Math 2135 Fall 2024

MATH 2135: Linear Algebra for Math Majors (Fall 2024)

Syllabus

Final exam

Schedule

Numbers are for orientation and refer to sections in Lay et al, Linear algebra and its applications.
  1. 08/26: some applications of linear algebra
  2. 08/28: systems of linear equations, matrix representation (1.1), matrix times vector
  3. 08/30: elementary row operations, row reduction, (reduced) echelon form (1.2)
  4. 09/04: free variables, solution in parametrized form, homogenous and inhomogenous systems
  5. 09/06: existence and number of solutions of Ax=b (1.2), vectors, linear combinations, span (1.3)
  6. 09/09: Ax=b is consisten iff b is in the span of the columns of A
  7. 09/11: solutions of homogenous and inhomogenous systems (1.5), nullspace of A
  8. 09/13: linear independent vectors (1.7)
  9. 09/16: linear transformations (1.8)
  10. 09/18: standard matrix of a linear transformation, every linear map is of the form x -> Ax (1.9)
  11. 09/20: characterizing injective, surjective x -> Ax by the columns of A (1.9)
  12. 09/23: matrix addition, composition of linear maps, matrix multiplication (2.1)
  13. 09/25: properties of matrix operations (2.1)
  14. 09/27: inverse matrix (2.2)
  15. 09/30: REVIEW [pdf]
  16. 10/02: MIDTERM 1
  17. 10/04: computing inverse matrix by row reduction (2.2)
  18. 10/07: characterizing invertible matrices
  19. 10/09: computations in Mathematica [Mathematica notebook]
  20. 10/11 axioms of vectors spaces and examples: tuples, matrices, sequences, functions as vector spaces (4.1)
  21. 10/14: subspaces (2.8, 4.1), spans and null spaces are subspaces (2.8, 4.2)
  22. 10/16: basis of subspaces, e.g. of null space (2.8, 4.3)
  23. 10/18: basis of column space, Spanning Set Theorem to remove vectors from a spanning set to obtain basis (2.8, 4.3)
  24. 10/21: basis of row space (4.6)
  25. 10/23: coordinates relative to a basis (existence and uniqueness) (2.9, 4.4)
  26. 10/25: dimension of vector spaces (4.5), isomorphisms
  27. 10/28: every linear independent set extends to a basis (4.5), row space, rank of matrix (4.6)
  28. 10/30: matrix of a linear map w.r.t bases B,C (cf 4.7), reflection on line
  29. 11/01: determinants, cofactor expansion by a row or column (3.1)
  30. 11/04: review for midterm [pdf]
  31. 11/06: MIDTERM 2
  32. 11/08: determinant by row reduction, A is invertible iff det A <> 0, det AB = det A det B (3.2)
  33. 11/11: determinant as area of parallelogram (3.3), eigenvalues, eigenvectors, eigenspaces (5.1)
  34. 11/13: eigenvalues of triangular matrix, characteristic polynomial of a matrix (5.2)
  35. 11/15: diagonalizable matrices, Diagonalization Theorem (5.3)
  36. 11/18: basis of eigenvectors (5.3)
  37. 11/20: dynamical systems (5.6), Fibonacci sequence
  38. 11/22: dot product, length of vectors over the reals (6.1)
  39. 12/02: orthogonal complement of a subspace (6.1), orthogonal and orthonormal sets (6.2)
  40. 12/04: orthogonal basis, coordinates via dot product (6.2), orthogonal projection onto a vector, onto a subspace of R^n (6.3)
  41. 12/06: least squares solution of inconsistent systems (6.5)
  42. 12/09: Google page rank [Mathematica notebook], review [pdf]
  43. 12/11: review [practice final][solutions]

Homework

  1. due 09/06 [pdf] [tex] [solutions]
  2. due 09/13 [pdf] [tex] [solutions]
  3. due 09/20 [pdf] [tex] [solutions]
  4. due 09/27 [pdf] [tex] [solutions]
  5. due 10/04 [pdf] [tex] part preparation for midterm 1 [solutions]
  6. due 10/11 [pdf] [tex] [solutions]
  7. due 10/18 [pdf] [tex] [solutions]
  8. due 10/25 [pdf] [tex] [solutions]
  9. due 11/01 [pdf] [tex] [solutions]
  10. due 11/08 [pdf] [tex] part preparation for midterm 2 [solutions]
  11. due 11/15 [pdf] [tex] [solutions]
  12. due 11/22 [pdf] [tex] [solutions]
  13. due 12/09 [pdf] [tex] [solutions]

Handouts

  1. Functions [pdf]