This is the website for the course MAT22A section 003 at the Department of Mathematics at UC Davis.
The course will have the textbook Introduction to Linear Algebra, 6th Edition by Gilbert Strang, Wellesley Cambridge Press.
The goal of the course is to introduce students to the fundamental objects and concepts in Linear Algebra, as indicated by the Department Syllabus. Linear Algebra is the study of linear maps on finite-dimensional vector spaces ( students will learn what all of these terms mean during the course).
Lectures: Monday, Wednesday, Friday 9:00-9:50 AM Young 194 .
Textbook: The textbook should be accessible through the UC Davis Equitable Access Program.
Syllabus: The syllabus contains the basic guidelines for the course.
Office Hours: Mondays and Wednesdays 3-4 PM at MSB 3135 or by appointment.
TA: Jonathan Erickson, jferickson@ucdavis.edu
TA's office hours: Monday, 12:10-1:00 PM and Wednesday 12:10-1:00 PM. MSB 2127
Important Dates:
Wednesday January 18th Quiz 1.
Monday January 30th Quiz 2.
Friday February 10th Midterm.
Wednesday February 22nd Quiz 3.
Monday March 6th Quiz 4.
Friday March 17th Last day of instruction.
Monday March 20th Final Exam (1:00 PM).
Problem Sets: Weekly assignments are due on Fridays, to be submitted through Gradescope.
MAT 22AL: MAT 22A students are required to take 22AL, unless they have taken Eng 6 or have a good knowledge of MATLAB and its use in Linear Algebra. If you are enrolled in Eng 6 this quarter, you still need to take MAT22AL. Click here for the MAT 22AL course webpage.
Tips on Mathematical Writing:
https://www.maths.ed.ac.uk/~tl/tips.pdf
https://math.rice.edu/~notlaw/Su-Guidelines_for_Good_Mathematical_Writing.pdf
Problem set 1: Available Jan 10. Due Jan 20
Problem set 2: Available Jan 20 . Due Jan 27
Problem set 3: Available Jan 29 . Due Feb 4
Problem set 4: Available Feb 11. Due Feb 18
Problem set 5: Available Feb 18 Due Feb 25
Problem set 6: Available Feb 25 . Due March 4
Redo midterm: Pick up midterm between Feb 24-March 1st. Due March 3rd in class.
Problem set 7: Available March 4 . Due March 11
Problem set 8: Available March 12. Due March 17
Practice Final 2 (from Strang)
Some partial answer keys/sketches of answer keys:
(with suggested readings and notes)
Monday Jan 9 : Vectors
1.1 Vectors and linear combinations
Wednesday Jan 11: The dot product
1.2 Lengths and dot products
Friday Jan 13: Vector spaces, subspaces and matrices
1.3 Matrices.
Monday Jan 16: MLK day - university holiday.
Wednesday Jan 17: Subspaces+ Solutions to linear systems of equations 1
2.1 Vectors and linear equations, 2.2 The idea of elimination.
Finished Lecture 3 and started lecture 4.
Friday Jan 20: Solutions to linear systems of equations 1 continued
2.1 Vectors and linear equations, 2.2 The idea of elimination.
Continued lecture 4.
Monday January 23: Solutions to linear systems of equations 2
2.3 Elimination using matrices, 2.4 Rules for matrix operations,
Wednesday Jan 25: Intro to matrix inverses
2.5 Inverse matrices, 2.6 Elimination=Factorization: A=LU 2.7 Transpose and permutations
Friday Jan 27: 12th day of instruction. Vector spaces and bases
3.1 Spaces and vectors. 3.4 Independence, Basis and Dimension
Monday Jan 20: Vector spaces and basis continued
3.4 Independence, Basis and Dimension
Wednesday Feb 1: Vector spaces and basis continued
finished
Friday Feb 3: Linear Transformations
8.1 Linear Transformations
Lecture 9
Monday Feb 6:
Extra on linear transformations
Wednesday Feb 8: 20th day of instruction: Review
Started: Lecture 11
Friday Feb 10: Midterm
Monday Feb 13: Nullspace and Range
3.4 Nullspace. Finished Lecture 11
Wednesday Feb 15: 25th day of instruction. Inverses of Matrices and the 4 subspaces associated to a matrix
3.5 Dimensions of the 4 subspaces
Covered 1/2 of Lecture on inverses and 1/2 of Lecture on change of basis.
Friday Feb 17: Change of basis and orthonormal basis
Finished Lecture on change of basis.
Monday Feb 20: Presidents' day - university holiday.
Wednesday Feb 22: Projections
4.1 Orthogonality of vectors and subspaces, 4.2 Projections
Finished Lecture on inverses covered how Row space of a matrix is orthogonal to the null space.
Lecture on Projections (started)
Friday Feb 24: 4.1 Orthogonality of vectors and subspaces, 4.2 Projections + 4.4 Orthogonal matrices and Gram Schmidt
Lecture on Projections
Monday Feb 27: Least square approximations
4.3 Least squares approximations
Lecture on Least square approximations
Wednesday March 1: The determinant of a matrix
5.3 Areas and volumes by determinants
5.1 3x3 determinants and cofactors, 5.2 Computing and using determinants
Lecture on determinants
Friday March 3: Determinants
Lecture on determinants finished, started lecture on Cramers rule
Monday March 6+ Wednesday March 8: Determinants
Lecture on cramers rule
Friday March 10th: Eigenvalues of a matrix
6.1 Introduction to eigenvalues.
6.2 Diagonalizing a Matrix,
Lecture on eigenvectors
Monday March 13: Eigenvectors continued
6.1 Introduction to eigenvalues.
6.2 Diagonalizing a Matrix,
Finish lecture on eigenvectors
start Lecture on eigenvectors+diagonalizing matrices and odes
Wednesday March 15:
: Eigenvectors continued and Solving Linear Differential equations
6.5Solving Linear Differential equations
Lecture on eigenvectors+diagonalizing matrices and odes
Friday March 17: Instruction Ends
Review!
Monday March 20 : Final exam