MATH 575 - Introduction to Theory of Numbers I
Fall 2013, Section 001
Instruction Mode: Section 001 is (see other Sections below)
Subject: Mathematics (MATH)
Department: LSA Mathematics
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Details

Credits:
1 - 3
Requirements & Distribution:
BS
Credit Exclusions:
Students with credit for MATH 475 can elect MATH 575 for 1 credit.
Waitlist Capacity:
10
Advisory Prerequisites:
MATH 451 and 420 or permission of instructor.
Other Course Info:
F.
BS:
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
Repeatability:
May not be repeated for credit.
Primary Instructor:

Description

Background and Goals: Many of the results of algebra and analysis were invented to solve problems in number theory. This field has long been admired for its beauty and elegance and recently has turned out to be extremely applicable to coding problems. This course is a survey of the basic techniques and results of elementary number theory. Students should have significant experience in writing proofs at the level of Math 451 and should have a basic understanding of groups, rings, and fields, at least at the level of Math 412 and preferably Math 512. Proofs are emphasized, but they are often pleasantly short. Content: Standard topics which are usually covered include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Diophantine equations, primitive roots, quadratic reciprocity and quadratic fields, application of these ideas to the solution of classical problems such as Fermat's last `theorem'(proved recently by A. Wiles). Other topics will depend on the instructor and may include continued fractions, p-adic numbers, elliptic curves, Diophantine approximation, fast multiplication and factorization, Public Key Cryptography, and transcendence. This material corresponds to Chapters 1--3 and selected parts of Chapters 4, 5, 7, 8, and 9 of Niven, Zuckerman, and Montgomery. Alternatives: Math 475 (Elementary Number Theory) is a non-honors version of Math 575 which puts much more emphasis on computation and less on proof. Only the standard topics above are covered, the pace is slower, and the exercises are easier. Subsequent Courses: All of the advanced number theory courses Math 675, 676, 677, 678, and 679 presuppose the material of Math 575. Each of these is devoted to a special subarea of number theory.

Schedule

MATH 575 - Introduction to Theory of Numbers I
Schedule Listing
001 (LEC)
 In Person
24809
Open
6
 
-
MWF 10:00AM - 11:00AM

Textbooks/Other Materials

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Syllabi

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