Math 5320 Introduction to Modern Algebra

Instructor: Mladen Bestvina

Office: JWB 210

Web page: http://www.math.utah.edu/~bestvina/5320

Office Hours: before class or by appointment

Textbook: Algebra 2nd edition, by Michael Artin, Pearson-Prentice Hall 2011.

Time: MWF 12:55-13:45

Room: JWB 208

The course is a continuation of 5310 and uses the same textbook. I plan to cover chapters 11-16 of the textbook.

The grades will be based on homework, exams and class participation.

Midterms: Feb 22 and Apr 11.
Final exam: Thursday Apr 28, 1-3pm.

Homework 1, due Jan 20: p.354 1.3, 2.1, 2.2
Handout on algebraic numbers. For "extra credit" work through the exercises.
Homework 2, due Jan 27: p.355 3.4, 4.1, 4.4 (hint on 4.4: kill 2 in both rings)
    On Monday we will discuss problems from sections 3 and 4 not assigned for homework. Come prepared!
Homework 3, due Feb 3. p.356: 5.3,6.4,8.3,8.4
    On Monday we will discuss problems in sections 5-8. Prepare 2 problems not assigned for homework.
Homework 4, due Feb 10. p.379: 2.6, 2.9, 3.1, 3.2, 3.5(a). Hint for 2.9: show it is a Euclidean domain
    We'll skip the problem session this week, but in return homework is harder.
Homework 5, due Feb 17, p.380: 4.3, 4.15(b), 5.1 (c),(d), 5.3,5.7. Also try 5.9 for "extra credit". On 4.15(b): the assumption is that f is monic, has no integer roots, reduces mod p to xⁿ+bx^n-1, and the constant term is not divisible by p².
    On Wed Feb 17 we'll have a problem session. Prepare a problem to present from sections 4 and 5.
No homework this week -- prepare for the midterm on Monday covering Chapters 11 and 12.
Homework 6, due March 2: p.408 #1.1,2.1,2.2,4.3. In addition 3.4(e) is "extra credit". I would really like you to think about it, and I encourage you to do it as a group. It's harder than the others, so it's extra credit. Hint: Cover with circles with radii 1,1/2 and 1/3 of |α|, referring to the notation of Prop 13.3.3. The class number is 2.
Homework 7, due March 9: p.438: 4.1,4.3,4.6.4.7,4.8
    On Monday we will discuss problems in Chapter 13. Prepare 2 problems not assigned for homework.
Homework 8, due March 23: p.439: 7.2, 7.3(c), 7.7, 7.9, p.440: M.1
Homework 9, due March 30: p.472: 1.1,1.3,2.3,3.3,4.2. For 3.3 you might find Theorem 12.4.9 useful.
Homework 10, due April 6: p.473: 5.4,6.1,6.2,7.6,7.7

Second midterm is on April 11, covering Ch 13-15. On Friday Apr 8 we will have a problem session -- prepare 1-2 problems from these chapters.

Homework 11, due Apr 22: p.506: 3.1,3.2,6.2,7.4,8.2