Dr. Z's Introduction to Number Theory Handouts

These are the handouts I gave out when I taught "Introduction to Number Theory", during the Fall 2013 semester.

• Lecture 1: Natural Numbers

• Lecture 2: Incomplete and Complete Mathematical Induction

• Lecture 3: Fibonacci numbers

• Lecture 4: Representation of integers; Addition and Multiplication

• Lecture 5: Prime Numbers, the sieve of Eratosthenes

• Lecture 6: The Fundamental Theorem of Arithmetic

• Lecture 7: The Greatest Common Divisor

• Lecture 8: The Euclidean Algorithm

• Lecture 9: Modular Arithmetics

• Lecture 10: Linear Congruences

• Lecture 11: The Chinese Remainder Theorem

• Lecture 12: Divisibility Rules and Perpetual Calendar

• Lecture 13: Wilson's Theorem and Fermat's little theorem

• Lecture 14: Pseudoprimes and Probablistic Primality Tests

• Lecture 15: Euler's Totient Function

• Lecture 16: Euler's Theorem and The RSA Encrypton

• Lecture 17: The Number and Sum of Divisors

• Lecture 18: Perfect Numbers and Mersenne Primes

• Lecture 19: The Mobius Function and the Mobius Inversion Formula

• Lecture 20: Quadratic residues and the law of Quadratic Reciprocity

• Lecture 21: Integer Partitions I

• Lecture 22: Integer Partitions II

• Lecture 23: Integer Partitions III

• Lecture 24: Continuted Fractions

Exams

• Exam 1   Full Solutions to Exam 1.

• Exam 2  Full Solutions to Exam 2 (by Josefina Mansour)

• Final Exam  

Attendance Quizzes with Solutions

See this directory

Real Quizzes with Solutions

See this directory