Jacob Bernstein






Math 201: Linear Algebra

Course Description

This is an introduction to linear algebra. There will be 10 problem sets (10% of final grade), two in class midterm exams (25% each) and one final exam (40%).


  • Jacob Bernstein
  • Email: bernstein@math.jhu.edu
  • Office: Krieger 408.

Course Assistants

  • Stephen Harrop
  • Email: sharrop1@jhu.edu
  • Office: Krieger 207.
  • Tianyi Ren
  • Email: tyren@math.jhu.edu
  • Office: Krieger 201.
  • Ethan Lee
  • Email: ylee157@jhu.edu
  • Office: Krieger 207.
  • Bilyana Tzolova
  • Email: btzolov1@jhu.edu
  • Office: Krieger 207.
  • Hanveen Koh
  • Email: hkoh5@math.jhu.edu
  • Office: Krieger 201.
  • Tslil Clingman
  • Email: tclingm1@math.jhu.edu
  • Office: Krieger 211.
  • Cheng Zhang
  • Email: czhang67@jhu.edu
  • Office: Krieger 211.


  • MWF 10:00–10:50 (Sections 1, 2, 3 and 4) in Krieger 205.
  • MWF 11:00–11:50 (Sections 5, 6, 7, 8 and 9) in Krieger 205.


  • Section 1: T 3:00–3:50 in Shaffer 300 (TA: Harrop).
  • Section 2: T 4:30–5:20 in Olin 305 (TA: Harrop).
  • Section 3: Th 1:30–2:20 in Maryland 104 (TA: Ren).
  • Section 4: Th 3:00–3:50 in Maryland 104 (TA: Lee).
  • Section 5: T 1:30–2:20 in Mergenthaler 111 (TA: Tzolova).
  • Section 6: T 3:00–3:50 in Mudd 26 (TA: Tzolova).
  • Section 7: Th 3:00–3:50 in Shaffer 301 (TA: Koh).
  • Section 8: Th 4:30–5:20 in Bloomberg 274 (TA: Clingman).
  • Section 9: T 4:30–5:20 in Krieger 309 (TA: Zhang).

Office Hours

  • Bernstein: Wednesday, 12:30-2:30 pm or by appointment in Krieger 408.
  • Harrop: W 11-12:30 pm.
  • Ren: Th 3-4 pm.
  • Lee: Tu 6-7 pm.
  • Tzolova: Th 1:30-2:30 pm.
  • Koh: W 4-5pm.
  • Clingman: Tu 5-6 pm.
  • Zhang: W 3-4 pm.


The syllabus is here.


The course text is
  • Linear Algebra with Applications (5th Edition), Otto Bretscher.

All references to the page numbers, chapters and problems correspond to this edition of the textbook. A copy is on reserve in the library.

Problem Sets

The problems sets will be posted on this website and be due at the beginning of lecture on Fridays. Problem sets recieved after this time will be considered late and will receive a grade of zero. They cannot be made up.

Homework counts for 10% of your final grade. Your lowest homework score will be dropped.


  • Staple your problem sets! Paper clips, folded corners, etc. are not acceptable.
  • Clearly write: your name, your TA and your section number on the first page. If your homework is too messy or illegible, the grader may choose not to grade it.
  • You are premitted to work together. However, you must write up your own solutions in your own words. Failure to do so will be consided plagarism.
  • Solving problems is the best way to learn math (or any subject). For that reason I highly encourage you to think about the assigned problems before working with others/seeking assistence.


There will be three exams. Two in class midterms and a comprehensive final.

The dates of the exames are
First Midterm: Friday, March 10.
Second Midterm: Friday, April 14.
Final Exam: Wednesday, May 10, 9am-12pm. Location: Hodson 110 (Sections 1-3, 5-8) and Hodson 210 (Sections 4 and 8)

No make-up exams will be offered in this course. If you have to miss an exam for a documented, legitimate reason, then your final grade will be calculated using your other exam grades.

Schedule (will be updated as the course progresses)

Try and read ahead -- you will get more out of lecture.

Week 1 (1/30 & 2/1 & 2/3): Course Information

Read: 1.1, 1.2, 1.3
Handout on RREF and related topics.
No homework due.

Week 2 (2/6 & 2/8 & 2/10): Linear Transformations

Read: 2.1, 2.2, 2.3
Problem Set 1 due. Selected Solutions.

Week 3 (2/13 & 2/15 & 2/17): Linear Transformations (cont.) and Subspaces

Read: 2.4, 3.1, 3.2
Handout on Linear Transforms.
Problem Set 2 due. Selected Solutions.

Week 4 (2/20 & 2/22 & 2/24): Subspaces and Dimensions

Read: 3.3, 3.4
Problem Set 3 due. Selected Solutions.

Week 5 (2/27 & 3/1 & 3/3): Linear Spaces

Read: 3.4, 4.1
Handout on kernel and image and Handout on subspaces.
Handout on linear coordinates.
Problem Set 4 due. Selected Solutions.

Week 6 (3/6 & 3/8 & 3/10): Linear Spaces (First Midterm)

Read: 4.1 4.2
Handout on similar matrices.
Practice midterms:
one (solutions), two (solutions), three (solutions), four (solutions), five (has solutions) and six (has solutions).
Solutions to first midterm.
No homework due.

Week 7 (3/13 & 3/15 & 3/17): Linear Spaces (cont)

Read: 4.2, 4.3
Office hours on Wednesday are cancelled. I will hold make-up office hours Th 10:30am-12:30pm.
Problem Set 5 due. Selected Solutions.

Week 8: Enjoy your Spring Break!

No homework due.

Week 9 (3/27 & 3/29 & 3/31): Orthogonality and Least Squares

Read: 5.1, 5.2, 5.3
Problem Set 6 due. Selected Solutions.

Week 10 (4/3 & 4/5 & 4/7): Orthogonality and Least Squares (cont.)

Read: 5.4, 5.5
Handout on change of basis matrices.
Problem Set 7 due. Selected Solutions.

Week 11 (4/10 & 4/12 & 4/14): Determinants (Second Midterm)

Read: 6.1, 6.2
No homework due
Handout on the dot product, Handout on Gram-Schmidt and the QR factorization. Handout on orthognal matrices and the transpose. Handout on least squares.
Practice Midterms: one, two (solutions), three (solutions), four (solutions), five (solutions), six (solutions), seven (solutions).
Solutions to second midterm.

Week 12 (4/17 & 4/19 & 4/21): Eigenvalues and Eigenvectors

Read: 6.3, 7.1, 7.2
Problem Set 8 due. Selected Solutions.

Week 13 (4/24 & 4/26 & 4/28): Eigenvalues and Eigenvectors (cont.)

Read: 7.3, 7.4
Problem Set 9. Selected Solutions.

Week 14 (5/1 & 5/3 & 5/5): Symmetric Matrices and the Singular Value Decomposition

Read: 8.1, 8.3
Handout on determinants. Handout on eigenvalues and related topics. Handout on spectral theorem.
Problem Set 10. Selected Solutions.

Final Exam (5/10)

Practice Finals: one, two, three.
Review Session: Monday 2-4pm in Remsen 101
Extra Office Hours: Monday and Tuesday 11am-2pm

Additional resources

  • Math Help Room. Located in 213 Kreiger Hall -- check link for schedule. Offers additional help from math graduate students.
  • PILOT Learning. A peer-lead team learning program.
  • The Learning Den. Free tutoring offered by the university.

Students with disabilities

Students with documented disabilities or other special needs who require accommodation must register with Student Disability Services. After that, remind the instructor of the specific needs at least two weeks prior to each exam; the instructor must be provided with the official letter stating all the needs from Student Disability Services.

There is a student in this class who requires the services of a note taker. This is an opportunity to share notes through the Student Disability Services Office. If you are interested in performing this service, please register as a notetaker with Student Disability Services via the following URL: https://andes.accessiblelearning.com/JHU

JHU ethics statement

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. Read the "Statement on Ethics" at the Ethics Board website for more information.

If a student is found responsible through the Office of Student Conduct for academic dishonesty on a graded item in this course, the student will receive a score of zero for that assignment, and the final grade for the course will be further reduced by one letter grade.

Spring 2017 -- Department of Mathematics, Johns Hopkins University.