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Linear Algebra and Applications (Math 301)


In this course, you will learn linear algebra...

Send me an e-mail

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
Office Mathematics 241A
Time Tuesday/Thursday 9:00-10:15
Place M135 (Mathematics Building)
Office Hours Tuesday 10:30AM-12:30PM
Prerequesites Math 175

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Required textbook and other resources

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Lectures

Below are the slides from lecture material that I can make available online.

Week #1 (Aug. 25)
Tuesday --  Introduction to Linear Algebra
Thursday --  Section 1.2 : The Geometry of Linear Equations

Week #2 (Sept. 1)
Tuesday --  Section 1.3 : An example of Gaussian Elimination
Thursday --  Section 1.4 : Matrix notation and matrix multiplication

Week #3 (Sept. 8)
Tuesday --  Section 1.5 : Triangular Factors and Row Exchanges
Lecture slides :
The LU factorization of a matrix A  (pdf)
Thursday --  Section 1.6 : Inverses and transposes
Lecture slides :
The matrix inverse  (pdf)

Week #4 (Sept. 15)
Tuesday --  Quiz on Chapter 1
Codes written or demonstrated in class :
solve.m  -- Using LU decomposition to solve a linear system
Thursday --  Section 2.1 : Vector spaces and subspaces

Week #5 (Sept. 22)
Tuesday --  Section 2.2 : Solving Ax=0 and Ax=b
Lecture slides :
Finding null space solutions  (pdf)
The Complete Solution  (pdf)
Thursday --  Review for midterm

Week #6 (Sept. 29)
Tuesday --  Midterm #1
Thursday --  Section 2.3 : Linear Independence, Basis and Dimension
Lecture slides :
Finding a basis of a vector space  (pdf)

Week #7 (Oct. 6)
Tuesday --  Section 2.4 : The four fundamental subspaces
Lecture slides :
The Four Fundamental Subspaces  (pdf)
Thursday --  Section 2.5 : Graphs and Networks

Week #8 (Oct. 13)
Tuesday --  Section 3.1 : Orthogonal Vectors and Subspaces
Lecture slides :
Orthogonality and projections  (pdf)
Thursday --  Section 3.2 : Cosines and projections onto lines

Week #9 (Oct. 20)
Tuesday --  Section 3.3 : Projections and least squares
Thursday --  In class review of Chapter 3 ideas.

Week #10 (Oct. 27 )
Tuesday --  Section 4.1-2 : Determinants; Properties of determinants
Thursday --  Section 4.3 : Formulas for the Determinant

Week #11 (Nov. 3)
Tuesday --  Review
Thursday --  No class

Week #12 (Nov. 10)
Tuesday --  Midterm #2
Thursday --  Section 5.1 : Eigenvalues and Eigenvectors
Videos :

Eigenvalues and Eigenvectors

Week #13 (Nov. 17)
Tuesday --  Section 5.2 : Diagonalization of a matrix
Thursday --  Section 5.2 : Difference equations and powers A^k

Week #14 (Dec. 1)
Tuesday --  Section 5.3 : Fibonacci sequences
Thursday --  Section 5.3 : Markov Matrices
Some useful or interesting links
See if you can solve problem A2! (2008 Putnam Question)

Week #15 (Dec. 8)
Tuesday --  Quiz on 5.1-5.3; Review for final exam
Thursday --  Review for final
Other resources :
practice.pdf

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Homework assignments

Homework assignments are due Thursday, at the start of class.

Homework #0

Due Aug. 28

Assignment :
hmwk0.pdf
Solutions :
hmwk0_solns.pdf  -- To give you more practice with Gaussian Elimination, the solutions are written as if we had already had the material in Section 1.3.

Homework #1

Due Sept. 4

Assignment :
hmwk1.pdf
Other resources :
chapter1.pdf  -- Chapter 1 of the textbook.

Homework #2

Due Sept. 11

Assignment :
hmwk2.pdf

Homework #3

Due Sept. 18

Assignment :
hmwk3.pdf

Homework #4

Due Sept. 26

Assignment :
hmwk4.pdf
Other resources :
Chapter2.pdf  -- Chapter 2 of our course textbook

Homework #5

Due Oct. 9th

Assignment :
hmwk5.pdf

Homework #6

Due Oct. 16th

Assignment :
hmwk6.pdf
Other resources :
Chapter3.pdf  -- Chapter 3 of our course textbook

Homework #7

Due Oct. 23th

Assignment :
hmwk7.pdf

Homework #8

Due Oct. 30th

Assignment :
hmwk8.pdf
Other resources :
Chapter4.pdf  -- Chapter 4 of our course textbook

Homework #9

Due Nov. 11th

Assignment :
hmwk9.pdf

Homework #10

Due Nov. 20th

Assignment :
hmwk10.pdf
Other resources :
Chapter5.pdf  -- Chapter 5 of our course textbook

Homework #11

Due Dec. 9th

Assignment :
hmwk11.pdf
Other resources :
grade_dist.pdf  -- Choose how to distribute your grades (to be turned in with your homework)

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Exams

We will have two midterm and one final exam

Midterm #1 Date: September 30

Midterm #2 Date: November 11

Final Date: Tuesday, December 16

The final is 9:30-11:30 (note time change), in our regular classroom


You can find the Final Exam calendar here.

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Grading policy

Homework will count for 20% of your final grade, quizzes will count towards 20% of your grade, and the two exams and final each be 20% of your final grade. Quizzes will be mostly on the homework, and you will be given plenty of notice (no pop quizzes!).

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