Math 113 - Introduction to Abstract Algebra

InstructorPaul Vojta
LecturesMWF 10–11, Cory 247
Class Number22058
Office883 Evans
E-Mailvojta@math.berkeley.edu
Office HoursMondays 11:30–12:30, Wednesdays 11:10–12; Fridays 11:30–12:30,
excluding university holidays and November 21.
Please email me to set up a time to meet if you cannot make any of these times.
PrerequisitesMath 54 or a course with equivalent linear algebra content
Required Text Fraleigh, A First Course in Abstract Algebra, 7th edition, ISBN: 9780201763904
Catalog DescriptionSets 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.
Syllabus Based on the last time I taught this course, I plan to cover the following sections of the textbook:

0–16, 18–23, 26, 27 (maybe), 29–31, 45, 46, 32, 47 (partial), 34

GradingGrading will be based on:
30%Homework Assigned weeklyDue in class, usually on Wednesdays
15%First midterm Wednesday, 26 September10:00–11:00 am
20%Second midterm Wednesday, 31 October10:00–11:00 am
35%Final exam Monday, December 10 8:00–11:00 am
HomeworkAssigned weekly, generally due on Wednesdays. Assignments are given below. Solutions will be posted on bCourses.
Comments
  • I tend to follow the book rather closely, but try to give interesting exercises and examples.
  • Note the final exam date given above (exam group 1). Do not enroll in this course if you cannot take the exam at that date and time, whether because of a conflict, too many exams on that day, or any other reason. The schedule of final exams is available at https://registrar.berkeley.edu/scheduling/academic-scheduling/final-exam-guide-schedules.

Homework Assignments

General rules on homework assignments are:

Homework assignments are due in class on the days indicated below (handed in on paper). The lowest two homework scores are dropped.

No. Due Section Problems Comments
1 August 29 0 9, 12, 16, 17, 26, 30, 32
1 3, 8, 22, 25, 32, 37
2 September 5 2 3, 6, 10, 22, 33, 34 For #34, don't just repeat the answer from class
3 2, 10, 16a, 27, 33
3 September 12 4 2, 6, 24, 30, 36, 37
5 4, 11, 13, 16, 22, 23, 45, 50
4 September 19 6 2, 6, 10, 18, 22, 34, 46, 48, 53, 56
7 4, 6, 7b, 8, 14, 18 For #7b, note that Figure 7.11(b) is on the top of the page.
5 Friday, September 28 8 2, 8, 12, 18, 32, 42, 48, 49
6 October 3 9 12, 13abce, 24, 29, 35, 39
10 4, 10, 24, 26, 28, 35, 40
11 6, 10
7 October 10 11 16, 22, 39, 50, 51, 54
13 4, 8, 18, 44, 46, 50
14 6, 12, 31, 34, 39, 40
8 October 17 14 35
15 4, 12, 28, 30, 36, 37 For #28, G/H must be nontrivial.
16 11
9 October 24 16 12, 13, 17
18 4, 6, 12, 18, 24, 38, 40, 42
19 10, 14, 23, 28, 29, 30 For #30, there is a typo.
When it says, “Let S=R×Z if R has characteristic 0,...,”
Z should be ℤ (referring to the ring of integers).
10 Friday, November 2 20 2, 6, 8, 12, 14, 27, 29
21 2, 6, 12, 13, 14 In #13, the element a should be nonzero (as well as not being a zero divisor).
11 November 7 22 2, 6, 10, 14, 22, 25, 28
234, 6, 10, 16, 18, 20, 34, 37
12 Monday, November 19
(rescheduled due to class cancellation)
26 4, 12, 14, 20, 21, 22, 28, 32
27 4, 8, 16, 18, 27, 32, 37

Course Handouts

No.DateTitle Download
1August 24 Equivalence relations and partitions pdf dvi
2September 10 On xn pdf dvi

Lecture Slides

Slides from lectures will be scanned and posted here, generally on the same day after the lecture has ended. Here are the slides that have been posted so far:

Fri. Aug. 24 Sections 0–1
Mon. Aug. 27 Sections 1–3
Wed. Aug. 29 Section 3
Fri. Aug. 31 Sections 3–4
Wed. Sept. 5 Section 4
Fri. Sept. 7 Section 5
Mon. Sept. 10 Sections 5–6
Wed. Sept. 12 Section 6
Fri. Sept. 14 Section 6
Mon. Sept. 17 Sections 6–7
Wed. Sept. 19 Section 8
Fri. Sept. 21 Section 9
Mon. Sept. 24 Sections 9–10
Fri. Sept. 28 Sections 10–11
Mon. Oct. 1 Section 11
Wed. Oct. 3 Sections 11 and 13
Fri. Oct. 5 Section 14
Mon. Oct. 8 Section 14
Wed. Oct. 10 Sections 14–15
Fri. Oct. 12 Sections 15–16
Mon. Oct. 15 Sections 16 and 18
Wed. Oct. 17 Sections 18–19
Fri. Oct. 19 Sections 19–20
Mon. Oct. 22 Section 20
Wed. Oct. 24 Sections 20–21
Fri. Oct. 26 Sections 21–22
Mon. Oct. 29 Section 23
Fri. Nov. 2 Section 23
Mon. Nov. 5 Sections 23 and 26
Wed. Nov. 7 Sections 26–27
Fri. Nov. 9 Section 27
Wed. Nov. 14 Sections 27 and 29

Exams (Generally)

Policies for exams are as follows.

The two midterms will be given during the normal class hours (10–11 am), and will be in our normal classroom (Cory 247).

Generally, about a week before each exam, a sample exam will be distributed in class and posted on bCourses. This will usually be an exam from an earlier Math 113 class that I've taught. Sample exams should be used to get a general idea of the likely length of an exam and the general nature of questions to be asked (e.g., the balance between computational and more theoretical questions). However, one should not (for example) note that a sample exam contains questions on material from Sections 1.5, 2.1, 2.7, 3.1, 3.4, etc., and expect to see questions from those sections on the actual exam.

Exams are cumulative, so the second midterm may have questions from material prior to the first midterm. Of course, the final exam will cover the whole course, but will have increased emphasis on the material not covered on the midterms.

Here is a link "How to lose marks on math exams" (by a former GSI Andrew Critch).

The Math Department maintains an archive of old exams (usually without answers). Here is the link for Math 113.

And finally, a word about regrades: Grade calculation errors are welcome for discussion or review. Whether this solution should be worth 4 or 5 points is not.

First Midterm

The first midterm was given on Wednesday, September 26, from 10:10 to 11:00 AM, in our usual classroom. It covered:

A sample midterm was distributed in class on September 19, and is also available on bCourses. Solutions to the sample midterm are also available on bCourses.

Solutions to the midterm itself are also now available on bCourses.

The (very rough) curve for the midterm is:

A55–75
B45–54
C30–44

The median was 46, the mean was 45.3, and the standard deviation was 15.5.

Second Midterm

The second midterm was given on Wednesday, October 31, from 10:10 to 11:00 AM, in our usual classroom. It covered:

A sample midterm was distributed in class on October 24, and is also available on bCourses. Solutions to this sample midterm are also available on bCourses.

Solutions to the midterm itself are also now available on bCourses.

The (very rough) curve for the midterm is:

A75–100
B50–74
C38–49

The median was 55, the mean was 57.4, and the standard deviation was 23.1.


Last updated 16 November 2018