- 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*

Assessment exam (updated May 31);

Questionnaire (due in class on Thu, Jan 21st)

- 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

- 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 from Fall 2010 Solutions
- First midterm from Spring 2015 Solutions
- Solutions to the first midterm from Spring 2016
- Solutions to the second midterm from Spring 2016

- 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

- 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.