MA 50300, Fall 2012

Course Info.

• Course Information

Resources

• Space symmetries
  • A5 and icosahedral symmetries
• Simplicity of the alternating group
• 15 puzzle
  • Comments
• Group of units mod prime power
  • Another weird prime
• Straightedge-and-compass constructions
  • Construction of a regular 17-gon
• Euclid's Elements
  • See also Wikipedia article
  • The original Euclidean Algorithm
• Adjoining a root of a polynomial
• Imaginary quadratic UFDs
• Survey of Euclidean algebraic number-rings
  • Euclidean rings of algebraic integers
• Integers as sums of two squares
  • For primes < 100 (Mathematica)
• Notes on Z[<span style="white-space: nowrap;"> &radic;<span style="text-decoration:overline;">&nbsp;-5&nbsp;</span> </span>]
• Notes on ordering (8/23/2012)
• Cardan: cubic equation (1545)
• Foundations of Analysis
  • Set-theoretic construction of numbers
  • Summary of the constructions

Exam Info.

• Midterm exam solutions

Assignments

• HW10, due Fri. Nov. 30
• HW9, due Fri. Nov. 16
• HW8, due Fri. Nov. 9
• HW7, due Wed. Oct. 31
• HW6, due Wed. Oct 24
• HW5, due Mon. Oct. 15
• HW4, due Fri. Sept. 28
• HW3, due Mon. Sept. 17
• HW2, due Fri. Sept. 7
• HW1, due Wed. Aug. 29

Other Information

• Campus Safety Message

Course Description

Credit Hours: 3.00. Group theory: definitions, examples, subgroups, quotient groups, homomorphisms, and isomorphism theorems. Ring theory: definitions, examples, homomorphisms, ideals, quotient rings, fraction fields, polynomial rings, Euclidean domains, and unique factorization domains. Field theory: algebraic field extensions, straightedge and compass constructions. Typically offered Fall.

Instructor Info.

Section	Room	Time		Instructor	Office
MA 50300 001	REC 112	10:30am	MWF	Lipman, Joseph	MATH 750

Course Materials

There are no materials for this course.

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