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