Mathematics

Number Theory and Cryptography

Investigate properties of integers, prime numbers, modular arithmetic, and applications to modern cryptography. Explore the mathematics behind internet security and encryption.

Skill focus

Apply divisibility rules and prime factorization
Use the Euclidean algorithm for GCD
Perform modular arithmetic operations
Understand basic cryptographic principles
Prove number theory theorems

Lesson map

Progress through the sequence or jump to any lesson. Estimated total time: 95 minutes.

Progress: 0/2 (0%)

INTERACTIVECore45 min
Prime Numbers and Divisibility
Discover the building blocks of all integers and their fascinating properties.
Learning objectives
- Identify and generate prime numbers
- Apply divisibility rules
- Factor integers into prime factors
- Understand the fundamental theorem of arithmetic
primesdivisibilityfactorization
INTERACTIVEChallenge50 min
Modular Arithmetic and Applications
Learn the clock arithmetic that powers modern internet security and digital signatures.
Learning objectives
- Perform arithmetic in modular systems
- Apply Fermat's Little Theorem
- Understand the mathematics behind RSA encryption
Prereq: primes-divisibilitymodular arithmeticcryptographysecurity

Overview

Level: Advanced
Guided time: 340 min
Prerequisites: Algebra fundamentalsMathematical reasoning
Keywords: #primes#divisibility#modular arithmetic#GCD#cryptography#RSA#number theory#prime factorization#Euclidean algorithm#Fermat's theorem#Euler's theorem#Chinese remainder theorem#Diophantine equations#congruences#encryption#public key cryptography#prime numbers#greatest common divisor#least common multiple

Lesson map

Progress through the sequence or jump to any lesson. Estimated total time: 95 minutes.

Progress: 0/2 (0%)

INTERACTIVECore45 min
Prime Numbers and Divisibility
Discover the building blocks of all integers and their fascinating properties.
Learning objectives
- Identify and generate prime numbers
- Apply divisibility rules
- Factor integers into prime factors
- Understand the fundamental theorem of arithmetic
primesdivisibilityfactorization
INTERACTIVEChallenge50 min
Modular Arithmetic and Applications
Learn the clock arithmetic that powers modern internet security and digital signatures.
Learning objectives
- Perform arithmetic in modular systems
- Apply Fermat's Little Theorem
- Understand the mathematics behind RSA encryption
Prereq: primes-divisibilitymodular arithmeticcryptographysecurity

Calculus Discovery

Connect limits, derivatives, and integrals with conceptual narratives and guided practice.

Advanced360 mins guided

#limits
#derivatives
#integrals
#rate of change

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Mathematics

Linear Algebra Foundations

Explore vectors, matrices, linear transformations, and their applications in computer graphics and data science. Master the mathematics of multidimensional spaces.

Advanced460 mins guided

#vectors
#matrices
#linear transformations
#eigenvalues

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Overview

Level

Advanced

Guided time

340 min

Prerequisites

Algebra fundamentalsMathematical reasoning

Keywords

#primes#divisibility#modular arithmetic#GCD#cryptography#RSA#number theory#prime factorization#Euclidean algorithm#Fermat's theorem#Euler's theorem#Chinese remainder theorem#Diophantine equations#congruences#encryption#public key cryptography#prime numbers#greatest common divisor#least common multiple

Number Theory and Cryptography

Skill focus

Lesson map

Prime Numbers and Divisibility

Modular Arithmetic and Applications

Related topics

Calculus Discovery

Linear Algebra Foundations

Overview

Number Theory and Cryptography

Skill focus

Lesson map

Prime Numbers and Divisibility

Modular Arithmetic and Applications

Related topics

Calculus Discovery

Linear Algebra Foundations

Overview