Math 271: Linear Algebra (Spring 2022)

This course concerns the core theory of linear algebra, with specific attention to the theoretical development necessary for pure mathematics. The primary objective is to introduce and examine the notion of a vector space, which is a simple model for geometry in any number of dimensions. A secondary objective is to develop and practice mathematical writing, especially the vocabulary, techniques, and mechanics of writing proofs.

Topics include the concepts of vector space, subspace, linear independence, basis, and dimension; systems of linear equations and their solution by Gaussian elimination; matrix operations; linear transformations and their representations by matrices; eigenvalues and eigenvectors; and inner product spaces.

Time and location

  • Monday, Wednesday, and Friday: 1:30-2:20pm in SMUD 204.
  • Tuesday: 2:00-2:50pm in SMUD 205.
  • See Moodle page for the Zoom link during the first week.

Help hours

  • My office hours in SMUD 401:
    • Tuesday 12:30-1:50
    • Wednesday 10:30-12:00
    • Friday 9:30-10:30
  • We have three wonderful Math Fellows (TAs) for 271, with office hours as follows. All Math Fellow hours are in SMUD 014.
    • Sunday 7:30-9:00pm (Mythili Subbanna)
    • Monday 6:00-7:30pm (Andressa Silva)
    • Tuesday 7:30-9:00pm (Mythili Subbanna)
    • Wednesday 6:00-7:30pm (Andressa) and 7:30-9:00pm (Noah)
    • Thursday 7:30-9:00pm (Noah Solomon)
  • Calvin Woods, our Q Center Fellow, is available
    • Monday through Thursday, from 1 to 4pm, in SMUD 007 for drop-in hours, and
    • by individual appointment at this link.

Handouts and other items

LaTeX resources

  • Allison Tanguay’s LaTeX resource page
  • Overleaf LaTeX tutorials: some tutorial videos and other links about learning LaTeX. These focus on using Overleaf, an online platform to write LaTeX documents online without installing any software.
  • Overleaf Primer by Kristin Heysse (Macalester). Another tutorial on writing in LaTeX on Overleaf.
  • Detexify: this is an absurdly useful tool that allows you to sketch a symbol and quickly learn the LaTeX command for it.

Homework

Exams

  • Midterm 1 will be held Wednesday, March 9, in class. Some resources for preparing are below.
  • Midterm 2 will be held Wednesday, April 13, in class.
  • Midterm 3 will be held Friday, May 13, in class.
    • Make a note sheet! You are allowed one sheet of paper, front and back, with whatever you want on it (printed or handwritten).
    • The exam covers material after midterm 2, and up to Section 4.3 of the textbook, but not after.
    • Practice Exam / Solutions
    • See also “Problem Set 10,” which is not to be handed in but provides practice on recent material. Solutions will be posted by midweek.
    • For additional practice, try the linear algebra problems on old comprehensive exams. Solutions to many of these exams, and a detailed linear algebra study guide, can be found via the links at that page. Focus on problems about change of basis, determinants, and eigenvectors/diagonalization, since those are the topics covered after midterm 2.
    • Exam / Solutions
  • There will be no final exam.