# Intro to Linear Algebra

 Item Date Information Textbook: There is no textbook. I will post all lecture notes on this webpage. For supplementary reading I recommend Gilbert Strang's Introduction to Linear Algebra (any edition). Lecture: 10:05-11:30 MTuWThF on Zoom Office Hours: 11:30-12:30 MTuWTh on Zoom Here is the course syllabus. Here is an article by Alan Tucker (1993) on The Growing Importance of Linear Algebra in Undergraduate Mathematics. Quote: This author is personally a bit frustrated that calculus gets all of the first year and half of the second year of the lower-divison core mathematics sequence. Hopefully early in the next century, there will be a 'redistricting' of the lower- division mathematics sequence and linear algebra will get equal time with calculus. Homework 1 Solutions Fri, May 22 Points vs. Vectors Vector Arithmetic, Pythagorean Theorem Lots of Examples Vector Space Concept, Introduction to Linear Equations HW1 Discussion, Lines and Hyperplanes Quiz1 Example Solutions Tues, May 26 20 minutes at the beginning of class Homework 2 Solutions Fri, May 29 Two or Three Lines in 2D, Two Planes in 3D The Idea of Elimination, Two or Three Planes in 3D Independence and Dimension, 2 Equations in 4 Unknowns HW2 Discussion, Determinant of a 2X2 Matrix Quiz2 Solutions Mon, Jun 1 20 minutes at the beginning of class Homework 3 Solutions Fri, June 5 Some Technical Definitions, Gaussian Elimination Gaussian Elimination on a Computer, Interpreting the RREF Review of RREF, Definition of Ax=b Fundamental Theorem of Linear Algebra HW3 Discussion, FTLA Discussion Quiz3 Solutions Mon, Jun 8 20 minutes at the beginning of class Homework 4 Solutions Fri, June 12 Matrices = Linear Functions Matrix Multiplication = Composition of Linear Functions Matrices in Calculus, Matrix Arithmetic Invertibility of Functions and Matrices HW4 Discussion, Orthogonal Matrices Quiz4 Solutions Mon, Jun 8 20 minutes at the beginning of class Homework 5 Solutions Mon, June 22 Least Squares Approximation Projection Onto a Subspace Review of Projection, Introduction to Diagonalization Computation of Eigenvalues and Eigenvectors Linear Systems of Recurrence and Differential Equations HW5 Discussion, Non-Orthogonal Projections Quiz5 Solutions Tues, June 23 20 minutes at the beginning of class Discussion and Review Why do we call it Diagonalization? Complex Numbers, Spectral Theorem, Singular Value Decomposition ... Final Project Fri, June 26 Write a summary of what you learned in the course. Minimum 2 pages, Maximum 10 pages