MA 55300, Fall 2011

Course Info.

• 2011 final + solutions
• 2009 final exam
• 2007 final exam
• 2005 final exam
• Course Introduction
• Dummit and Foote--errata

Resources

• Splitting field of X^n-a
• Fundamental Theorem of Galois theory
• On separability
• Introduction to Euclid
  • From "The four pillars of Geometry," by John Stillwell (Springer 2005)
• Straightedge and compass constructibility
  • Constructibility axioms
• Sums of two squares
• x^3 + y^3 + z^3 = 0
• Lemmermeyer: Euclidean algorithm in number fields
• GAP-a group theory calculator
• Isomorphism of semi-direct products
• Groups of order p^2q

Assignments

• HW12: due Wed. Dec. 7
• HW11: due Fri. Dec. 2
• HW10: due Wed. Nov. 16
• HW9: due Wed. Nov. 9
• HW8: due Wed. Nov. 2
  • HW8 solutions
• HW7: due Wed. Oct. 26
• HW6: due Wed. Oct. 19
• HW5: due Wed. Sept. 28
• HW4: due Wed. Sept. 21
  • Solution for HW4, no. 3
• HW3: due Wed. Sept. 14
• HW2: due Wed. Sept 7
• HW1: due Wed. Aug. 31

Course Description

Credit Hours: 3.00. Group theory: Sylow theorems, Jordan Hlder theorem, solvable groups. Ring theory: unique factorization in polynomial rings and principal ideal domains. Field theory: ruler and compass constructions, roots of unity, finite fields, Galois theory, solvability of equations by radicals. Typically offered Fall.

Instructor Info.

Section	Room	Time		Instructor	Office
MA 55300 001	MATH 211	11:30am	MWF	Lipman, Joseph	MATH 750

Course Materials

There are no materials for this course.

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