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.