Number Theory

This field studies complex numbers that are roots of non-zero polynomials with rational coefficients. Learners will understand the algebraic properties of these numbers, analyze field extensions, and distinguish them from transcendental numbers.

This branch of mathematics uses methods from mathematical analysis to solve problems about integers. Learners will understand the distribution of prime numbers, the properties of the Riemann zeta function, and how to apply complex analysis to number theory.

This area of number theory studies the equivalence of integers relative to a given modulus. Learners will understand how to solve linear and quadratic congruences, apply modular arithmetic, and use key results like Fermat's Little Theorem.

This field focuses on techniques for securing communication and data against unauthorized access. Learners will understand symmetric and asymmetric encryption, cryptographic hash functions, digital signatures, and how these concepts secure modern digital infrastructure.

This subject focuses on polynomial equations for which only integer or rational solutions are sought. Learners will understand classical methods for finding solutions, analyze solvability, and explore the connections between geometry and number theory.

This fundamental concept of arithmetic examines how integers divide one another without leaving a remainder. Learners will understand prime factorization, the Euclidean algorithm, greatest common divisors, and the foundational properties of the integers.

This system of arithmetic deals with integers that wrap around a fixed value called a modulus. Learners will understand how to perform modular operations, solve systems of congruences, and apply these concepts to cryptography and computer science.

This area of algebraic number theory studies finite-dimensional field extensions of the rational numbers. Learners will understand the ring of integers, prime ideal factorization, class groups, and how to generalize arithmetic concepts beyond standard integers.

Number theory is the study of the properties and relationships of integers. You will understand concepts like prime factorization, divisibility, modular arithmetic, and cryptography, enabling you to solve complex mathematical puzzles and secure digital communications.

Prime numbers are integers greater than one divisible only by themselves and one. Learners will understand their distribution, factorization properties, and fundamental role in number theory and modern encryption algorithms.

Quadratic residues are integers that have a square root modulo a given prime. Learners will understand Euler's criterion, quadratic reciprocity, and how to solve quadratic congruences in number theory.