Instructor  Paul Vojta  

Lectures  MWF 10–11, Cory 247  
Class Number  22058  
Office  883 Evans  
vojta@math.berkeley.edu  
Office Hours  Mondays 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.  
Prerequisites  Math 54 or a course with equivalent linear algebra content  
Required Text  Fraleigh, A First Course in Abstract Algebra, 7th edition, ISBN: 9780201763904  
Catalog Description  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.  
Syllabus 
The course included the following sections of the textbook:
 
Grading  Grading will be based on:
 
Homework  Assigned weekly, generally due on Wednesdays. Assignments are given below. Solutions will be posted on bCourses.  
Comments 

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  
23  4, 6, 10, 16, 18, 20, 34, 37  
12  Monday, November 26 (rescheduled due to class cancellation) 
26  4, 12, 14, 20, 21, 22, 28, 32  
27  4, 8, 16, 18, 27, 32, 37  
13  Friday, November 30  29  2, 10, 12, 14, 16, 26, 32, 34  
30  6, 10, 16, 20, 21, 24, 26  
14  Do not hand in Solutions will be posted Thurs. 6 Dec. 
31  8, 10, 23, 27, 29, 31, 33, 37  
45  2, 4, 10, 22, 25, 26, 30 
No.  Date  Title  Download  

1  August 24  Equivalence relations and partitions  dvi  
2  September 10  On x^{n}  dvi 
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 
Mon. Nov. 26  Section 29 
Wed. Nov. 28  Sections 30–31 
Fri. Nov. 30  Sections 31 and 45 
Mon. Dec. 3  Section 45 
Wed. Dec. 5  Review 
Fri. Dec. 7  Review 
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.
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:
A  55–75 
B  45–54 
C  30–44 
The median was 46, the mean was 45.3, and the standard deviation was 15.5.
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:
A  75–100 
B  50–74 
C  38–49 
The median was 55, the mean was 57.4, and the standard deviation was 23.1.
A sample final exam was distributed on Wednesday, 5 December. The sample final and solutions for it are also available on bCourses.
The final exam was given on Monday, December 10, 8–11 am, in our usual classroom (Cory 247). It covered the whole course (all of the reading, homework problems, and lectures). The list of sections covered is listed in “Syllabus” above (it has been updated now that the lectures have all been given). Approximately 70% of the exam will be on new material not covered on either of the midterms.
The mean and median were both 111, and the standard deviation was 38.9.
The overall homework score has now been posted on bCourses.
Note that the homework score has not been computed on a percentage basis. Homework scores were first adjusted so that the mean on each homework (among those turned in) was the same across homeworks. Then the bottom two were dropped. The resulting scores were added. Scores in roughly the bottom half of the class were brought up, so that homework would not have a disproportionate effect on the final grade. And, finally, the resulting score was adjusted to make its standard deviation proportionate to the standard deviations of the midterms and finals (as if it were a hypothetical exam worth 150 points). I also made it so that the top score was 150.
Last updated 18 December 2018