18.781 Fall 2007 Class Schedule

Homework Assignments

Important Note: This schedule is only tentative, and may be adjusted as necessary during the semester.

NZM=Niven-Zuckerman-Montgomery,
HW=Hardy-Wright (and HW reading is always optional)

September

Monday Tuesday Wednesday Thursday Friday
3 4 5

NZM Sect. 1.1

Introduction, Diophantine Equations

 6 7

NZM Sect. 1.2

Divisibility
10

NZM Sect. 1.3

Primes I

 11 12

HW Ch. 1

Primes II

 13

 14

NZM 2.1

Congruences I

HW 1 due
17

NZM 2.2

Congruences II

 18 19

NZM 2.3

Chinese Remainder Theorem

 20 21

NZM 2.6

Hensel's Lemma

HW 2 due
24

Student Holiday - No Class

 25 26

NZM 2.7

Solving congruences for prime moduli

 27 28

NZM 2.8

Primitive Roots

HW 3 due

October

Monday Tuesday Wednesday Thursday Friday
1

HW Ch. 5

Power Residues

 2 3

NZM 2.10,2.11

Group Theory

 4 5

NZM 3.1,3.2

Quadratic Reciprocity

HW 4 due
8

Columbus Day -- No Class

 9 10

HW Ch. 6

Proof of Quadratic Reciprocity I

 11 12

NZM 3.3

Proof of Quadratic Reciprocity II

HW 5 due
15

Quadratic Binary Forms, Midterm Review

 16 17

MIDTERM I

In-Class		 18 19

Ireland-Rosen, Ch. 7

Finite Fields
22

Ireland-Rosen 8.1-8.2

Characters and Gauss sums

 23 24

Ireland-Rosen 8.3-8.5

Jacobi Sums

 25 26

NZM 9.1-9.4

Intro to Algebraic Number Theory

HW 6 due
29

Ireland-Rosen 9.1-9.3

Cubic Reciprocity

 30 31

Ireland-Rosen 9.4

Proof of Cubic Reciprocity

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