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Introduction to Linear Algebra (Math 301)


Linear algebra from a matrix perspective with applications from the applied sciences. Topics include the algebra of matrices, methods for solving linear systems of equations, eigenvalues and eigenvectors, matrix decompositions, vector spaces, linear transformations, least squares, and numerical techniques. Prerequisites: Math 170, Math 175.

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 Wednesday/Friday 9:00-10:15
Place Interactive Learning Center (ILC) 302
Office Hours Wednesday 1:30PM-3:30PM, or by appointment
Prerequesites Math 175

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Required textbook and other resources

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Lectures

We will stick the following schedule as much as possible.

Week #1 (Aug. 22)
Wednesday --  Introduction to Linear Algebra; Sections 1.1
Friday --  Section 1.2

Week #2 (Aug. 29)
Wednesday --  Section 1.3 : Matrices
Friday --  Section 2.1 : Vectors and linear equations

Week #3 (Sept. 5)
Wednesday --  Section 2.2 : The Idea of Elimination
Lecture slides :
Gaussian Elimination (matrix form)  (pdf)
Friday --  Section 2.3 : Elimination using matrices

Week #4 (Sept. 12)
Wednesday --  Section 2.4 : Rules for matrix operations; Section 2.5 : Inverse Matrices
Lecture slides :
The matrix inverse  (pdf)
Friday --  Section 2.6 : Elimination = Factorization : A = LU
Lecture slides :
The LU factorization of a matrix A  (pdf)

Week #5 (Sept. 19)
Wednesday --  Section 2.7 : Permutations and Transposes
Friday --  Section 3.1 : Spaces of Vectors

Week #6 (Sept. 26)
Wednesday --  Section 3.2 : The nullspace of A : Solving Ax=0
Lecture slides :
Finding null space solutions  (pdf)
Friday --  Section 3.3 : The Complete Solution to Ax=b
Lecture slides :
The Complete Solution  (pdf)

Week #7 (Oct. 3)
Wednesday --  Midterm Review
Friday --  Midterm #1 : Chapters 1,2 and 3.1-3.3

Week #8 (Oct. 10)
Wednesday --  Section 3.4 : Independence, Basis and Dimension
Friday --  Section 3.5 :Independence, Basis and dimension
Lecture slides :
Finding a basis of a vector space  (pdf)

Week #9 (Oct. 17)
Wednesday --  Section 3.5 : Dimensions of the four subspaces
Lecture slides :
The Four Fundamental Subspaces  (pdf)
Friday --  Four Fundamental Subspaces, continued

Week #10 (Oct. 24)
Wednesday --  Section 4.1 : Orthogonality of the four subspaces
Lecture slides :
Orthogonality and projections  (pdf)
Friday --  Section 4.2 : Projections

Week #11 (Oct. 31)
Wednesday --  Section 4.3 : Least squares approximations
Lecture slides :
Linear least squares projections  (pdf)
Friday --  Section 5.1 : Properties of the Determinant

Week #12 (Nov. 7)
Wednesday --  Review for Midterm #2
Friday --  Midterm #2

Week #13 (Nov. 14)
Wednesday -- 
Wednesday -- 
Friday -- 

Week #14 (Nov. 28)
Wednesday -- 
Friday -- 

Week #15 (Dec. 5)
Wednesday -- 
Friday -- 

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Homework assignments

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

Homework #1

Due Sept. 2

Assignment :
hmwk1.pdf

Homework #2

Due Sept. 9

Assignment :
hmwk2.pdf

Homework #3

Due Sept. 16

Assignment :
hmwk3.pdf

Homework #4

Due Sept. 23

Assignment :
hmwk4.pdf

Homework #5

Due Sept. 30

Assignment :
hmwk5.pdf

Homework #6

Due Oct. 14th

Assignment :
hmwk6.pdf

Homework #7

Due Oct. 21th

Assignment :
hmwk7.pdf

Homework #8

Due Oct. 28th

Assignment :
hmwk8.pdf

Homework #9

Due Nov. 9th

Assignment :
hmwk9.pdf

Homework #10

Due Nov. 18th

Assignment :
hmwk10.pdf

Homework #11

Due Dec. 7th

Assignment :
hmwk11.pdf

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Exams

We will have two midterms and one final exam

Midterm #1 Date: Friday, October 7

Midterm #2 Date: Friday, November 11th

Final Date: Friday December 16th

10AM - 12PM


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. A 90% and above will earn you an A, between 80% and 90% will earn you at least a B, between 70% and 80% will be at least a C, and below 60% will be a D or F. If there is any deviation from this grading policy, it will be to lower the percentages, i.e. you could still earn an A with less than 90%, but you will never need more than 90%. Quizzes will be mostly on the homework, and you will be given plenty of notice (no pop quizzes!).

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