Math 412 Elementary Number Theory (Fall 2017)



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Tetative Syllabus for Math 412
(subject to change with time)

Week Class Section covered Remarks                     
1 R Aug 31 Introduction to the course; well-ordering principle, divisibility and division theorem 1.1, 1.3, 1.5
2 T Sept 5 GCD, Euclidean Algorithm, and linear Diophantine equations 3.3, 3.4, 3.7 PRIMES is in P
2 R Sept 7 primes numbers and unique factorization and Twin prime conjecture. 3.1, 3.2, 3.5 Erdos-Selberg Dipute
3 T Sept 12 Congruence 4.1
3 R Sept 14 Congruence equations 4.2, 4.3, 4.4
4 T Sept 19 Congruence system and congruence classes 4.1, 4.4
4 R Sept 21 Reduced system of residues and Wilson's Theorem 6.1 (part) and 6.3 (part)
5 T Sept 26 Euler's Theorem and Euler-phi function 6.3, 7.1
5 R Sept 28 Euler phi-function and sum and number of divisors 7.1, 7.2
6 T Oct 3 multiplicative functions and Perfect numbers and Mersenne Primes , (GIMPS) 7.2, 7.3 prime page
6 R Oct 5 Mobius Inversion 7.4
7 T Oct 10 partition 7.5
7 R Oct 12 Applications Cryptography---Caesar Cipher and RSA Journey to Cryptography 8.1 and 8.4
8 T Oct 17 Fall break
8 R Oct 19 order of elements 9.1-9.2
9 T Oct 24 primitive root 9.2
9 R Oct 26 existence of primitive roots, and Discrete Logarithm 9.3-9.4
10 T Oct 31 Quadratic residues and nonresidues 11.1
10 R Nov 2 The Law of quadratic reciprocity 11.1-11.2
11 T Nov 7 the Jacobi Symbol 11.2-11.3
11 R Nov 9 Continued fractions I 12.2-12.3
12 T Nov 14 Continued fraction II 12.3-12.4
12 R Nov 16 Periodic continued fractions and Pell equation 13.4
13 T Nov 21 Pythagorean triples and Fermat's Last Theorem 13.1-13.2
14 R Nov 23 Thanksgiving Day
13 R Nov 28 Sum of squares and congruent numbers 14.1-14.2
14 T Nov 30 Gaussian Integers, GCD Circles and squares...and Primes
15 T Dec 5 Prime factorization, sums of squares 14.2-14.3
15 R Dec 8 Review (of homework problems)
16 W Dec 20 Final exam 9-12