Honors Linear Algebra – Mathematics 0540
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 ***

Text Linear Algebra Done Right, Sheldon Axler, Springer, (3rd edition, corrected printing 2014), ISBN 978-3319110790
We will also cover some of the material on determinants in Chapter 3 of Linear Algebra Done Wrong (LADW) by Sergei Treil.
        You can download LADW by clicking this link.
Time permitting, we will also use material from Additional Topics in Linear Algebra (ATLA).
        You can download ATLA by clicking this link.
Videos The author of Linear Algebra Done Right has recorded 50 videos on the material. Click here to view the videos.
Office Mathematics Department, Kassar House, Room 202
Phone 863-1124
Email jhs@math.brown.edu
Web Site www.math.brown.edu/~jhs/MA0054/MA0054HomePage.html
Office Hours Monday 10:00–10:45 AM and Thursday 3:00–3:45 PM
Course Time TuTh 10:30–11:50 AM (I Hour)
Course Location Barus Holley 141
Recitation/ Homework Sessions Canceled for the rest of the semester
Friday, 1:30–2:30pm, CIT 227. Our TA is Dhruv Bhatia.
Students should plan to attend as often as possible.
I will keep a list of reading and homework assignments on the following web page:
Click here to go to the Math 0540 Homework Page.
*** Assignments and due dates have been modified ***
*** Instructions for submitting homework online will be sent via email before classes resume ***
Math 540 is the honors version of linear algebra. It is a fast-paced theoretically oriented course. We'll be covering lots of interesting material, but you should be prepared to spend a lot of time on this course. There will be challenging problems that require you to work hard, be frustrated, put them aside for a few hours or a days, and then come back to them. If you leave the problem sets until the last day before they're due, you're setting yourself up to do poorly in this class.
      Linear algebra is a very important subject, both for its use in theoretical mathematics and for it applicability in the real world. So the computational side of linear algebra is quite important, but due to time constraints, computations will not be the primary focus of the lectures in this course. Homework sets will consist of two different sorts of problems. Some problems will be theoretical, and you'll learn to construct your own proofs. These will generally build on material that we've covered in class. Other problems will ask you to gain familiarity with computational aspects of linear algebra that we discuss only briefly in class.
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.
  • Homework assignments should be submitted using Gradescope.
  • Relaxed Late/Missing HW Rule: In place of the following strict rule, I will not penalize people if some homework is incomplete or late, although late homework probably won't be graded.
    Late homework will not be accepted under any circumstances. (One or two missing homeworks is unlikely to affect your grade, and it's an imposition on the grader to have to go back and grade late homeworks.)
  • 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.
Math Resource
Center (MRC)
The Math Resource Center (MRC) is a walk-in help center designed for students taking calculus and linear algebra courses at Brown University. The MRC is staffed by 1-2 graduate students and 2-3 undergraduates per night who help students on an individual or small group basis. The MRC is open from 8-10 PM, Monday-Thursday during the academic year except during academic vacations/breaks. It is open during reading period, but closes once final exams start.
MRC Location: Foxboro Auditorium (Monday/Tuesday/Thursday) and MacMillan 115 (Wednesday).

Dates to Remember: There will be two in-class hour exams and a final exam.
There will be one in-class hour exam, one take-home midterm exam, and a take-home final exam.

Hour Exam #1

Thursday, February 20

In class: Chapter 1 & 2
Exam 1 Solutions

Hour Exam #2

Mon Apr 13 – Fri Apr 17
Due at 5:00pm EDT

Take-home exam

Final Exam

Tues May 5 – Weds May 13
Due 5:00pm EDT

Take-home exam
(will include essay questions)

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 540 introduces students to fundamental topics in linear 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 vector spaces and linear transformations. 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

Syllabus (as time allows)

  1. Vector Spaces
  2. Finite-Dimensional Vector Spaces
  3. Linear Maps
  4. Polynomials
  5. Eigenvalues and Eigenvectors
  6. Determinants
  7. Inner-Product Spaces
  8. Operators on Inner-Product Spaces
  9. Jordan Normal Form
  10. Linear Recurrences (if time permits)

Go to Professor Silverman's Home Page.