Linear Algebra (Math 301), Spring 2013
Course description
We discuss linear algebra from a matrix perspective. Topics to be covered include the algebra of vectors and matrices, elimination and decomposition methods for solving linear systems of equations, applications of eigenvalues and eigenvectors, vector spaces, linear transformations, and least squares techniques.
Course details
- Basic course information, including office hours.
- Text book
- Lectures
- Homework
- Quizzes
- In class exercises
- Midterm exams
- Final exam
- Grading
- Make-up exams and late homeworks
- Amusing quotes, news items, etc
Send me an e-mail
If you haven't already done so, please send me an e-mail at donnacalhoun@boisestate.edu so that I can compile an e-mail list for the class. At the very least, include a subject header that says "Math 301". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.
Basic course information
Instructor | Prof. Donna Calhoun |
Time | MW 12:00-1:15 |
Place | ILC 402 |
Office Hours (in my office, MG241A) | Tuesdays, 11:00-12:00, or by special appt. |
Prerequisites | Math 175 (Calculus II) |
Course textbook
The required text for this course is
- Introduction to Linear Algebra, 4th edition by Gilbert Strang, Wellesley-Cambridge Press, 2009.
We will cover the material from topics from Chapters 1-6, with applications from Chapter 8 of the text.
Course schedule and lectures
Below is a tentative course schedule, and electronic lecture material. Chapter and sections from the text book are indicated in parenthesis.
Links to assigned homework based on material covered lecture are also provided below. The .html version seems to work best on the Mac Safari browser. Please let me know about your experience with other browsers.
You are encouraged to read ahead in sections that will be covered in lectures. Thanks!
Week #1 (Jan. 23) |
Wednesday : Review of linear systems of equations Homework #1 due on Wednesday January 30. |
Week #2 (Jan 28) |
Monday : Introduction to vectors (1.1 and 1.2) (Lecture #2 : .m4v, .html, .pdf) (Beta) Wednesday : Matrices and solving linear systems (1.3 and 2.1) (Lecture #3 : .m4v, .html, .pdf) (Corrected) Homework #2 due on Wednesday February 6 |
Week #3 (Feb 4) |
Monday : Using elimination to solve systems (2.2) (Lecture #4 : .m4v, .html, .pdf) (Corrected) Wednesday : Elimination using matrices; Matrix operations (2.3, 2.4) (Lecture #5 : .m4v, .html, .pdf) (Corrected) Homework #3 due on Wednesday February 13 |
Week #4 (Feb 11) |
Monday : Inverse matrices; LU Factorization (2.5, 2.6) (Lecture #6 : .m4v, .html, .pdf) (Final) Wednesday : Tranposes and permutations (2.7) (Lecture #7 : .m4v (coming soon), .html, .pdf) (Final) Homework #4 due on Wednesday February 20th.
You may turn in your homework on Monday 2/18, if you'd like me to grade it before the midterm. |
Week #5 (Feb 18) |
Monday : President's Day Wednesday : Review for Midterm #1 (Chapters 1-2) No homework due next week |
Week #6 (Feb 25) |
Monday : Midterm #1 (Chapters 1-2) Wednesday : Vectors and subspaces (3.1) Homework #5 due on Wednesday March 6. |
Week #7 (Mar 4) |
Monday : The Nullspace (3.2) (Lecture #8 : .m4v (coming soon), .html, .pdf) (Final) Wednesday : Rank and row reduced form; the complete solution; (3.3, 3.4) (Lecture #9 : .m4v, .html, .pdf) (Final) Homework #6 due on Wednesday March 13 |
Week #8 (Mar 11) |
Monday : Rank and the complete solution (3.3, 3.4) (see Lecture #9, Wednesday 3/6) Wednesday : Independence, Basis and Dimension; dimensions of the four subspaces (3.5, 3.6) (Lecture #10 : .m4v (upon request), .html, .pdf) (Final) Homework #7 due on Wednesday March 20. |
Week #9 (Mar 18) |
Monday : Orthogonality; Projections; (4.1, 4.2) (Lecture #11 : .m4v (upon request), .html, .pdf) Wednesday : Least squares (4.3) (Lecture #12 : .m4v (upon request), .html, .pdf) Homework #8 due on Wednesday April 3rd. You may turn in your homework on Monday if you'd like me to grade it before the midterm |
Spring Break | |
Week #10 (Apr 1) |
Monday : Gram-Schmidt Orthogonalization (4.4) Wednesday : Review for Midterm #2 (Chapters 3-4) No homework due next week |
Week #11 (Apr 8) |
Monday : Midterm #2 (Chapters 3-4) Wednesday : Determinants (5.1, 5.2, 5.3) Homework #9 due on Wednesday April 17th |
Week #12 (Apr 15) |
Monday : Introduction to Eigenvalues; Diagonalizing a matrix (6.1) Wednesday : Introduction to Eigenvalues (6.1, continued) Homework #10 due on Wednesday April 24 |
Week #13 (Apr 22) |
Monday : Diagonalizing a matrix (6.2) Wednesday : Diagonalizing a matrix (cont); Quiz #2 (6.2) No homework assigned |
Week #14 (Apr 22) |
Monday : Symmetric Matrices (6.4) Wednesday : Positive definite matrices (6.5) Homework #11 due on Wednesday May 8 |
Week #15 (Apr 29) |
Monday : Similar matrices; Singular Value Decomposition (6.6, 6.7) Wednesday : Review for final |
Homeworks
Homework will be collected once a week and will generally be taken from the course textbook. You should hand in all problems to get credit for the assignment, but these will not be graded in detail. The problems which will be graded, are to be turned in are on a separate sheet, available at links below.
Homework #1 | Due Wednesday, Jan 28, at the start of class.
No graded portion of the assignment for this week |
Homework #2 | Due Wednesday, Feb. 6, at the start of class.
Graded assignment (.pdf) |
Homework #3 | Due Wednesday, Feb. 13, at the start of class.
Graded assignment (.pdf) |
Homework #4 | Due Wednesday, Feb. 20, at the start of class.
You may turn in your homework on Monday 2/18, if you'd like me to grade it before the midterm.
Graded assignment (.pdf) |
Homework #5 | Due Wednesday, Mar. 6, at the start of class.
Graded assignment (.pdf) |
Homework #6 | Due Wednesday, Mar. 13, at the start of class.
Graded assignment (.pdf) |
Homework #7 | Due Wednesday, Mar. 20, at the start of class.
Graded assignment (.pdf) Quiz on Wednesday March 20th! |
Homework #8 | Due Wednesday, Apr. 3rd, at the start of class.
You may turn in your homework on Monday 4/1 if you'd like me to grade it before the midterm
Graded assignment (.pdf) |
Homework #9 | Due Wednesday, Apr. 17, at the start of class.
Graded assignment (.pdf) |
Homework #10 | Due Wednesday, Apr. 24, at the start of class.
No Graded assignment this week, but you will have a homework quiz on Wednesday 4/24. Please turn in the book problems as usual. |
Homework #11 | Due Wednesday, May 8, at the start of class.
No graded assignment, but there may be a short quiz on Wednesday 5/8 covering the homework. |
Quizzes
Quizzes will be short homework quizzes.
Quiz #1 | Wednesday, March 20th
Copy of quiz1.pdf |
Quiz #2 | Wednesday, April 24th
Material will be from Chapters 6.1 and 6.2 Copy of quiz2.pdf |
Quiz #4 | Wednesday, May 8
Material will be from Chapters 6.4-6.7 Copy of quiz3.pdf Solutions quiz3_solns.pdf |
In-class exercises
In class exercises will be done in-class and collected periodically, and will count towards attendance.
In-class exercise #1 | Wednesday Jan. 23.
Practice solving linear systems (.pdf) |
Midterms
Midterm #1 | Monday, February 25th.
Exam will cover material from Chapters 1 and 2. |
Midterm #2 | Monday April 8th.
Exam will cover material from Chapters 3 and 4. You can download a practice set of questions here. Thanks to Sam (solns (very complete)), Jarad (solns), Eric (solns), Jerry (solns), Adam (solns), Stephanie (solns) Ted (solns,unedited), Bobby (solns,unedited) for letting me post their solutions to the practice exam! You will also be allowed to use a page of notes (both sides of an 8.5 by 11 sheet of paper) on the midterm. Solutions to exam #2 (page 1, page 2, page 3, page 4, page 5, page 6) |
Final
Our final will be held in our regular class room.
Final | Wednesday, May 15th, 2:30 - 4:30
To review for the final, retake old exams (midterm_1.pdf, midterm_2.pdf, midterm_1_alt.pdf) or quizzes (quiz1.pdf, quiz2.pdf, quiz3.pdf). The last quiz may be especially helpful for reviewing the material we hav covered since the last midterm. The solutions to this quiz are posted above. Final exam : final. Solutions to the final : (final_solns_page1, final_solns_page2, final_solns_page3, final_solns_page4, final_solns_page5) |
Grading
Homeworks and quizzes will count towards 15% of your grade, each of the two midterms will be 25% of your final grade, and the final exam will be worth 30% of your final grade. In-class exercises will count towards 5% of your grade.
Make-up exams, late homework
If you should miss an exam, you may be given an opportunity to take a comprehensive make-up exam during the final week of class. This score will be used in place of the exam you missed. The decision as to whether to allow this option is made by the instructor.
Late homeworks will not be accepted.
Other useful information
Linear Algebra, finite element design, and the auto industry (posted 1/21/2013)
Finite element design is a computational tool widely used in the auto industry to optimize the design of cars. A key feature in making finite element analysis a feasible tool is advanced techniques for solving large linear systems (millions of equations). In a recent radio interview, a Wall Street journalist talks about his impressions of a recent (2011) auto show, and mentions "finite element design" and computational advances in general as the key to the latest design innovations in the car industry. Listen to the podcast here.
One of the most widely used finite element analysis (FEA) packages in the automotive industry is NASTRAN. They advertise "direct solvers" (such as LU factorization we will learn in class) and "iterative solvers" (e.g. Conjugate Gradient) for linear systems which can handle up to 25 million "degrees of freedom", i.e. number of equations, or number of unknowns. Read about the solvers in NASTRAN here.
History of Gaussian Elimination (posted 1/21/2013)
You might think that Gaussian Elimination is such an obvious idea, that it is hard to imagine a time when there was no such algorithm. To get a feel for the history that dates back as far as 2000BC, see this link.
Lectures by G. Strang
Did you know that you can watch on-line lectures given Gilbert Strang (author of our course text), lecturing from an earlier edition of our class textbook? This would be a great way to get a different view of the material, taught by one of the major contributors to the field of Linear Algebra. His lectures are available on the MIT Open Course Ware website at this link.
Last modified: Mon Aug 5 10:33:40 PDT 2013