Department of Mathematics

Van Vleck Hall, 480 Lincoln Drive, Madison, WI

Math 542: Modern Algebra

Frequency: 

Spring

 
Student Body: 

Math majors and graduate student in related areas

Background and Goals: 

Math 541 and 542 together constitute an introduction to modern algebra at the undergraduate level. Math 542 covers linear algebra at a level deeper than Math 340, and a little field theory. It is essential for students preparing for graduate studies in mathematics and in some related fields.

Alternatives: 

n/a

Subsequent Courses: 

n/a

Course Content: 
  • Modules: submodules, homomorphisms, quotients, simple modules, cyclic modules, free modules, linear transformations
  • Matrices: determinants, elementary matrices, Smith normal form over a PID, characteristic roots
  • Finitely generated modules over a PID
  • Classification of Finite abelian groups
  • Normal forms for matrices: rational canonical form, Jordan canonical form
  • Field extensions, roots of polynomials
credits: 
3. (N-A)
semester: 
Spring
prereqs: 
Math 541

UW-Madison Department of Mathematics
Van Vleck Hall
480 Lincoln Drive
Madison, Wi  53706

(608) 263-3054

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