H O N O R S L I N E A R A L G E B R A - S P R I N G 2 0 1 6

LECTURES: Monday, Wednesday, Friday 11:00am-12:00pm, in PSY B36.

DISCUSSION: Wednesday 10:00am-11:00am, in PSY B55. These will be used for going over lecture material and assignments in a way that is less structured than the lectures. Attendence of discussions is highly recommended.

INSTRUCTOR: Solesne Bourguin, office hours Monday 5:00pm-6:00pm, Wednesday 10:00am-11:00am. You can also email me (bourguin@math.bu.edu) to set up an appointment.

COURSE DESCRIPTION: Linear algebra is the study of vector spaces. The study of linear algebra begins with the determination of the solution set of a system of linear equations. This class focuses on abstract vector spaces, rather than on Euclidean space. Topics include: Linear transformations, characteristic polynomials, diagonalization and Jordan normal form, inner products, and spectral theory. The different parts of the class could be summarized as follows:

- Vector spaces: subspaces, linear combinations and systems of linear equations, linear dependence and independence, bases and dimension, maximal linearly independent subsets. |

- Linear transforations and matrices: null spaces, ranges, matrix representation of a linear transformation, composition and matrix multiplication, invertibility and isomorphisms, change of coordinates matrices, dual spaces. |

- Elementary matrix operations: elementary matrices and operations, rank of a matrix and matrix inverses, systems of linear equations. |

- Determinants: determinants of order two, determinants of order n, properties of determinants. |

- Diagonalization: eigenvalues and eigenvectors, diagonalizability, matrix limits. |

- Inner product spaces: inner products and norms, Gram-Schmidt orthogonalization process, orthogonal complements, adjoints of linear operators, normal and self-adjoint operators, unitary and orthogonal operators and their matrices. |

- Canonical forms: Jordan canonical form I, Jordan canonical form II. |

TEXTBOOK: Linear Algebra, by Friedberg, Insel, and Spence, 4th ed., Prentice Hall.

GRADING: problem sets (50%), midterm (15%) and a final exam (35%). Because emergencies sometimes arise, I will drop the lowest homework grade from your homework average.

HOMEWORK: Every Friday for the next Friday. Late homeworks will not be accepted at all.

SCHEDULE OF EXAMS: The midterm will be held on Wednesday, March 2nd from 11:00am to 11:50am and will cover all that has been done up to Friday, February 26th included. The final exam is scheduled for Wednesday, May 4th from 12:30pm to 2:30 pm.

PROBLEM SETS: The following table summarizes the homework assignments (to be found in the exercises sections of the textbook) and due dates.

Table of homework assignments | ||||
---|---|---|---|---|

Homework | Assignment | Due date | ||

HW #1 | §1.2: 1, 3, 8, 12, 13, 17, 18, 21. §1.3: 5, 8(a)(b)(c), 19, 20, 23. |
Friday, January 29th | ||

HW #2 | §1.4: 1, 2(a)(b), 8, 13, 14, 15. |
Friday, February 5th | ||

HW #3 | §1.5: 1, 9, 10, 13(a). §1.6: 1, 4, 12, 13, 15. |
Friday, February 12th | ||

HW #4 | §1.6: 20, 26. §2.1: 1, 2, 3, 5, 6. |
Friday, February 19th | ||

HW #5 | §2.1: 15, 16, 17, 21. §2.2: 1, 2(a)(b)(c)(d), 4, 8. |
Friday, February 26th | ||

HW #6 | §2.2: 15. §2.4: 4, 6, 9, 17. |
Friday, March 4th | ||

HW #7 | §2.5: 3(a)(b), 4, 5. §2.6: 3, 5. |
Friday, March 18th | ||

HW #8 | §3.2: 1, 5(a)(c)(e), 6(a), 14, 19, 21, 22. §3.3: 1, 2(d), 3(d). |
Friday, March 25th | ||

HW #9 | §4.1: 1, 5, 6, 9. §4.2: 2, 3, 5, 7, 25, 26. §4.3: 10, 11, 12, 15. |
Friday, April 1st | ||

HW #10 | §5.1: 3(a)(c), 8(a)(b), 11, 15(a), 17. |
Friday, April 8th | ||

HW #11 | §5.2: 2(a)(b)(c), 3(a)(b). §6.1: 1, 3, 11, 12, 16. |
Friday, April 15th | ||

HW #12 | §6.2: 2(a)(i), 6, 13(a)(b)(c). §6.3: 12, 13, 14, 24. |
Monday, April 25th |