Math 7210 Algebra Fall 2012

Professor James J. Madden, LSU

Final Study Problems are listed below the schedule.

Date Link to Lecture Notes Notes
Monday, August 20 1. Integers  
Wednesday, August 22 2. Polynomials Supplement
Friday, August 24 3. Permutations  
Monday, August 27 4. Vectors: span and independence  
Wednesday, August 29 5. Bases and matrices Hurricane Isaac
Friday, August 31 6. Linear maps and matrix notation  
Monday, September 3 Labor Day Holiday  
Wednesday, September 5 7. Dual spaces  
Friday, September 7 8. Double dual, quotient spaces  
Monday, September 10 9. Products, sums and UMP  
Wednesday, September 12 10. Determinants  
Friday, September 14 11. Eigenvalues and eigenvectors  
Monday, September 17 Class cancelled (campus security threat)  
Wednesday, September 19 12. Inner product spaces Supplemental project
Friday, September 21 13. Orthonormal bases  
Monday, September 24 14. Adjoints  
Wednesday, September 26 15. Inroduction to groups  
Friday, September 28 16. Quotient groups, homomorphisms, cosets  
Monday, October 1 17. G-sets  
Wednesday, October 3 18. Congugacy classes  
Friday, October 5 19. Products and semidirect products  
Monday, October 8 20. Categories  
Wednesday, October 10 21. Modules & Abelian Groups (Free Objects)  
Friday, October 12 22. Modules & Abelian Groups (Sums)  
Monday, October 15 23. Morphisms of free modules and matrices  
Wednesday, October 17 24. Abelian Groups (Classifying fin. gen. ones)  
Friday, October 19 25. Abelian Groups (Classifying fin. gen. ones)  
Monday, October 22 26. Commutative Rings: Intro.  
Wednesday, October 24 27. Com. Rings: Examples in number theory  
Friday, October 26 28. Com. Rings: Units and zero-divisors  
Monday, October 29 29. Com. Rings: Ideals (prime and maximal)  
Wednesday, October 31 30. Factorization in Domains  
Friday, November 2 31. Factorizationin Polynomial Rings 1  
Monday, November 5 32. Factorization in Polynomial Rings 2 How about A[[x]]?
Wednesday, November 7 33. Cyclic Modules and F[x]-modules  
Friday, November 9 34. Cyclic F[x] modules  
Monday, November 12 35. Analysis of a single linear endomorphism  
Wednesday, November 14 --  
Friday, November 16 36. Analysis . . . endomorphism (cont.)  
Monday, November 19 37. Cayley-Hamilton Theorem and applications  
Wednesday, November 21 Review Problems (Modules)  
Friday, November 23 Thanksgiving Holiday  
Monday, November 26 38. Sylow Theorems  
Wednesday, November 28 Other topics or review problems  
Friday, November 30 Other topics or review problems  

Study Problems (from "June 2, 1999 Algebra Exam Syllabus")