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Theory of Numbers >> Content Detail



Lecture Notes



Lecture Notes

The lecture notes are courtesy of one of the students, Anna Marie Bohmann. Used with permission.

SES #TOPICS
1Divisibility (PDF)
2Greatest Common Divisor (PDF)
3More on Greatest Common Divisor and Division Algorithm (PDF)
4Prime Factorization and Binomial (PDF)
5Binomial Theorem and Congruences (PDF)
6Congruences (PDF)
7Residue Systems, Fermat's Little Theorem, Euler's Theorem, and Wilson's Theorem (PDF)
8Review for Midterm
9Midterm 1
10More on Factorization (PDF)
11Chinese Remainder Theorem (PDF)
12RSA Cryptography (PDF)
13Hensel's Lemma (PDF)
14Solving Equations Modulo Primes (PDF)
15More on Solving Equations Modulo Primes (PDF)
16Quadratic Residue Symbol (PDF)
17More on Quadratic Residues (PDF)
18More on Quadratic Residues (cont.) (PDF)
19Quadratic Reciprocity (PDF)
20More on Quadratic Reciprocity (PDF)
21Continued Fractions (PDF)
22More on Continued Fractions (PDF)
23More on Continued Fractions (cont.) (PDF)
24More on Continued Fractions (cont.) (PDF)
25More on Continued Fractions (cont.) (PDF)
26More on Continued Fractions (cont.) (PDF)
27More on Continued Fractions (cont.) and Solving Equations (PDF)
28Midterm 2
29Curves in Projective Space (PDF)
30More on Curves in Projective Space and Statement of Falting's Theorem (Mordell Conjecture) (PDF)
31Singular Points and Smoothness (PDF)
32Elliptic Curves (PDF)
33More on Elliptic Curves (PDF)
34Abelian Groops, Torsion Points and Finite Generation of Group of Torsion Points (PDF)
35Mazur's Theorem and Calculating the Torsion Subgroup (PDF)
36More Calculations (PDF)
37Advanced Topics (PDF)



 








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