Introduction to Number Theory

Introduction to Number Theory consists of twenty-four lectures taught by Professor Edward B. Burger, exploring the world of numbers. Throughout the lectures, Professor Burger explains all the fundamentals of number theory exploring the many different types of numbers: natural numbers, prime numbers, integers, irrational numbers, algebraic numbers, imaginary numbers, transcendental numbers. And also Professor Burger shows how number theory is applied to modern technology such as credit card encryption.


Lecture 01 - Number Theory and Mathematical Research
Lecture 02 - Natural Numbers and Their Personalities
Lecture 03 - Triangular Numbers and Their Progressions
Lecture 04 - Geometric Progressions, Exponential Growth
Lecture 05 - Recurrence Sequences
Lecture 06 - The Binet Formula and the Towers of Hanoi
Lecture 07 - The Classical Theory of Prime Numbers
Lecture 08 - Euler's Product Formula and Divisibility
Lecture 09 - The Prime Number Theorem and Riemann
Lecture 10 - Division Algorithm and Modular Arithmetic
Lecture 11 - Cryptography and Fermat's Little Theorem
Lecture 12 - The RSA Encryption Scheme
Lecture 13 - Fermat's Method of Ascent
Lecture 14 - Fermat's Last Theorem
Lecture 15 - Factorization and Algebraic Number Theory
Lecture 16 - Pythagorean Triples
Lecture 17 - An Introduction to Algebraic Geometry
Lecture 18 - The Complex Structure of Elliptic Curves
Lecture 19 - The Abundance of Irrational Numbers
Lecture 20 - Transcending the Algebraic Numbers
Lecture 21 - Diophantine Approximation
Lecture 22 - Writing Real Numbers as Continued Fractions
Lecture 23 - Applications Involving Continued Fractions
Lecture 24 - A Journey's End and the Journey Ahead