Math 2135 Fall 2019

MATH 2135: Linear Algebra for Math Majors (Fall 2019)

Syllabus and details on accomodations, honor code, etc

Final exam:

Monday, December 16, 1:30-4:00 pm, STAD 135

Office hours:

Tuesday 10-11 am, Wednesday 3-4 pm


Numbers refer to sections in Treil, Linear algebra done wrong, if not indicated otherwise.
  1. 08/26: some applications of linear algebra
  2. 08/28: column vectors over the reals, addition, scalar multiples (1.1), systems of linear equations, augmented matrix,
  3. 08/30: matrix times column vector (1.3.2), row reduction (2.2)
  4. 09/04: (reduced) echelon form, elementary row operations, free variables, solution in parametrized form (2.3)
  5. 09/06: existence and number of solutions of Ax=b (2.3), homogenous and inhomogenous systems (2.6), nullspace of A (2.6)
  6. 09/09: axioms and properties of fields (Halmos 1.1)
  7. 09/11: integers modulo n, axioms of vector spaces over arbitrary fields (1.1)
  8. 09/13: tuples, matrices, sequences, functions as vector spaces (1.1), properties of vector spaces
  9. 09/16: linear combinations, span of vectors (1.2)
  10. 09/18: column space, Ax=b is consistent iff b is in Col A, row space, transpose of matrix
  11. 09/20: properties of subspaces, spans and null space as subspaces (1.7)
  12. 09/23: linear independent vectors (1.2)


  1. due 08/30 [pdf]
  2. due 09/06 [pdf]
  3. due 09/13 [pdf]
  4. due 09/20 [pdf]
  5. due 09/27 [pdf]


  1. Integers modulo n [pdf]


We will mainly use the following book which is available for free online: Some additional textbooks:

How to succeed in this class

  1. Go to class! It seems obvious, but learning the material in small portions 3 times a week is easier than reading up on it in some book by yourself. Always keep up with the topics. You also get nerdy Math jokes.
  2. Ask questions early and often! If you are not sure about something, ask about it immediately -- no matter whether in class, in office hours, or by mail. Do not assume that you can skip or figure out things later that you do not understand now. If you are missing the basics, you may fall behind and struggle with more complicated concepts later in class.
  3. Do the work! The only way to learn stuff is to try it yourself. Strive to do all the homework assignments. Some will be more challenging than others. If you are stuck on the hard ones, discuss them with colleagues or ask for possible hints in office hours or by mail.
  4. Learn from mistakes! Look at all feedback you get on graded homework, quizzes, exams, etc. Make sure you understand where you went wrong and how to get the correct solution. In particular revise all relevant graded work before exams.
  5. Organize in study groups! Meet with classmates a couple of times a week to discuss lectures and homework. Still write up your solutions to assignments when you are alone, never in a group.
  6. Take advantage of office hours! If you cannot make it to the official hours, ask to meet at some other time. Office hours are an additional resource for you to discuss stuff for which there is no time during class. Come prepared! Try to solve homework problems alone before you ask for help and be ready to explain your thoughts and where you are stuck.

Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like Overleaf.