Number Theory (정수론)

Class Info Class Number: MATH 235-001 Dates: Sep 01 2023 - Dec 20 2023 Room: NS 318 Meeting time for Section 001: Mon 10:30 - 11:50 (2B) Fri 9:00 - 10:20 (1A) Meeting time for Section 002: Mon 15:00 - 16:20 (7A) Fri 15:00 - 16:20 (7A) Prof: Mark Siggers Office Hours Text: Joseph Silverman's "A Friendly Introduction to Number Theory"

Links Class Infomation Classnotes Using Sage

Syllabus

In this gentle introduction to number theory, we look at basic number theoretical ideas as they apply to the integers. We see such topics as pythagorean triples, the fundamental theorem of arithmetic, congruences and Eulers's theorems, multiplicative functions, the chinese remainder theorem, perfect numbers, and quadratic reciprocity. We will cover approximately the first 30 chapters of the text. Here is an approximate schedule.

Week	Chapters	Topics
1	1 - 3	Pythagorean Triples
2	4 - 5	Divisibility and GCD
3	6 - 7	The Fundamental Theorem
4	8 - 10	Congruences
5	11 - 13	Chinese Remainder Theorem, properties of primes
6	14 - 15	Mersenne primes and perfect numbers
7	-	Test 1
8	16 - 18	The RSA Cryptosystem
9	19 - 21	Primality Testing and squares mod p
10	22 - 23	Quadratic Reciprocity
11	24 - 25	Sums of two squares
12	26 - 27	The Euler Phi Function
13	28 - 29	Primitive Roots
14	30	X4 +Y4 =Z4
15	-	Test 2

Homework and Quizzes

There will be homework problems for each class. You need not hand them in, but we will have a quiz chosen from the homework problems most weeks. Many of these problems will also come up on the tests.

Attendence

Quizzes will serve as a record of attendence.

Tests

There will be two tests. The first will be on Oct. 23 or 27, the second on Dec. 15 or 18. We will decide the date of the exams at least 2 weeks before the exam.

Evaluation

Quizzes and Attendence: 10% Tests: 2 x 45%.