Math 25a: Honors Linear Algebra and Real Analysis I, Fall 2017


  • (9/22): Solutions to HW3 are posted below. 
  • Yifei will hold a midterm review session Sunday (Sept 24) 4-6 in SC 309. Please email him if you have topics you'd like to hear discussed. 
  • Bena's office hours (Monday and Friday 3-4) will be in SC 232 from now on. 
  • (9/20): There will be a midterm next Wednesday, September 27. There is no homework due that day. Some practice problems have been posted below. 

Course Information

A rigorous treatment of linear algebra. Topics include: construction of number systems; fields, vector spaces and linear transformations; eigenvalues and eigenvectors; determinants and inner products. The plan is to work through Axler's Linear algebra done right after a short introduction using Chapter 1 of Simmons' Introduction to topology and modern analysis. This course is part one of a two-part course -- the plan for the second semester is to work through Spivak's Calculus on manifolds

Grading: Weekly homeworks (30%), two midterms (40%), final exam (30%)

Contact Info

  • Bena Tshishiku (Lecturer) bena at
  • Yifei Zhao (Teaching fellow) yifei at
  • Ellen Li (CA) eyli at
  • Charles O'Mara (CA) comara at
  • Michele Tienni (CA) micheletienni at
  • Natalia M. Pacheco-Tallaj (CA) pachecotallaj at

Course Events

Class: MWF 10-11am in SC 507

Math Night (collaborative homework session): Monday 8-10pm, Leverett House Dining Hall (more info)

Office Hours. 

  • Bena: Monday and Friday 3-4 in SC 232, or by appointment in SC 525
  • Yifei: Friday 3:30-4:30 in SC 321g
  • Ellen & Natalia: Monday 8-10p, Leverett dining hall (Math night)
  • Michele & Charlie: Tuesday 8:30-10:30p, Lowell dining hall 

Important Dates

  • Drop deadline: Monday, Sept 18
  • Deadline to switch between 21/23/25/55: Monday, Oct 2
  • Midterm 1: Wednesday, Sept 27
  • Midterm 2: Wednesday, Nov 1
  • Final exam: December 13, 2pm


There will be 10 assignments posted below as the semester progresses. Homework will be due each Wednesday before 10am in the CA's mailboxes on the 2nd floor of the Science Center. As a rule (with very few exceptions), late homework will not be accepted. 

Collaboration: You are encouraged to work together on the assignments (c.f. Math Night). In your solutions, you should acknowledge the students with whom you worked. 

LaTeX: It is required that you type your solutions in LaTeX. You can either download LaTex or use sharelatex which allows you download, edit, and compile LaTeX files online. See here for a guide to notation in LaTeX. Also Detexify is a useful tool for finding the commands for various symbols. The source code for the assignments should be a helpful guide. The most basic thing to know/remember is that math always goes in between dollar signs. 

  • Due Sept 6: HW1, solutions
  • Due Sept 13: HW2, exploration problem (designed by Yifei -- for extra credit), solutions
  • Due Sept 20: HW3, exploration problem (due Oct 4), solutions
  • No homework due Sept 27. Instead please work on the practice midterm problems. It won't be turned it (so I'm not giving you the TeX file), but you are strongly encouraged to do all of them! 
  • Due Oct 4: 
  • Due Oct 11: 
  • Due Oct 18: 
  • Due Oct 25: 
  • No homework due Nov 1. Instead there will be a practice midterm.
  • Due Nov 8: 
  • Due Nov 15: 
  • No homework due Nov 22 (Thanksgiving)
  • Due Nov 29: 

Course Materials

  • Main textbook: Linear algebra done right (3rd edition) by Axler. This is the main text of the course. It's available in the book store.
  • Additional text: Introduction to topology and modern analysis by Simmons. The first two weeks of the course will be centered around the material in Chapter 1.  I suggest you avoid buying it and use the digital copy found here
  • Supplementary videos (by Axler) accompanying the text