Time/Location: MWF 1:50-2:45, Central Classroom Building 0326
Instructor: Hsian-Hua Tseng
Office: 642 Math Tower
Office Phone: 614-292-5581
E-mail: hhtseng-at-math-dot-ohio-state-dot-edu
Office Hours: MW 12:50-1:50pm, or by appointment.
Textbook: Math 4581 course notes by R. Solomon (available at OSU bookstores, Barnes & Noble, and SBX). Be sure to acquire the latest edition designed for the semester-long course.
Description: The main goal of this course is to discuss various topics in abstract algebra. We will closely follow the textbook.
Grading: Weekly Homework (35%) + Midterm 1 (15%) + Midterm 2 (15%) + Final exam (35%).
Midterm 1: February 11 (Monday), in class. The exam covers everything discussed for Chapters 1, 2, 3, including Homework 1, 2, 3. Solutions.
Midterm 2: March 25 (Monday), in class. The exam covers everything discussed for Chapters 1, 2, 3, 4, 5, 6, 7, including Homework 1, 2, 3, 4, 5, 6, 7. Emphasis will be placed on Chapters 4, 5, 6, 7. Solutions.
Final Exam: April 26 (Friday), 4:00pm-5:45pm. The exam covers everything discussed, including homeworks and past exams. See here for exam scheduling.
Homework Assignments: updated periodically.
Homework 1 (due January 23): Chapter 1 Exercise 3, 4, 5, 6, 8. Solutions.
Homework 2 (due January 30): Chapter 2, Exercise 1, 5, 6, 8(a)(b)(c). Solutions.
Homework 3 (due February 6): Chapter 3, Exercise 1, 2, 4, 5, 6. Solutions.
Homework 4 (due February 13): Chapter 4, Exercise 1, 3. Solutions.
Homework 5 (due February 20): Chapter 4, Exercise 5, 6, 8, 9, 10. Solutions,
Homework 6 (due February 27): Chapter 4, Exercise 12, 13, 14, 18 and Chapter 5 Exercise 5 Solutions.
Homework 7 (due March 8): Chapter 6, Exercise 10, Chapter 7, Exercise 3, 4, 5, 9(a) Solutions.
Homework 8 (due March 20): Chapter 8, Exercise 1, 4, 8(a)(b)(c), 11 Solutions.
Homework 9 (due March 27): Chapter 9, Exercise 1, 2(a) Solutions.
Homework 10 (due April 3): Chapter 9, Exercise 4, 5, 6, Chapter 10, Exercise 2(a), 9 Solutions.
(Problem 4(b): by part (a), p(x) is always reducible if its degree is bigger than 2. So deg p(x) is 2 or 1. If deg p(x) is 1 then it's irreducible, if deg p(x) is 2, then p(x)=a_2x^2+a_1x+a_0. In this case being irreducible means p(x) has no real roots. By the quadratic formula this is the same as saying that a_1^2-4a_2a_1<0. So the final answer is: p(x) is irreducible if and only if either deg p(x)=1 or p(x)=a_2x^2+a_1x+a_0 with a_1^2-4a_2a_1<0. )
Homework 11 (due April 10): Chapter 11, Exercise 2, 3, 6, Chapter 12, Exercise 8(a)(b)(c) Solutions.
Homework 12 (due April 17): Chapter 12, Exercise 8(d)(e)(f) Solutions.
(Problem 8(b): there are 4 more subfields missing in the solutions, they are Q(\sqrt{3}i), Q(\sqrt{2}i), Q(\sqrt{6}), and Q(\sqrt{6}i).)
Homework 13 (due never): Chapter 13, Exercise 2, 3, 4, 6, 12 Solutions.