Algebra – Mathematics 1530 (CRN: 16449)
Brown University – Fall, 2019
Professor Joseph Silverman

Text Integrated Introduction to Abstract Algebra (IIAA) Ch. 1–7 — Click to download a copy
Integrated Introduction to Abstract Algebra (IIAA) Ch. 10 — Click to download a copy
by Joseph H. Silverman
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Web Site
Office Hours Monday 1:30–2:30pm and Wednesday 9:30–10:30am
Last day of office hours is Wednesday December 11
Final Exam Review Session: I will run a review and Q&A session on
Tuesday, December 17, 1:00-3:00pm in CIT 165.
Feel free to come for part of all of it.
Course Time MWF 11:00–11:50 AM (D hour)
Course Location Salomon 003
Class Meeting Notes There will be no class or office hours on Monday September 30 and Wednesday October 9 due to Rosh Hashanah and Yom Kippur. Class will meet during reading period. The last regular class meeting is Wednesday, December 11. The final exam is on December 18.
TA Meeting Barus-Holley 168, Tuesdays 4:30–6:30pm
Problem Sets Note: The problem sets are challenging. Don't leave them until the last minute! We will be moving rapidly. In order to learn the material, it is very important to DO THE HOMEWORK WHEN IT IS ASSIGNED.
Late homework will NOT be accepted. There are NO exceptions to this rule.
Homework must be stapled, with your name legibly written at the upper right of the first page. It is due at the start of class.
Homework should generally be done on your own. If you occasionally work with someone else in the class, you must indicate who you worked with. Further, you are not allowed to get help from people not in the class, nor may you search or ask for solutions on the internet. Doing so is a form of plagiarism and will be treated as such. The grader and I reserve the right to do our own internet searches and compare your solutions with those that we find.
Solutions to the homework will be posted on the homework web page after the due date.
Homework will be returned during the TA Meeting on Tuesdays. If you aren't able to pick up your homework from the TA, you can pick it up at my office hours, although it may be a few days before I have it available.
Homework on the Web The homework assignments include reading assignments, due the next class, and written assignments, generally due each Wednesday.
Click here to go to the Math 1530 Web Homework Page.

Dates to Remember: There will be two in-class hour exams and a final exam.

Hour Exam #1

Mon Oct 7

In class — Exam #1 Solutions

Hour Exam #2

Mon Nov 11

In class — Exam # 2 Solutions

Final Exam

Weds Dec 18
Exam Group 16

Barus–Holley 168
Final Exam Solutions

Grading: The course grade will be determined on the following basis:

Problem Sets


Hour Exam 1


Hour Exam 2


Final Exam


Course and Unit Goals: Math 1530 introduces students to fundamental topics in algebra, which is one of the building blocks of modern mathematics. The course has two main goals. The first is to cover key concepts including groups, rings, abstract vector spaces, and fields. The second is to gain proficiency with constructing and writing proofs, which is one of the primary activities of modern mathematics.

Learning Activities and Time Allocation: Learning activities include class attendance, weekly problem sets, two mid-term exams and a final exam. The time to complete these activities are (1) attending lectures, approximately 3 hours/week; (2) reading material in the book, approximately 3 hours/week; (3) working on the problem sets, approximately 7 hours/week; (4) studying for exams, approximately 10 hours/semester.

Assessment: Course grades will be determined by the quality of problem sets submitted and by grades on the two mid-term exams and the final exam.

Expectations of Students: It is expected that students will attend all lectures and participate in class discussion in an appropriate manner. Assignments are due on the listed dates. All students are expected to abide by Brown's academic code, which may found here

Brief Syllabus and Schedule:

Click here for a detailed syllabus and list of homework assignments.

Schedule — Math 1530 — Fall 2019
Dates Class # Topic Material
Weds Sept 4–Fri Sept 6 1–2 Preliminary Topics
Number Theory
Chapter 1*
Section 1.7
Mon Sept 9–Mon Sept 16 3–6 Groups 1 Chapter 2
Weds Sept 18–Weds Oct 2 7–12 Rings 1 Chapter 3
Fri Oct 4–Weds Oct 16 13, 15, 16 Vector Spaces 1 Chapter 4
Mon Oct 7 14 Exam #1
Fri Oct 18 17 Combinatorics
Section 1.8.1
Section 1.6
Mon Oct 21–Mon Oct 28 18–21 Fields 1 Chapter 5
Weds Oct 30–Weds Nov 13 22–26 Groups 2 Chapter 6
Weds Nov 13 28 Groups 2
Equivalence Relations
Chapter 6
Section 1.4.2
Mon Nov 11 27 Exam #2
Fri Nov 15–Mon Nov 25 29–33 Rings 2 Chapter 7
Mon Fri Dec 2–Mon Dec 9 34–37 Fields 2 Chapter 10
Weds Dec 11 38 Review
*Sections 1.1–1.2, Section 1.4 (Set theory: definitions and notation), Section 1.5 (Functions: definitions and notation)
No Class: Mon Sept 30, Rosh Hashanah
Weds Oct 9, Yom Kippur
Mon Oct 14, Brown closed
Weds Nov 27, Class canceled
Fri Nov 29, Brown closed

Go to Professor Silverman's Home Page.