Honors Linear Algebra — Mathematics 540
*** The homework assignments and due dates on this page have been changed ***
*** Instructions concerning remote classes, homework submission, etc. will be sent by email ***
Detailed Syllabus and Homework Assignments
Brown University — Spring, 2020
Professor Joseph Silverman
There may be some additional homework problems that are not in the text. They are labeled X.1, X.2, ... You can find them by following this link, or by clicking on the links provided below for each problem.
Click on the indicated links for solutions to selected homework problems.
For material on determinants, we will be using Chapter 3 of the book
Linear Algebra Done Wrong by Sergei Treil.
(Yes, Professor Treil's title is adapted from Axler's title!)
You can download the book for free by clicking the following link:
Download Linear Algebra Done Wrong.
You can get further information about the book, including errata (if any),
at
Home page of Linear Algebra Done Wrong.
In the reading and homework assignments, material from Treil's book
will be denoted by LADW.
For the last few classes we may use material from
Additional Topics in Linear Algebra
which you should download by clicking the above link.
In the reading and homework assignments, material from these
notes will be denoted ATLA, and exercises
are labeled C.1, C.2, etc.
Return to the Math 540 Home Page
| Class # | Date | Topic | Chapter | Sections | HW Assignment | HW Due | Bonus Problems* |
|---|---|---|---|---|---|---|---|
| 1 | Thurs Jan 23, 2020 | Vector Spaces | 1 | A-B | p 11. 1.A # 2, 3, 10, 11, 15 | Tues Jan 28 | |
| 2 | Tues Jan 28, 2020 | Vector Spaces | 1 | B-C | p 17. 1.B # 1, 2, 4 / p 25. 1.C # 1, 4, 5 | Tues Feb 4 | 1.B.6 |
| 3 | Thurs Jan 30, 2020 | Vector Spaces / Finite Dim'l Vector Spaces | 1 / 2 | C / A | p 25. 1.C # 10, 12, 15, 19 / p. 37. 2.A # 1, 3, 6 | Tues Feb 4 | 1.C.6, 1.C.8, 1.C.13 |
| 4 | Tues Feb 4, 2020 | Finite Dim'l Vector Spaces | 2 | A-B | p. 37. 2.A # 8, 11, 14 / p 43. 2.B # 1, 3, 4 | Tues, Feb 11 | 2.A.16, 2.A.17 |
| 5 | Thurs Feb 6, 2020 | Finite Dim'l Vector Spaces | 2 | B-C | p 43. 2.B # 6, 8 / p.48. 2.C # 1, 3, 6, 12, 14 | Tues, Feb 11 | 2.C.7, 2.C.8, 2.C.13, 2.C.16, 2.C.17 |
| 6 | Tues Feb 11, 2020 | Linear Maps | 3 | A | p. 57 3.A # 1, 3, 4, 11, 14 | Tues, Feb 25 | 3.A.8, 3.A.9, 3.A.12 |
| 7 | Thurs Feb 13, 2020 | Linear Maps | 3 | B | p. 67 3.B # 1, 2, 3, 9, 20, 21, 24 | Tues, Feb 25 | 3.B.29, 3.B.30, 3.B.31 |
| — | Tues Feb 18, 2020 | Brown closed | — | ||||
| 8 | Thurs Feb 20, 2020 | Exam #1 (Chapter 1 & 2) Exam 1 Solutions | — | ||||
| 9 | Tues Feb 25, 2020 | Linear Maps | 3 | C | p. 78 3.C # 3, 4, 9, 12, 13 | Tues Mar 3 | 3.C.6 |
| 10 | Thurs Feb 27, 2020 | Linear Maps | 3 | D | p. 88. 3.D # 1, 4, 7 | Tues Mar 3 | 3.D.16, 3.D.18, 3.D.19 |
| 11 | Tues Mar 3, 2020 | Linear Maps / Polynomials | 3D / 4 | p. 88. 3.D # 10, 20 | Tues Mar 10 | ||
| 12 | Thurs Mar 5, 2020 | Polynomials | 4 | p 129. Ch.4 # 2, 3, 4, 7, 9 | Tues Mar 10 | Ch 4. #5, 6 | |
| 13 | Tues Mar 10, 2020 | Invariant Subspaces and Eigenvalues | 5 | A | p.138. 5.A # 2, 5, 8, 10, 15, 21, 25 | Tues Mar 31 | 5.A.6, 5.A.11, 5.A.12, 5.A.16, 5.A.18, 5.A.19, 5.A.20 |
| 14 | Thurs Mar 12, 2020 | Invariant Subspaces and Eigenvalues | 5 | B | p 153 5.B # 1, 3, 4, 5, 10 | Tues Mar 31 | 5.B.6, 5.B.8 |
| — | Tues Mar 17, 2020 | Brown classes canceled | — | ||||
| — | Thurs Mar 19, 2020 | Brown classes canceled | — | ||||
| — | Tues Mar 24, 2020 | Brown closed | — | ||||
| — | Thurs Mar 26, 2020 | Brown closed | — | ||||
| 15 | Tues Mar 31, 2020 | Invariant Subspaces and Eigenvalues | 5 | B-C | p 153 5.B # 7, 14, 15 ; p 160. 5.C # 1, 3, 6 | Tues Apr 7 | 5.C.4 |
| 16 | Thurs Apr 2, 2020 | Invariant Subspaces and Eigenvalues | 5 | C | p 160. 5.C # 7, 8, 10, 14 | Tues Apr 7 | 5.C.16 |
| 17 | Tues Apr 7, 2020 | Determinants | LADW** 3 | LADW 3.1-3.3 | LADW p 85 # 3.4, 3.5, 3.7 | Tues Apr 14 | |
| 18 | Thurs Apr 9, 2020 | Determinants | LADW** 3 | LADW 3.3-3.5 | LADW p 94 #5.1, 5.3 ; p 96 # 7.1, 7.2., 7.3 | Tues Apr 14 | |
| Distributed Mon Apr 13 Due Fri Apr 17 at 5:00pm EDT | Exam #2 (Take-home) | ||||||
| 19 | Tues Apr 14, 2020 | Inner Product Spaces | 6 | A | p 175 6.A # 4, 5, 6, 8, 10, 12 | Tues Apr 21 | 6.A.11, 6.A.13, 16 |
| 20 | Thurs Apr 16, 2020 | Inner Product Spaces | 6 | A-B | p 175 6.A # 19, 24, 25 ; p 189 6.B # 1, 2, 3 | Tues Apr 21 | 6.A.20, 6.A.21, 6.A.26, 6.A.31; 6.B.4, 6.B.6, 6.B.9, 6.B.12 |
| 21 | Tues Apr 21, 2020 | Inner Product Spaces | 6 | B | p 189 6.B # 5, 8, 11,14, 16 | Tues Apr 28 | |
| 22 | Thurs Apr 23, 2020 | Operators on Inner Prod Spaces | 7 | A-B | p 217 7.A # 1, 3, 4, 5, 14 | Tues Apr 28 | 7.A.7, 7.A.8, 7.A.12, 7.A.16, 7.A.17 |
| 23 | Tues Apr 28, 2020 | Operators on Inner Product Characteristic Polynomials | 7 LADW 1 ATLA*** | 7.B 1.1–1.2 | p 223 7.B # 2, 3, 4, 7, 9 | Tues May 5 | 7.B.12 |
| 24 | Thurs Apr 30, 2020 | Characteristic Polynomials Jordan Normal Form | 1 ATLA*** | 1.3–1.4 | p 13 Section 1 - # C.1, C.2, C.4, C.5 | Tues May 5 | C.3, C.6 |
| 25 | Tues May 5, 2020 | Linear Recurrences | 2 ATLA*** | 1.4 | — | p 24 Section 2 - # C.8, C.9, C.10 | |
| Distributed Tues May 5 Due Weds May 13 at 5:00pm EDT | Take-home Final Exam |
*Note on Bonus Problems: Bonus problems are for those who enjoy working on challenging problems for the sake of working on challenging problems. They will not earn you extra credit, but doing them will earn you the warm satisfaction of doing a hard problem or gaining further mathematical insight.
**LADW: These readings and problems refer to Linear Algebra Done Wrong by Sergei Treil. (Click on the link to download a free copy.)
***ATLA: These readings and problems refer to Additional Topics in Linear Algebra. (Click on the link to download a free copy.)
Return to the Math 540 Home Page