Lecture Notes

• Lecture 1 (01/23) Math Induction
• Lecture 2 (01/28) Binomial Coefficients
• Lecture 3 (01/30) An explicit form for binomial coefficients
• Lecture 4 (02/02) Divisibility and the greatest common divisor
• Lecture 5 (02/04) Linear equations and the greatest common divisor
• Lecture 6 (02/06) Factorization and the fundamental theorem of arithmetic
• Lecture 7 (02/09) Applciations of the fundamental theorem of arithmetic
• Lecture 8 (02/11) Counting primes
• Lecture 9 (02/13) Congruences
• Lecture 10 (02/18) Linear congruent equations
• Lecture 11 (02/20) Fermat’s Little Theorem: first proof
• Lecture 12 (02/25) Fermat’s Little Theorem: second proof
• Lecture 13 (02/27) Wilson's Theorem
• Lecture 14 (03/02) Euler's formula
• Lecture 15 (03/04) Arithmetic functions I
• Lecture 16 (03/06) Arithmetic functions II
• Lecture 17 (03/09) Arithmetic functions III
• Lecture 18 (03/11) Squares modulo p
• Lecture 19 (03/13) Some preparations
• Lecture 20 (03/16) Is -1 a square modulo p?
• Lecture 21 (03/18) Is 2 a square modulo p?
• Lecture 22 (03/20) Quadratic Reciprocity
• Lecture 23 (03/30) Proof of Quadratic Reciprocity I
• Lecture 24 (04/01) Proof of Quadratic Reciprocity II
• Lecture 25 (04/03) Which primes are sums of two squares?
• Lecture 26 (04/06) Which integers are sums of two squares?
• Lecture 27 (04/08) Pythagorean triples
• Lecture 28 (04/10) Fermat’s Last Theorem for exponent 4
• Lecture 29 (04/13) Rational numbers and irrational numbers
• Lecture 30 (04/15) Complex numbers
• Lecture 31 (04/17) Algebraic integers, algebraic numbers and transcendental numbers
• Lecture 32 (04/20) Dirichlet’s Diophantine Approximation Theorem
• Lecture 33 (04/22) Pell's equation