Introduction to Higher Mathematics
Mathematics 760 – Unit 5: Algebra
Brown University – Spring, 2018
Professor Joseph Silverman

Topic We will study topics from modern abstract algebra, including groups, rings fields, and vector spaces.
Text The text for this unit of Math 760 may be downloaded from:
Introduction to Higher Mathematics: Unit 5: Algebra .
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Web Site Math 750–760 Course Website
Math 750–760 Unit #5 Website
Office Hours Mondays 11:00-11:45am, Thursdays 10:00-10:45am
Office hours start Monday March 5 and end on Thursday April 5
Click here for Information about Office Hours and Other Academic Resources
Course Time TuTh 1:00–2:20pm (J hour)
Course Location Barus & Holley 160
Homework Homework assignments are posted below. It is best if you do the reading before the class where we cover the material.

Schedule, Reading Assignments, HW Assignments
Class Chapter Reading Topic Homework Due Date Optional Challenge Problems
1 Thurs, March 1 1 §§1.1–1.3 Groups # 1.3, 1.4(b), 1.5, 1.7(b,c) Tues, March 6
2 Tues, March 6 1 §§1.4–1.5 Groups # 1.15, 1.19, 1.22 Thurs March 8 1.23
3 Thurs, March 8 2 §§2.1–2.4 Rings # 2.1, 2.2(a), 2.4, 2.12, 2.13(a,b,c) Tues, March 15
Thurs, March 13 No class due to weather
4 Thurs, March 15 2 §§2.5–2.6 Rings # 2.18(a), 2.19, 2.21, 2.25 Tues, March 20
5 Tues, March 20 3 §§3.1–3.3 Vector Spaces # 3.1, 3.3, 3.4, 3.8 Thurs, March 22
6 Thurs, March 22 3 §3.4 Vector Spaces # 3.9, 3.10, 3.12, 3.13 Tues, April 3
Tues, March 27 Brown Spring Break
Thurs, March 29 Brown Spring Break
7 Tues, April 3 4 §§4.1–4.6 Fields # 4.1, 4.3(a,b), 4.4, 4.6(a), 4.7 Thurs, April 5 4.3(c)
8 Thurs, April 5 4 §§4.6–4.7 Fields # 4.12, 4.14, 4.15
+ Additional Problems to be Chosen
Tues, April 10 This last problem set serves
as a takehome unit exam.

Course and Unit Goals: Math 760 is a year-long class that exposes students to six basic areas of mathematics. It is team taught by six members of the faculty. Fall topics include logic, set theory, combinatorics, and analysis. Spring topics include number theory, abstract algebra, and geometry. The class emphasizes rigorous proofs and concrete interesting examples. The specific goals for the Algebra Unit are to learn fundamentals topics from modern abstract algebra, including groups, rings, fields, and vector spaces.

Learning Activities and Time Allocation: Learning activities for this part of the course include class attendance, weekly problem sets, and a unit exam. The time to complete these activities are (1) attending lectures, approximately 3 hours/week; (2) reading material in the book, approximately 2 hours/week; (3) working on the problem sets, approximately 7 hours/week.

Assessment: Course grades will be determined by the quality of problem sets submitted and by grades on the unit 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


  1. Groups
  2. Rings
  3. Vector Spaces
  4. Fields
  5. Further topics as time permits:
    • Finite fields and designs
    • RSA public key cryptography
    • Fundamental theorem of algebra

Go to Professor Silverman's Home Page.