Introduction to Higher Mathematics
Mathematics 760 – Unit 5: Algebra
Brown University – Spring, 2020
Professor Joseph Silverman
*** Classes and Office Hours are canceled during the week of March 16–20 ***
*** Instructions concerning remote classes, homework submission, etc. will be sent by email ***
*** The homework assignments and due dates on this page have been changed ***
| Topic | We will study topics from modern abstract algebra, including groups, rings, and fields. |
|---|---|
| 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 |
| jhs@math.brown.edu | |
| Web Site |
Math 750–760 Course Website
Math 750–760 Unit #5 Website |
| Office Hours |
Mondays 2:00-2:45pm, Thursdays 9:15-10:00am Office hours start Thursday January 23 and end on Thursday April 2 Click here for Information about Office Hours and Other Academic Resources |
| Course Time | TuTh 1:00–2:20pm (J hour) |
| Course Location | Barus & Holley 163 |
| Homework | Homework assignments are posted below. It is best if you do the reading before the class where we cover the material. |
| Class | Chapter | Reading | Topic | Homework | Due Date | Optional Challenge Problems** | |
|---|---|---|---|---|---|---|---|
| 1 | Thurs, Feb 27 | 1 | §§1.1–1.3 | Groups | #1.1, 1.2, 1.3, 1.4, 1.5 | Tues, March 3 | |
| 2 | Tues, March 3 | 2 | §§2.1–2.2 | Groups | # 2.1, 2.2(b,c,d), 2.4(b,c), 2.7, 2.9, 2.11(a) (Typo in 2.9, "S—5" should be "S5") | Thurs, March 5 | # 2.2(e–i), 2.12 |
| 3 | Thurs, March 5 | 3 | §§3.1–3.2 | Groups | # 3.1, 3.2, 3.4, 3.5, 3.6, 3.7 | Tues, March 10 | |
| 4 | Tues, March 10 | 4 | §§4.1–4.2 | Groups | # 4.2, 4.4, 4.5, 4.6, 4.7 | Thurs, March 12 | |
| 5 | Thurs, March 12 | 5 | §5.1 | Groups | # 5.1*, 5.2, 5.3, 5.4, 5.5 | Tues, March 31 | # 5.6, 5.7 |
| Tues, March 17 | Class canceled | ||||||
| Thurs, March 19 | Class canceled | ||||||
| Tues, March 24 | Brown Spring Break | ||||||
| Thurs, March 26 | Brown Spring Break | ||||||
| 6 | Tues, March 31 | 6 | §§6.1–6.3 | Rings/Fields | # 6.1, 6.2, 6.3(a), 6.5, 6.13, 6.14(a,b,c) | Thurs, Apr 2 | # 6.7, 6.8, 6.9, 6.11, 6.12, 6.15 |
| 7 | Thurs, Apr 2 | 7 | §§7.1–7.2 | Rings/Fields | # 7.1, 7.2, 7.4, 7.5(a,b,c), 7.6 | Tues, Apr 7 | # 7.5(d) |
| 8 | Tues, Apr 7 | 8 | §§8.1–8.2 | Rings/Fields | # 8.1*, 8.2, 8.3, 8.4 | Thurs, April 9 |
Course and Unit Goals: Math 750-760 is a year-long class that exposes students to six basic areas of mathematics. It is team taught by several 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, and fields.
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
Syllabus: