Lecture Notes

• Lecture 1 (09/06) Math Induction
• Lecture 2 (09/09) Binomial coefficients and Pascal's triangle
• Lecture 3 (09/11) An explicit formula for binomial coefficients
• Lecture 4 (09/13) Divisibility and the greatest common divisor
• Lecture 5 (09/16) Linear equations and the greatest common divisor
• Lecture 6 (09/18) Factorization and the fundamental theorem of arithmetic
• Lecture 7 (09/20) Factorization and the fundamental theorem of arithmetic (continued)
• Lecture 8 (09/23) There are infinitely many primes
• Lecture 9 (09/25) Counting primes
• Lecture 10 (09/27) Congruences
• Lecture 11 (09/30) Linear Congruent Equations
• Lecture 12 (10/02) Fermat's Little Theorem: first proof
• Lecture 13 (10/04) Fermat's Little Theorem: second proof
• Lecture 14 (10/07) Wilson's Theorem
• Lecture 15 (10/09) Euler's Formula
• Lecture 16 (10/11) Arithmetic functions I
• Lecture 17 (10/16) Arithmetic functions II
• Lecture 18 (10/18) Arithmetic functions III
• Lecture 19 (10/21) Squares modulo p
• Lecture 20 (10/23) Some Preparations
• Lecture 21 (10/25) Is -1 a square modulo p?
• Lecture 22 (10/28) Is 2 a square modulo p?
• Lecture 23 (10/30) Quadratic Reciprocity
• Lecture 24 (11/01) Proof of Quadratic Reciprocity I
• Lecture 25 (11/04) Proof of Quadratic Reciprocity II
• Lecture 26 (11/06) Which primes are sums of two squares?
• Lecture 27 (11/08) Which integers are sums of two squares?
• Lecture 28 (11/11) Pythagorean Triples
• Lecture 29 (11/13) Fermat’s Last Theorem for exponent 4
• Lecture 30 (11/15) Rational numbers and irrational numbers
• Lecture 31 (11/18) Complex numbers
• Lecture 32 (11/20) Dirichlet’s Diophantine Approximation Theorem
• Lecture 33 (11/22) Pell's equation