MATH2360 -- Linear Algebra

Fall 2015

Instructor: Josh Engwer

"Mathematics, you see, is not a spectator sport." -- George Polya, circa 1969.

Course Calendar:

(DEMOS) -- Visual Demonstrations of Key Concepts. Requires the free Wolfram CDF Player.

DATE:		OUTLINES:	SLIDES:	DEMOS:	NOTES:	DESCRIPTION:
08/24	Mon	1.1	1.1		[GREEK-ALPHABET] [LOGIC-SETS]	Linear Systems (Ax=b): Intro, Interpretation
08/26	Wed	1.2	1.2		Some matrices on WeBWorK look "crammed" --> PNG	Solving Ax=b: Gauss-Jordan Elimination
08/28	Fri	1.2	1.2		[EX 1.2.{3-8} SOLUTIONS]	Solving Ax=b: Gauss-Jordan Elimination (cont'd)
08/31	Mon	1.3	1.3		[EX 1.3.{1,2} SOLUTIONS]	Constructing Ax=b: Curve Interpolation
09/02	Wed	2.1	2.1			Matrix Algebra: Matrix+Matrix, Scalar*Matrix, Transposes
09/04	Fri	2.1	2.1		[EX 2.1.3 SOLUTIONS]	Matrix Algebra: MatrixMatrix, MatrixVector
09/07	Mon	********	********	********	LABOR DAY	<< NO CLASS >>
09/09	Wed	2.2	2.2			Matrix Algebra: Properties, Zero/Identity/Diagonal Matrices
09/11	Fri	2.3	2.3		[EX 2.3.{1,2,3,4} SOLUTIONS]	Solving Square Ax=b: Inverse of a Square Matrix, Properties
09/14	Mon	2.4	2.4		[EX 2.4.1{1,2,3} SOLUTIONS]	Solving Ax=b with different b's:A=LU, Triangular Matrices
09/16	Wed	********	********	********		REVIEW FOR EXAM 1
09/17	Thurs	********	********	********	Time: 7pm - 11pm Location: MATH 108	LAST-MINUTE HELP SESSION FOR EXAM 1
09/18	Fri	********	********	********	EXAM 1 Info/Logistics/Advice	EXAM 1
09/21	Mon	3.1	3.1		[EX 3.1.{2,4,5} SOLUTIONS]	Determinants of Sparse Square Matrices: Minors/Cofactors
09/23	Wed	3.2	3.2		[EX 3.2.2 SOLUTIONS]	Determinants of Dense Square Matrices: Elementary Row Operations
09/25	Fri	3.3	3.3			Determinants: Products, Inverses, Transposes
09/28	Mon	3.4	3.4			Determinants: Adjoints, Cramer's Rule, Applications in Geometry
09/30	Wed	4.2	4.2		[EX 4.2.{2,3,4} SOLUTIONS]	Vector Spaces: Definition, Counterexamples
10/02	Fri	4.3	4.3		[EX 4.3.{1-6} SOLUTIONS]	Vector Spaces: Subspaces, Counterexamples
10/05	Mon	4.4	4.4		[EX 4.4.{3,4,5,6} SOLUTIONS]	Vector Spaces: Linear Combinations
10/07	Wed	4.4	4.4		[EX 4.4.{10,11} SOLUTIONS]	Vector Spaces: Spanning Sets, Linear Independence (of vectors)
10/09	Fri	4.5	4.5		[EX 4.5.{1-6} SOLUTIONS]	Vector Spaces: Bases, Dimension
10/12	Mon	4.6	4.6		[EX 4.6.{1,2,3} SOLUTIONS]	Subspaces of a Matrix: Row Space, Column Space, Rank
10/14	Wed	4.6	4.6		[EX 4.6.{4-9} SOLUTIONS]	Subspaces of a Matrix: Null Space, Homogeneous Solns to Ax=b
10/16	Fri	4.7	4.7		[EX 4.7.{1-4} SOLUTIONS]	Change of Basis: Coordinate Vector, Transition Matrix
10/19	Mon	********	********	********		REVIEW FOR EXAM 2
10/21	Wed	********	********	********		REVIEW FOR EXAM 2
10/22	Thurs	********	********	********	Time: 7pm - 11pm Location: MATH 108	LAST-MINUTE HELP SESSION FOR EXAM 2
10/23	Fri	********	********	********	EXAM 2 Info/Logistics/Advice	EXAM 2
10/26	Mon	5.1	5.1		[EX 5.1.3 SOLUTIONS] LAST DAY TO DROP	Vectors: Norms, Dot Products, Projections, Projection Matrices
10/28	Wed	5.2	5.2		[EX 5.2.{1-4} SOLUTIONS]	Inner Product Spaces: Norms, Inner Products, Projections
10/30	Fri	5.3	5.3		[EX 5.3.{2,3} SOLUTIONS]	Orthonormal Bases, Subspace Projections, Gram-Schmidt, Reduced A=QR
11/02	Mon	5.4	5.4			Orthogonal Complements, Full A=QR, Orthogonal Matrices
11/04	Wed	5.4	5.4		[EX 5.4.{1,2,3,4,5,6} SOLUTIONS]	Best Approx. to Overdetermined Ax=b: Full-Rank Least-Squares
11/06	Fri	6.1	6.1		[EX 6.1.{1-19} SOLUTIONS]	Linear Transformations: Definition, Image, Range
11/09	Mon	6.2	6.2		[EX 6.2.{2,3} SOLUTIONS]	Linear Transformations: Preimage, Kernel, Isomorphisms
11/11	Wed	6.3	6.3			Linear Transformations: Standard Matrix (part 1)
11/13	Fri	6.3	6.3		[EX 6.3.{2-5} SOLUTIONS]	Linear Transformations: Standard Matrix (part 2)
11/16	Mon	********	********	********		REVIEW FOR EXAM 3
11/17	Tues	********	********	********	Time: 7pm - 11pm Location: MATH 108	LAST-MINUTE HELP SESSION FOR EXAM 3
11/18	Wed	********	********	********	EXAM 3 Info/Logistics/Advice	EXAM 3
11/20	Fri	7.1	7.1		[EX 7.1.{2,3} SOLUTIONS]	Solving Square Ax=λx: Eigenvalues, Eigenvectors, Eigenspaces (part 1)
11/23	Mon	7.1	7.1		[EX 7.1.{5,6,7} SOLUTIONS]	Solving Square Ax=λx: Eigenvalues, Eigenvectors, Eigenspaces (parts 2&3)
11/25	Wed	********	********	********	THANKSGIVING	<< NO CLASS >>
11/27	Fri	********	********	********	THANKSGIVING	<< NO CLASS >>
11/30	Mon	7.2	7.2		[EX 7.2.3 SOLUTIONS]	Diagonalization (A=XΛX^-1), Powers of a Square Matrix (revisited)
12/02	Wed	7.3	7.3		[EX 7.3.{4,5,6} SOLUTIONS]	Symmetric Matrices, Orthogonal Matrices, Orthogonal Diagonalization (S=QΛQ^T)
12/07	Mon	********	********	********	EXTENDED OFFICE HOURS: 8:30am - 3:30pm	EXTENDED OFFICE HOURS (FOR LAST-MINUTE HELP)
12/08	Tues	********	********	********	FINAL EXAM Info/Logistics/Advice	FINAL EXAM 7:30am - 10:00am

Course Epilogue

Singular Value Decomposition (A=UΣV^T) (Slides) (Outline) (Outline Solutions)
Householder Reflectors (Slides) (Outline) (Outline Solutions)

Back to Courses

Best viewed at 1280x720 (720p) screen resolution or higher.