Mathematics 113, Fall 1999, section 1. (Under construction; use at your own risk!)

Professor: Richard Borcherds

Office hours: Tuesday, Thursday 11:00-12:30, 927 Evans Hall
Fax number: 642 8204 Secretary: 642 6526 (Faye Yeager)

Our class meets in 70 Evans Hall , TuTh 9:30-11:00, last lecture Dec 2 (no lecture on thanksgiving, Thursday Nov 25). This is the course home page (address www.math.berkeley.edu/~reb/113).

Course Description: Mathematics 113

Introduction to Abstract Algebra. (4) Three hours of lectures per week. Prerequisites: 53 and 54. Sets and relations. The integers, congruences and  the Fundamental Theorem of Arithmetic. Groups and their factor groups. Commutative rings, ideals and quotient fields. The theory of polynomials:  Euclidean algorithm and unique factorizations. The Fundamental Theorem of Algebra. Fields and field extensions.

Textbook:

Abstract Algebra by Herstein. You want the third edition, published by Prentice Hall, 1996. The course will cover chapters 1 to 5 of the textbook, and will also cover part of chapter 6 if there is enough time.

Examinations:

Please bring blue books to the examinations. Almost all the questions in the midterms or finals will be randomly selected homework questions, possibly with some minor changes. So if you understand how to do all the homework questions you will be able to do all the questions on the exams. The second midterm will be on the material taught between the two midterms. The final exam will cover the whole course, though probably more than half the questions will be on the material taught after the second midterm. The midterms and final will be closed book and calculators are not allowed. No make-up exams will be given. If you do not take midterm 1, your grade on midterm 2 will count as 40% of your final grade. If you take midterm 1 but miss midterm 2, your final will count for 60% of your final grade. If you miss both midterms or the final you will fail the course.

Grading:

Homework will account for 20% of the grade, midterm 1 will account for 20% of the grade, midterm 2 will account for 20% of the grade, and the final will account for 40% of the grade. Marks for exams will only be changed if there is a clear error on the part of the marker, such as adding up marks incorrectly or forgetting to mark a question. Marks for incomplete answers will never be increased on request, because this is unfair to students who do not ask for their marks to be increased.

Incompletes:

These will only be given for serious problems, such as medical problems that require a stay in hospital. They will not be given just because a student has fallen too far behind in work.

Homework:

Homework will be assigned every week. There is a list of homework assignments for each class below. The homework assignments for each week are given out on Tuesday that week and are due on 11:00am on Tuesday of the next week. Homework can be given to me in class or placed (at your own risk) in the envelope outside my office door (897). Homework given in late will get no credit. The final homework grade will be computed from the 10 best homeworks you hand in on time, so it does not matter much if you forget one or two. I have tried to make the homework solutions available in HTML. Unfortunately many netscape browsers running under X windows do not have the necessary symbol fonts enabled; see the tex2html home page for details of how to fix this.

  1. Assignment due August 31: Read sections 1.1, 1.2, 1.3, 1.4. Do problems 1.3, 2.11, 2.21, 3.1, 3.9, 3.17, 3.18, 4.9, 4.19, 4.23. Solutions.
  2. Assignment due September 7: Read sections 1.5, 1.6, 1.7. Do problems 1.5.1, 1.5.5, 1.5.8, 1.5.11, 1.5.12, 1.5.14, 1.6.1, 1.6.3, 1.6.7, 1.6.8. Solutions.
  3. Assignment due September 14: Read sections 2.1,2.2,2.3. Do problems 2.1.1, 2.1.9, 2.1.15, 2.1.19, 2.1.20, 2.3.1, 2.3.2, 2.3.3, 2.3.7, 2.3.15. Solutions.
  4. Assignment due September 21: Read section 2.4. Do problems 2.4.1, 2.4.2, 2.4.5, 2.4.6, 2.4.9, 2.4.13, 2.4.19, 2.4.21, 2.4.22, 2.4.23. Solutions.
  5. Assignment due September 28: Read sections 2.5, 2.6. Do problems 2.5.1, 2.5.8, 2.5.10, 2.5.17, 2.5.22, 2.5.24, 2.6.1, 2.6.2, 2.6.6, 2.6.7 Solutions.

    There is no assignment for October 5 because of the midterm on September 30. There are some notes on the midterm.

  6. Assignment due October 12: Read sections 3.1,3.2,3.3. Do problems 3.1.1, 3.1.2, 3.2.2,3.2.3, 3.2.6,3.2.8, 3.2.11, 3.3.1, 3.3.2, 3.3.5. Solutions. Optional extra hard problems: 3.2.17, 3.2.24, 3.3.9, 3.3.10.
  7. Assignment due October 19: Read sections 4.1, 4.2. Do problems 4.1.1, 4.1.6, 4.1.8, 4.1.9, 4.1.11, 4.1.12, 4.1.13, 4.1.16, 4.1.17, 4.1.20 Optional extra hard problems: 4.2.9, 4.2.10. Solutions.
  8. Assignment due October 26: Read sections 4.3, 4.4. Do problems 4.3.1, 4.3.2, 4.3.15, 4.3.18, 4.3.20, 4.3.21, 4.4.1, 4.4.2, 4.4.7, 4.4.8. Optional extra hard problems: 4.3.23, 4.3.25, 4.4.9-13. Solutions.
  9. Assignment due November 2: Read section 4.5. Do problems 4.5.1, 4.5.3, 4.5.5, 4.5.10, 4.5.11, 4.5.13, 4.5.14, 4.5.16, 4.5.18, 4.5.20, Optional extra hard problems: 4.5.25, 4.5.29. Solutions. Solutions in pdf format.

    There is no assignment for November 9 because of the midterm on November 4. There are some notes on the midterm (also in pdf format).

  10. Assignment due November 16: Read sections 4.6, 4.7. Do problems 4.6.2, 4.6.3, 4.6.4, 4.6.5, 4.6.6, 4.6.7, 4.6.12, 4.6.14, 4.7.1, 4.7.2. Optional extra hard problems: 4.5.25, 4.5.29. Solutions. Solutions in pdf format.
  11. Assignment due November 23: Read sections 5.1, 5.2. Do problems 5.1.7, 5.1.8, 5.1.9, 5.1.10, 5.2.1, 5.2.2, 5.2.3, 5.2.6, 5.2.8, 5.2.11. Optional extra hard problems: 5.2.19, 5.2.20. Solutions. Solutions in pdf format.
  12. Last assignment (due November 30 if you want it returned by Dec 2, or due Dec 2 if you are willing to collect it from my office): Read sections 5.3, 5.4, 5.6. Do problems 5.3.1, 5.3.2, 5.3.5, 5.4.1, 5.4.3, 5.4.4, 5.4.5, 5.6.6, 5.6.7, 5.6.8. Solutions. Solutions in pdf format.

    Final (also in pdf format). Solutions. Solutions in pdf format.

Links related to the course: