Math 25

Number Theory

Last updated June 17, 2019 14:18:34 EDT

General Information	Syllabus	HW Assignments	Course Resources

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Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures	Sections in Text	Brief Description
9/16	1.1, 1.2	Introduction, Division and Euclidean Algorithms
9/18	1.2, 1.3	Bezout's identity, least common multiples
9/21	1.3, 1.4	LCMs, Linear Diophantine Equations
9/23	2.1, 2.2	Fundamental Theorem of Arithmetic, Distribution of primes
9/25	2.2, 2.4	Distribution of primes, primality testing
9/28	3.1	Modular arithmetic
9/30	3.2	Linear Congruences
10/2	3.3, 3.4	Chinese remainer theorem
10/5	3.4, 4.1	Polynomials and polynomial congruences
10/6 (x-hour)	4.1	The Arithmetic of ${\mathbb Z}_p$
10/7	Midterm I	In class part; all material through 10/2; takehome part due 10/9
10/9	4.2	Pseudoprimes and Carmichael Numbers
10/12	class notes	Strong pseudprimes and Miller's test
10/14	5.1, 8.1	Euler's function
10/16	5.2, class notes	Multiplicative functions; Euler's function, General remarks about cryptography and public key cryptosystems, signatures, authentication
10/19	class notes	Cryptography review, RSA
10/21	6.1, 6.2	$U_n$ and primitive roots
10/23	6.3-6.5	Primitive roots for composite moduli, indices
10/26	6.6, 7.1	Indices, applications of primitive roots, quadratic residues
10/28	Midterm II	In class part; all material through 10/23
10/30	7.1, 7.2	Quadratic residues
11/2	7.3	The Legendre symbol and properties
11/4	7.4	Quadratic reciprocity and Fermat numbers
11/6	7.4, 7.5	Mersenne numbers, Pepins' test, quadratic residues mod $p^e$
11/9	8.2-8.6, class notes	Perfect, abundant, deficient numbers; Mobius inversion
11/11	8.2-8.6	Mobius inversion; Dirichlet convolution
11/13	Chapter 10	Sums of squares
11/16	Chapter 10	Sums of squares
11/20	Final Exam	8-11am

T. R. Shemanske
Last updated June 17, 2019 14:18:34 EDT