Learn Number Theory Through Computation
Number theory can be taught as a lab course, in the same way that chemistry and physics are customarily taught. Students attend lectures three hours a week, then meet on a fourth day in a computer-equipped lab. Our comprehensive lab manual and specialized software create an immersive learning experience where students develop both theoretical understanding and practical algorithmic skills.
Interactive Learning
Step-by-step algorithm demonstrations guide students through complex number theoretic computations, building understanding at each stage.
Pattern Discovery
Table generation programs help students identify mathematical patterns and develop intuition about number theoretic relationships.
Algorithm Focus
Software limited to algorithms students have studied ensures conceptual understanding comes first before computational power.
Featured Programs
Explore our interactive computational tools designed to illuminate number theoretic concepts through hands-on experimentation.
Carmichael Function
Calculate λ(n), the exponent of the multiplicative group modulo n
Jacobi Symbol
Compute Jacobi symbols step-by-step using quadratic reciprocity
Polynomial Solver
Find all solutions to polynomial congruences modulo n
Chinese Remainder Theorem
Solve systems of linear congruences simultaneously
Primitive Roots
Find a primitive root modulo a prime, that is, a generator of the multiplicative group structure
Class Numbers
Display class numbers, the number of reduced binary quadratic forms with a given discriminant
Featured Labs
Dive deep into number theory with our comprehensive lab exercises that combine theory, computation, and discovery.
GCDs and Euclidean Algorithm
Explore the fundamental Euclidean algorithm through linear combinations, quotient patterns, and the surprising statistics of randomly chosen integers
→RSA Public Key Cryptography
Discover how modern encryption revolutionized cryptography using trap door functions, from the mathematics behind RSA-129 to practical message encryption
→Primality Testing
Master efficient powering algorithms and strong pseudoprime tests to distinguish primes from Carmichael numbers and other composites
→Quadratic Residues
Investigate patterns in quadratic residues using Jacobi symbols, from consecutive residue pairs to Dirichlet's class number formula
→Primitive Roots
Study multiplicative orders and primitive roots, exploring the cyclic structure of reduced residue systems and Artin's conjecture
→Continued Fractions
Uncover the periodic structure of quadratic irrationals and their connection to Pell's equation through convergent approximations
→Why This Approach Works
🎯 Focused Learning
Algorithms are limited to those students have studied, so computers only handle the computational drudgery that students could theoretically do by hand.
👥 Step-by-Step Guidance
Demo programs walk students through algorithm execution one step at a time, building deep understanding of each process.
📈 Pattern Recognition
Table generation programs create numerical datasets where students can identify mathematical patterns and develop insights.
Ready to Transform Your Number Theory Course?
Join educators worldwide who are using computational labs to enhance student understanding