Math 3354, Section 3. Survey of Algebra.

Survey of Algebra. Math 3354, Section 3. Spring 2016

TuTh 2-3:15 pm, Cabell 323.

Instructor: Mikhail Ershov
Office: Kerchoff 302
e-mail: ershov at virginia dot edu
Office hours: 3 hrs TBA
Course webpage: http://people.virginia.edu/~mve2x/3354_Spring2016

SYLLABUS
Assessment exam (updated May 31);
Questionnaire (due in class on Thu, Jan 21st)

Final info:

The final exam will be given on Fri, May 6, 9am-12:10pm in Monroe 124
Review session will be held on Sun, May 1, 2-4pm in Clark 102
Study guide for the final
Final from Spring 2015 Solutions
Office hours next week: 2-4pm on Monday, 3:30-5:30pm on Wednesday and 4-6pm on Thursday

Second midterm info:

The second midterm will be given on Thu, April 14, in class
Review session will be held on Sun, April 10, 4-6pm in Maury 115
Extra office hours: Mon, April 11, 2:30-4:30pm
Study guide for the second midterm
Second midterm from Spring 2015 Solutions

First midterm info:

Homework assignments:

Homework #1 (due on Friday, January 29th, by 3pm) Solutions
Homework #2 (due on Thursday, February 4th, in class) Solutions
Homework #3 (due on Thursday, February 11th, in class) Solutions
Homework #4 (due on Thursday, February 18th, in class) Solutions
Homework #5 (due on Thursday, February 25th, in class) Solutions
Homework #6 (due on Thursday, March 17th, in class) Solutions
Homework #7 (due on Thursday, March 24th, in class) Solutions
Homework #8 (due on Thursday, March 31st, in class) Solutions
Homework #9 (due on Thursday, April 7th, in class) Solutions
Homework #10 (due on Thursday, April 21st, in class) Solutions
Homework #11 (due on Thursday, April 28th, in class) Solutions
Homework #12 (not due) Solutions

Some notes:

A short note on functions
Even and odd permutations
Lecture 1. Commutative rings and fields.
Lecture 2. More examples of rings.
Lecture 3. Mathematical induction.
Lecture 4. Divisibility and greatest common divisor.
Lecture 5. Primes and unique factorization theorem.
Lecture 6. Congruences.
Lecture 7. Congruences (continued). Chinese Remainder Theorem.
Lecture 8. Equivalence relations. Congruence classes and rings Z_n.
Lecture 9. More on the rings Z_n.
Lecture 10. Definition and examples of groups.
Lecture 11. Properties of group elements.
Lecture 12. Subgroups.
Lecture 13. Orders of elements and cyclic groups.
Lecture 14. Structure theorem of finite cyclic groups. Isomorphisms.
Lecture 15. Isomorphisms (continued).
Lecture 16. Homomorphisms. New: Theorem 16.3 added
Lecture 16A. Classification of finite abelian groups.
Lecture 17. Symmetric groups I. Cayley's theorem.
Lecture 18. Lagrange theorem and its elementary consequences.
Lecture 19. Cosets and proof of Lagrange theorem.
Lecture 20. Normal subgroups.
Lecture 21. Symmetric groups II. Conjugacy classes.
Lecture 22. Quotient Groups.
Lecture 23. Quotient Groups and Homomorphisms.
Lecture 24. Rings.
Lecture 25. Ideals and Quotient Rings.
Lecture 26. Examples of Quotient Rings.