026
Courses Completed: Linear Algebra
This course gives a perspective on Linear algebra that no traditional course does. I’d say i gained much more intuition for this subject from the DC course than my friends who took traditional courses elsewhere. As a cs major, this version of learning with visualization has helped me a lot in understand ML models. However the course doesn’t have videos for the last 2 chapers so i had to self learn with the mathematica notebooks. Response times are a little slow but since it’s a remote class, i guess it’s justified. Overall amazing course and definitely take this over traditional lin alg classes.
Posted: Jun 24, 2026
Courses Completed: Calculus I
As a full-time business owner completing an Executive MBA, I needed to satisfy a calculus prerequisite without putting my work on hold. Distance Calculus made that possible. The fully self-paced structure let me work early mornings and weekends around an unpredictable schedule, which a fixed-semester classroom course never would have allowed.
The course covered the core business calculus material thoroughly — derivatives, optimization, integration techniques including u-substitution, the Fundamental Theorem of Calculus, improper integrals, and numerical methods. The LiveMath computer algebra environment was central to the experience: it forced me to build each step explicitly rather than just arriving at an answer, which actually deepened my understanding of the mechanics.
Communication through the student portal was responsive when I had questions. For working professionals who need a rigorous, accredited calculus course on a flexible timeline, I'd recommend it.
The course covered the core business calculus material thoroughly — derivatives, optimization, integration techniques including u-substitution, the Fundamental Theorem of Calculus, improper integrals, and numerical methods. The LiveMath computer algebra environment was central to the experience: it forced me to build each step explicitly rather than just arriving at an answer, which actually deepened my understanding of the mechanics.
Communication through the student portal was responsive when I had questions. For working professionals who need a rigorous, accredited calculus course on a flexible timeline, I'd recommend it.
Transferred Credits To: MIT Ebma
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