18.06 Linear Algebra, Fall 2014

18.06 Fall 2014
Professor: Alexander Postnikov (office E17-428, email apost at math.mit.edu)
Lectures: MWF 11 am, in 54-100.
Course coordinator: Michael Andrews (office E17-301B, email mjandr at math.mit.edu)
Textbook: Gilbert Strang's, Introduction to Linear Algebra, 4th edition.

Course Information and Syllabus


On December 17, the Final Exam will took place. Here are the solutions.

Final Exam Topics: All topics from the syllabus, except graphs and networks, Fourier series, orthogonal polynomials, matrices in engineering, linear programming, fast Fourier transform, numerical linear algebra.

Michael's recitation notes are here. Michael's final review is here.

Practice final is here. Solutions here.

Past exams can be found here. Suggested problems are as follows:

Spring '14: 2; Fall '13: 1; Spring '13: 2; Fall '12: 1, 3, 7; Spring '12: 6; Fall '11: 2, 5; Fall '10: 2, 4; Spring '10: 1, 6; Spring '08: 1, 9, 10; Spring '07: 1, 2, 3, 4, 5, 6, 7, 8.

Previous review material is here:

Carlos and Michael Midterm 1 review, Solutions.

Midterm 2 review, Solutions.

Alex Midterm 3 review, Solutions. Alex Midterm 3 review 2. Darij Midterm 3 review.

Office hours for review will take place at the times below. Notice these are completely different to the usual office hour times.

Instructor Time of office hours Location
Carlos Sauer Friday 5-7 E18-358
Carlos Sauer Saturday 1-3 E18-358
Darij Grinberg Sunday 1-3 E18-358
Michael Andrews Sunday 3-5 (extendable by appointment) E18-358
Michael Andrews Monday 2-4 E18-358
Tanya Khovanova Tuesday 3-5 (extendable by appointment) E18-420
Darij Grinberg Tuesday 4-6 E18-358

You can access E18-358 through the elevators in building E19 at any time.


Recitations meet on Tuesdays starting from Sep 9. No recitation on Nov 11. You must enroll in a specific section. Your homework and exams will go to that section. Default recitation sections are assigned by the Registrar. You may change your recitation on Membership module and view your grades on Gradebook.

TimeRoomInstructorOfficeE-mailOffice hour (in office unless noted)
Lec. MWF 11 54-100 A. Postnikov E17-428 apost at math.mit.edu Monday 12-1
R01 T 9 E17-136 Darij Grinberg E17-401S darij at math.mit.edu Monday 2-4
R02 T 10 E17-136 Darij Grinberg E17-401S darij at math.mit.edu Monday 2-4
R03 T 10 24-307 Carlos Sauer E18-401P csauer at math.mit.edu Wednesday 1-3 (E18-358)
R04 T 11 24-307 Carlos Sauer E18-401P csauer at math.mit.edu Wednesday 1-3 (E18-358)
R05 T 12 E17-136 Tanya Khovanova E18-420 tanya at math.mit.edu Tuesday 3-4
R06 T 1 E17-139 Michael Andrews E17-301B mjandr at math.mit.edu Tuesday 4-6 (E18-358)
R07 T 2 E17-139 Tanya Khovanova E18-420 tanya at math.mit.edu Tuesday 3-4

Homework and Collaboration

Homework will be posted weekly in the Problem Sets section of the class website. Assignments will be due on Thursday, BEFORE 4PM. Please put them in the box for your section in E17-131. Please staple them (you may use the math stapler). They are due every week except exam weeks and are returned in recitation.

Late homework will not be accepted and no extensions are granted. However, your lowest homework grade will be dropped.

The homeworks are essential in learning linear algebra. They are not a test and you are encouraged to talk to other students about difficult problems---after you have found them difficult. Talking about linear algebra is healthy. But you must write your own solutions.


Many students find the second exam more challenging than the first exam. It is not surprising to see a much lower mean on the second exam as this part of the course trains students to go past the mechanical and computational, emphasizing the conceptual and the ability to tackle new problems.

The use of calculators or notes is not permitted during the exams. Taking another course at the same time is not an excuse for missing the in-class hour exam. There will be no make-up exams in this course.

Concerns about homework, grading, exams: see your recitation instructor.

Checking grade records: online at Gradebook.

Changing recitation: online at Membership module.

Related Resources

  • Open Courseware
  • Math learning center: a place to get extra help on problem sets, find a study group and get answers to your questions. Available in 4-159, Mondays to Thursdays 3-5pm and 7:30-9:30pm.


    Julia is a new programming language that is freely available and has a very active and vibrant development community. We encourage trying out Julia but you may use any computer language that you are comfortable with. For example, Matlab, Python, Maple, Mathematica, or Sage are available through MIT IS&T. While you still have the option of downloading Julia on your own machine, you also have the option to use it online. For more information click here.

    Download and Install | Online
    Julia cheat sheet
    Our first ever (Jan 2013) Julia Tutorial Videos and Slides at MIT
    iJulia pages from lectures:
    Live (requires iJulia) Static (publicly readable)
    Lecture 3: Matmul and Inverses (download and drag into IJulia) (view in browser)
    Lecture 4: Gauss Jordan and LU (download and drag into IJulia) (view in browser)
    Lecture 6: Symmetric Matrices and Vector Spaces (download and drag into IJulia) (view in browser)

    Some helpful overviews of Linear Algebra:

  • Goals of the Linear Algebra Course (html)
  • Starting with Two Matrices (pdf)
  • A Factorization Review (ps, pdf)
  • Glossary for Linear Algebra (ps, pdf)
  • Linear Algebra in a Nutshell (ps, pdf)

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