Math 2130 (Fall 2023):
Linear Algebra for Non-Mathematics Majors

1. Exam 1 (Wednesday, 20 September) — Vectors and matrices (Chapters 1 and 2)
• vectors, matrices, matrix multiplication, systems of linear equations, row reduction, linear independence, linear transformations (§§1.1–5, 1.7–9, 2.1)
2. Exam 2 (Wednesday, 18 October) — Matrices, determinants, and vector spaces (Chapters 2, 3 and 4)
• matrix inversion, subspaces, dimension, rank, cofactor expansion, row and column operations, volume and orientation, Cramer's rule, determinants and matrix inversion, abstract vector spaces, null space, column space, abstract linear transformations (§§2.2–5, 2.8–9, 3.1–3, §§4.1–2)
3. Exam 3 (Wednesday, 1 November) — same topics as Exam 2. The lowest of your grades on Exams 1, 2, and 3 will be dropped.
4. Exam 4 (Wednesday, 15 November) — Vector spaces, eigenvalues, eigenvectors, and inner products
• linear independence, bases, change of coordinates, dimension, characteristic polynomial, diagonalization, eigenvectors and eigenvalues of abstract linear transformations, geometric significance of eigenvectors and eigenvalues, complex eigenvalues, inner product, angles and length, orthogonal projection (§§4.3–6, 5.1–5, 6.1–3)
5. Final Exam (Sunday, 17 December) — Inner products and quadratic forms
• Gram–Schmidt, least squares, inner product spaces, quadratic forms, the spectral theorem, quadratic forms, singular value decomposition (§§6.4–5, 6.7, 7.1–2, 7.4

1. Week 1 (28 Aug — 1 Sep): §§1.1–3
2. Week 2 (6 Sep — 8 Sep): §§1.4–5
3. Week 3 (11 Sep — 15 Sep): §§1.7–9
4. Week 4 (18 Sep — 22 Sep): §§2.1–2, Exam 1
5. Week 5 (25 Sep — 29 Sep): §§2.3–2.5
6. Week 6 (2 Oct — 6 Oct): §§2.8–2.9, 3.1
7. Week 7 (9 Oct — 13 Oct): §§3.2–3, 4.1
8. Week 8 (16 Oct — 20 Oct): §§4.2–4.3, Exam 2
9. Week 9 (23 Oct — 27 Oct): §§4.4–5, 5.1
10. Week 10 (30 Oct — 3 Nov): §§5.2–5.4
11. Week 11 (6 Nov — 10 Nov): §§5.5, 6.1–2
12. Week 12 (13 Nov — 17 Nov): §§6.3–6.4, Exam 3
13. Week 13 (27 Nov — 1 Dec): §§6.5, 6.7, 7.1
14. Week 14 (4 Dec — 8 Dec): §§7.2–7.4
15. Week 15 (11 Dec — 13 Dec): Review

Course goals

We will learn quite a few definitions, theorems, and algorithms in this class. The following list is meant to give an idea of the different levels of mastery you can achieve with them. The letters should also give a rough idea of how those levels of mastery will correspond to a final grade.

4. Execute an algorithm correctly in familiar situations.
5. Reproduce statements of definitions and theorems. Execute an algorithm correctly in novel situations. Use the algorithm as part of a solution to familiar types of problems.
6. Recognize situations where a definition or theorem does or does not apply. Appreciate subtleties and edge cases in definitions, theorems, and algorithms. Identify opporunities to use an algorithm.
7. Use multiple ideas in the same problem. Understand how an algorithm works. Transform problems into forms suitable for application of an algorithm or theorem. Identify opportunities to use linear algebra in other contexts.

For example, one of the most important things we will learn in this class is the Gaussian elimination algorithm for putting a matrix in row echelon or reduced row echelon form. Here is an idea of how I might interpret the above criteria for the Gaussian elimination algorithm:

4. Find the reduced row echelon form of a matrix when given one.
5. Explain the Gaussian elimination algorithm. Use Gaussian elimination to compute the column space, null space, and determinant of a matrix.
6. Recognize situations that where Gaussian elimination can provide useful information. Convert problems to forms suitable for the use of Gaussian elimination.
7. Apply the idea behind Gaussian elimination in novel situations. Explain why Gaussian elimination can be used to compute the column space, null space, or determinant.

In case you are curious: ChatGPT-3.5 and ChatGPT-4 tend to perform between a B and a C when I have tested them with linear algebra problems.

Homework

Your homework will consist of reading the textbook, watching recorded lectures, and completing ungraded problems. None of these will be graded directly, but they are essential preparation for the next class's activities.

Because this class operates in a flipped model, it is extremely important that we all come to class prepared. This means that you should come to class having read the assigned text and/or watched the assigned video, and having made a reasonable effort on the homework problems.

I recognize that occasionally circumstances will prevent you from completing your homework before class, or will cause you to miss class. To minimize the negative effects when this happens, you will be allowed to complete up to 5 of the in-class assignments at home. Please contact me if you need to make use of this option.

Academic honesty

I encourage you to consult outside sources, use the internet, and collaborate with your peers. However, there are important rules to ensure that you use these opportunities in an academically honest way.