Kalina Mincheva

Linear Algebra and Matrix Theory

The course Math 225 is a rigorous proof-based introduction to linear algebra. Math 225 (as opposed to Math 222) is focused on the abstract aspects of linear algebra and will demand a fair amount of maturity of mathematical thinking, as opposed to just problem solving. The main topics covered will be vector spaces, linear transformations, matrices, systems of linear equations, determinants, eigenvalues, eigenvectors, diagonalization, and applications. Problem sets will consist of a mix of computational and proof-based problems.

Course info

  • Lectures: TTh 9:00-10:15
  • Classroom: WTS A51
  • Office: DL 406, Tuesdays 4:30 - 6 pm

Syllabus

You can find the syllabus here.

Exams

  • Quiz 1: September 19 - in class
  • Midterm: October 15 - tentatively 7-8:30 pm
  • Quiz 2: November 7 - in class
  • Final: December 15, 7pm

Resources

While a concept can be obvious to some it can be completely mysterious to others. Moreover, different instructors will emphasize different points of the material. This is why it is very useful to hear the material discussed by someone else even if you think you understand everything taught in class! So I encourage you to visit the discussion sessions. Spending more time with challenging concepts always pays off. Bellow you can find a list of the available resources for this class. Take advantage of them! Of course, these are the perfect places to visit if you struggle with a concept, if the lectures/homework don't make sense or if you just have a small question regarding the material:

  • Peer tutor sessions with Joy Qiu
    • Office Hours: Sunday 1-3pm, Wednesday 7:30-9:30pm, Wright Reading Rooms (either B65 or B67) for now
  • TA discussion sessions with Mikey Chow
    • Discussion session: Monday, 8-9 pm, LOM 200
    • Office Hours: Wednesday, 5-6 pm, DL 415
  • Guides for writing proofs can be found here.
  • Some excellent linear algebra videos.

Office hours

If you need help with the course or you have questions regarding the material or the homeworks or you would just want to pick up your homework, please don't hesitate to stop by my office or write me an email. If the time is inconvenient you can arrange an appointment.

Office hours: Tuesdays 4:30 - 6pm

Review Materials

  • Midterm Review problems can be found here. In addition to those, you can also try the following exercises from the book: 1.2.17, 1.2.18, 1.3.8 a,b,f, 1.3.19, 1.4.5 f,g, 1.5.1, 1.5.2 g, 1.5.19, 1.6.4, 1.6.13, 1.6.24, 2.2.1, 2.2.2 b, 2.2.3.
  • Final Review problems can be found here.

Homework Sets

Solutions to Homeworks

Schedule

Week Dates Textbook sections
1 28 August - 1 September 1.1, 1.2, Appendix C
2 2 September - 8 September 1.2, 1.3, 1.4 only the definition of linear combination
3 9 September - 15 September 1.4, 1.5
4 16 September - 22 September 1.6, Quiz 1
5 23 September - 29 September 1.6, 2.1
6 30 September - 6 October 2.1, 2.2
7 7 October - 13 October 2.3, 2.4
8 14 October - 20 October 2.4, MT 1
9 21 October - 27 October 2.5, handout
10 28 October - 3 November 3.1, 3.2
11 4 November - 10 November 3.3, 3.4, 4.1, 4.2, Quiz 2
12 11 November - 17 November 5.1, 5.2
13 18 November - 24 November 6.1, 6.4, 6.6
14 2 December - 8 December 6.6, 6.2, Review