Math 2135 Fall 18

MATH 2135: Linear Algebra for Math Majors (Fall 2018)

Syllabus and details on accomodations, honor code, etc

Final exam::

December 19, 1:30 - 4:00 pm, DUAN G2B41

Office hours:

Tuesday 11-12 am, Wednesday 10-11 pm

Schedule

Numbers refer to sections in Andrelli, Hecker, Elementary Linear Algebra, 2016.
1. 08/27: some applications of linear algebra, vectors over the reals, Pythagorean Theorem, length (1.1)
2. 08/29: scalar multiples, addition of vectors and their properties (Thm 1.3)
3. 08/31: line given by 2 points, law of cosines, angle between vectors, dot product (1.2)
4. 09/05: projections (1.2)
5. 09/07: Cauchy-Schwartz inequality, triangle inequality (1.2)
6. 09/10: matrices, addition, scalar multiples (1.4), multiplication and their properties (1.5)
7. 09/12: systems of linear equations, Gaussian elimination, free variables, parametrized solutions (2.1)
8. 09/14: coefficient and augmented matrix, row echelon form (2.2)
9. 09/17: existence and number of solutions of linear systems
10. 09/19: linear combinations, span of vectors
11. 09/21: consistency of Ax=b for all vectors b
12. 09/24: homogenous systems, nullspace of a matrix,
13. 09/26: axioms and properties of fields
14. 09/28: axioms of vectorspaces over arbitrary fields (4.1)
15. 10/01: review for 1st midterm [pdf]
16. 10/03: 1st midterm
17. 10/05: subspaces (4.2)
18. 10/08: spans and nullspaces are subspaces
19. 10/08: linear independence of vectors (4.3)
20. 10/12: basis of a vector space as minimal spanning set, standard basis of F^n (4.5)
21. 10/15: basis for F^n, basis for polynomials of degree at most n
22. 10/17: basis of column spaces
23. 10/19: each basis has the same size, dimension of a vector space (4.5)
24. 10/22: any n linear independent vectors in F^n form a basis, any n spanning vectors of F^n form a basis
25. 10/24: coordinates w.r.t. a basis, change-of-coordinates-matrix (4.7)
26. 10/26: inverse of a square matrix (2.4)
27. 10/29: linear transformations (5.1), isomorphisms between vector spaces (5.5)
28. 10/31: standard matrix of a linear transformation (5.2)
29. 11/02: standard matrices of rotation, reflection in R^2 (5.2)
30. 11/05: review for 2nd midterm [pdf]
31. 11/07: 2nd midterm
32. 11/09: interview
33. 11/12: discussion of 2nd midterm, matrices for linear maps with respect to arbitrary bases (5.2)
34. 11/14: range and kernel of linear maps as subspaces, injective, surjective maps, dimensions of range and kernel (5.4)
35. 11/16: determinant of a matrix, definition by cofactor expansion, rule of Sarrus for 3x3 matrices (3.1)
36. 11/26: determinant via row reduction, invertible matrices have non-zero determinant (3.2)
37. 11/28: eigenvectors and eigenvalues of matrices (3.4)
38. 11/30: characteristic polynomial (3.4)
39. 12/03: diagonalization of matrices (3.4)
40. 12/05: dynamic systems, Fibonacci numbers
41. 12/07: orthogonal and orthonormal basis (6.1)
42. 12/10: least square solutions of linear systems
43. 12/12: review for the final [pdf]

Homework

1. due 08/31 [pdf]
2. due 09/07 [pdf] [tex]
3. due 09/14 [pdf] [tex]
4. due 09/21 [pdf] [tex]
5. due 09/28 [pdf] [tex]
6. due 10/05 [pdf] [tex]
7. due 10/12 [pdf] [tex]
8. due 10/19 [pdf] [tex]
9. due 10/26 [pdf] [tex]
10. due 11/02 [pdf] [tex]
11. due 11/09 [pdf] [tex]
12. due 11/16 [pdf] [tex]
13. due 11/30 [pdf] [tex]
14. due 12/10 [pdf] [tex]

Handouts

1. Integers modulo n [pdf]
2. Functions [pdf]

Scientific writing

There is a variety of word-processing software for writing Mathematics. LaTeX is the most widespread. You can use it with many text editors or via some cloud-based service, like ShareLaTeX.