Foundational Number Theory

Unlock the fascinating world of integers and their intricate relationships. This course provides a clear and accessible entry point into number theory, a cornerstone of mathematics. By the end of this course, you will possess a robust understanding of core number theory principles, from divisibility and prime numbers to modular arithmetic and Diophantine equations. You will be equipped to apply these concepts to analyze numerical patterns and solve complex problems with confidence. What you'll learn: * Understand fundamental concepts including divisibility, prime factorization, and common divisors. * Master the Euclidean Algorithm and its extended form for finding modular inverses. * Learn the principles of modular arithmetic, congruences, and their practical applications. * Explore key number theoretic functions such as Euler's totient function. * Apply techniques to solve linear Diophantine equations and systems of congruences. * Practice problem-solving using classic theorems like Fermat's Little Theorem and Wilson's Theorem. The course begins with essential definitions and properties of integers, gradually progressing to more complex topics like congruences and number theoretic functions. Each section builds upon previous knowledge, reinforcing understanding through practical examples. This course is designed for absolute beginners with no prior knowledge of number theory, as well as anyone looking to solidify their foundational understanding of the subject. Embark on your journey into the captivating world of numbers today.