MATH 2130: Linear Algebra for Non-Math Majors (Fall 2021)

Syllabus

Final exam:

Schedule

1. 08/23: some applications of linear algebra
2. 08/25: systems of linear equations, matrix representation (1.1), matrix times vector
3. 08/27: elementary row operations, row reduction, (reduced) echelon form (1.2)
4. 08/30: free variables, solution in parametrized form, homogenous and inhomogenous systems
5. 09/01: existence and number of solutions of Ax=b (1.2), vectors, linear combinations, span (1.3)
6. 09/03: Ax=b is consisten iff b is in the span of the columns of A
7. 09/08: solutions of homogenous and inhomogenous systems (1.5), nullspace of A
8. 09/10: linear independent vectors (1.7)
9. 09/13: linear transformations (1.8)
10. 09/15: standard matrix of a linear transformation, every linear map is of the form x -> Ax (1.9)
11. 09/17: injective, surjective, bijective linear maps (1.9)
12. 09/20: characterizing injective, surjective x -> Ax by the columns of A (1.9), matrix addition (2.1)
13. 09/22: composition of linear maps, matrix multiplication (2.1)
14. 09/24: inverse matrix (2.2)
15. 09/27: REVIEW [pdf]
16. 09/29: MIDTERM 1
17. 10/01: computing inverse matrix by row reduction (2.2)
18. 10/04: characterizing invertible matrices
19. 10/06: computations in Mathematica, axioms of vectors spaces and examples: tuples, matrices, sequences, functions as vector spaces (4.1) [Mathematica notebook]
20. 10/08: subspaces (2.8, 4.1), spans and null spaces are subspaces (2.8, 4.2)
21. 10/11: linear independence, basis of subspaces, e.g. of null space (2.8, 4.3)
22. 10/13: basis of column space, Spanning Set Theorem to remove vectors from a spanning set to obtain basis (2.8, 4.3)
23. 10/15: coordinates relative to a basis (existence and uniqueness) (2.9, 4.4)
24. 10/18: dimension of vector spaces (4.5), isomorphisms
25. 10/20: every linear independent set extends to a basis (4.5), row space, rank of matrix (4.6)
26. 10/22: matrix of a linear map w.r.t bases B,C (cf 4.7), reflection on line, integration of polynomials
27. 10/25: determinants, cofactor expansion by a row or column (3.1)
28. 10/27: determinant by row reduction (3.2)
29. 10/29: A is invertible iff det A <> 0, det AB = det A det B, determinant as area of parallelogram (3.3)
30. 11/01: review for midterm [pdf]
31. 11/03: MIDTERM
32. 11/05: eigenvalues, eigenvectors, eigenspaces, eigenvalues of triangular matrix
33. 11/08: characteristic polynomial of a matrix (5.2)
34. 11/10: diagonalizable matrices, Diagonalization Theorem (5.3), basis of eigenvectors
35. 11/12: dynamical systems (5.6), Fibonacci sequence
36. 11/15: dot product, length of vectors over the reals (6.1)
37. 11/17: orthogonal complement of a subspace (6.1), orthogonal and orthonormal sets (6.2)
38. 11/19: orthogonal basis, coordinates via dot product (6.2), orthogonal projection onto a vector (6.3)
39. 11/29: orthogonal projection onto a subspace of R^n (6.3), Gram-Schmidt algorithm for finding orthogonal basis (6.4)
40. 12/01: least squares solution of inconsistent systems (6.5)
41. 12/03: least squares error (6.5), Google page rank
42. 12/06: Google page rank [Mathematica notebook], review [pdf]
43. 12/08: review [practice final][solutions]

Homework

1. due 09/03 [pdf] [solutions]
2. due 09/10 [pdf] [solutions]
3. due 09/17 [pdf] [solutions]
4. due 09/24 [pdf] [solutions]
5. due 10/01 [pdf] part preparation for midterm 1, [solutions]
6. due 10/08 [pdf] [solutions]
7. due 10/15 [pdf] [solutions]
8. due 10/22 [pdf] [solutions]
9. due 10/29 [pdf] [solutions]
10. due 11/05 [pdf] part preparation for midterm 2 [solutions]
11. due 11/12 [pdf] [solutions]
12. due 11/19 [pdf] [solutions]
13. due 12/03 [pdf] [solutions]

Handouts

1. Functions [pdf]