Fall 2015: MTH 309
Course: MTH 309, Linear Algebra I
- Course syllabus -- read this!
- Meeting times: MWF, 10:20 am - 11:10 am, A320 Wells Hall
- Mid-term exam dates (tentatively):
- Exam 1: Wednesday, October 7, in-class
- Exam 2: Friday, November 13, in-class
- Final exam date: 12:45 pm - 2:45 pm, December 16, 2015, A320 Wells Hall
- Textbook: Although it is not strictly required, you may want to follow along with the book Linear Algebra with Applications, 8th edition or newer, by Steven J. Leon. I will be covering most of the material from chapters 1 through 6 (reordered and with a heavier emphasis on theory), and having a book in addition to lecture notes will be very helpful. Even more, a linear algebra book will be a useful resource for future classes and beyond.
- Homework: homework assignments will be posted here, due approximately weekly, so keep an eye on this page. The homework will rely heavily on proofs, although some applications will appear along the way. For all proofs, make sure to use complete mathematical sentences and clearly indicate your reasoning for each step, citing any previous results we have seen. An example of a well-written proof is here:
- Proof that 1+2+3+...+n = (n^2 + n)/2
- Homework will be collected at the beginning of class on the day it is due. Late homework will be accepted up to 3 days (72 hours) after the original due date, with a 10% penalty for each day late.
- Homework 1 (due 9/9) | Solutions
- Homework 2 (due 9/16) | Solutions
- Homework 3 (due 9/23) | Solutions
- Homework 4 (due 9/28) | Solutions
- Homework 5 (due 10/2) | Solutions
- Homework 6 (due 10/16) | Solutions
- Homework 7 (due 10/23) | Solutions
- Homework 8 (due 10/28) | Solutions
- Homework 9 (due 11/4) | Solutions
- Homework 10 (due 11/20) | Solutions
- Homework 11 (due 11/30) | Solutions
- Homework 12 (due 12/4) | Solutions
- Proof that 1+2+3+...+n = (n^2 + n)/2
- Gram-Schmidt Exercises
- Review for Second Exam | Solutions
- Exam Solutions:
- Exam 1 Solutions
- Exam 2 Solutions
- Tentative schedule of topics:
- Week 1: Sets and logic; begin systems of linear equations
- Week 2: Systems of linear equations (cont.); Begin vector spaces
- Week 3: Vector spaces; examples of vector spaces
- Week 4: Subspaces; linear combinations; span;
- Week 5: Linear independence; bases
- Week 6: Review, Exam 1
- Week 7: Coordinates; matrices
- Week 8: Inverses; linearity
- Week 9: Composition, inverses, and matrices of transformations
- Week 10: Change of basis; images and kernels; isomorphisms
- Week 11: Review, Exam 2
- Week 12: Determinants; eigenvalues and eigenvectors
- Week 13: Diagonalizability; similarity
- Week 14: Inner products; the Gram-Schmidt process
- Week 15: Review for final exam