Mathematics 110A-2 - Algebra - Winter 2014 - UCLA

Time: 12 MWF for lectures and 12 Th for discussion.
Place: Lectures: MS 5137. Discussion: MS 5137.

Instructor: Burt Totaro.
E-mail: totaro@math.ucla.edu.

Course webpage: www.math.ucla.edu/~totaro/110a.2.14w/index.html

Office hours: 2-3 MW and 2:15-3 F in my office, MS 6136, or e-mail me to make an appointment.
TA: Eden Prywes (eprywes@math.ucla.edu).
TA office hours: 3-4 Th in MS 2961.

Book: Hungerford, Abstract Algebra: An Introduction, Cengage Learning, ISBN: 978-1111569624. We will cover chapters 1-6.

Homework 1-9. The homework listed there is due each Friday, starting with the first week (Friday, Jan. 10). Assignments will be returned the next Thursday in discussion. There will be no makeup or late homework accepted, but the lowest two homework grades will be dropped.

Midterm Exams: We will have two midterm exams. The dates are January 31 and February 21. There will be no makeup exams.

Final Exam: The final exam is on Tuesday, March 18, 2014 from 8 AM to 11 AM. You must take the final to pass the class! If you have a documented reason that you are unable to take the final, you will receive an Incomplete.

Grading: Grades will be assigned based on the higher of the following two schemes:
10% homework + 25% first midterm + 25% second midterm + 40% final
10% homework + 35% (best of two midterms) + 55% final

1/20 - Martin Luther King Holiday. No class.
1/31 - First midterm exam.
2/17 - President's Day Holiday. No class.
2/21 - Second midterm exam.
3/18 - Final exam. The final will be cumulative and will take place from 8:00 AM to 11:00 AM on Tuesday, March 18.

Evaluation:

Every exam will include at least one problem taken from the homework, possibly with minor variations.
Part of the homework grading will be based simply on whether you hand in the problems (without copying from someone else). However, at the top of each homework, you may mark a problem you wish to be read carefully. We will read that problem carefully and give you detailed feedback so that you can get better and better at writing solutions.
It is your responsibility to know how to do the problems. Practicing that is the only way to study for the exams.
A grade of 'F' will be assigned to any student who misses the final. Incompletes are reserved for those who have completed all of the work for the class, including both midterms, but who, for a legitimate, documented reason, miss the final.

Course schedule:

Week of Jan. 6: Sections 1.1 to 1.3. Division algorithm, divisibility, primes, unique factorization.
Week of Jan. 13: Sections 2.1 to 2.3. Congruence and congruence classes, modular arithmetic, Z/pZ when p is a prime number.
Week of Jan. 20: Sections 3.1 and 3.2. Definition and examples of rings, basic properties.
Week of Jan. 27: Section 3.3. Homomorphisms and isomorphisms of rings. Review and first midterm.
Week of Feb. 3: Sections 4.1 to 4.3. Polynomials and the division algorithm, divisibility in F[x], irreducibles, and unique factorization.
Week of Feb. 10: Sections 4.4 and 4.5. Polynomial functions, roots and reducibility, irreducibility in Q[x].
Week of Feb. 17: Review, second midterm. Section 5.1: Congruence in F[x] and congruence classes.
Week of Feb. 24: Sections 5.2 and 5.3. Congruence class arithmetic. The structure of F[x]/(p(x)) when p(x) is irreducible.
Weeks of March 3 and March 10: Sections 6.1 and 6.2. Ideals and congruence, quotient rings and homomorphisms.

Miscellanea:

If you wish to request an accommodation due to a disability, please contact the Office for Students with Disabilities as soon as possible at A255 Murphy Hall, (310) 825-1501, (310) 206-6083 (telephone device for the deaf). Website: www.osd.ucla.edu.

Catalogue description: 110A. Algebra. (4) Lecture, three hours; discussion, one hour. Requisite: course 115A. Not open for credit to students with credit for course 117. Ring of integers, integral domains, fields, polynomial domains, unique factorization. P/NP or letter grading.