Spring 2016 Math 13 (Linear Algebra) (4294) 7:35-8:55 PM MW (MC-67) Instructor: Discussion Class: E-Mail: Web Site: Sohail Askarian Monday & Wednesday 6:25-7:15 PM (MC-63) Askarian_Sohail@smc.edu http://www.mathjoys.com Prerequisites: Required Text: Math 8 with a grade of C or better (Math 11 and 15 are recommended) Recommended Text: Grossman, Stanley; Elementary Linear Algebra, 5th Edition, Saunders College Publishing, 1994 (On reserve in the library) Course Objectives: SLO: Larson, R. and D. Falvo, Elementary Linear Algebra, 7th Ed., Cengage, 2013 Apply the concepts and theorems of linear algebra, and appropriate proof-writing techniques, to show the consequences of a given definition, prove statements, and disprove statements using counterexamples. Perform matrix computations and prove general properties of matrix algebra. Express a matrix as a product of elementary matrices and an upper triangular matrix. Compute the inverse, if possible, of a square matrix, and express it as a product of elementary matrices. Solve systems of linear equations using Gaussian and Gauss-Jordan elimination and matrix inverses, and, where necessary, express solutions using parameters or as a linear combination of basis vectors. Apply fundamental determinant theorems. Prove whether or not a set and operations form a vector space (or subspace). Apply the concepts of linear independence and spanning to find a basis for a vector space. Prove whether or not a function between two vector spaces is a linear transformation or isomorphism. Find the matrix representation of a linear transformation with respect to two given ordered bases. Find the dimension of spaces such as those associated with matrices and linear transformations. Express the kernel and range of a linear transformation as a span of basis vectors. Compute the eigenvalues for a matrix, find a basis for the corresponding eigenspaces, and where possible, diagonalize the matrix. Use eigenvalues and eigenvectors in applications. Use the Gram-Schmidt process to compute an orthonormal basis of a space. Use bases and orthonormal bases to solve problems in linear algebra. Student Learning Outcome: Apply definitions and theorems of linear algebra, with topics including linear independence, spanning, dimension, subspaces and linear transformations, to establish consequences of new definitions, prove additional results, and illustrate arguments with specific examples. Additional Resources: Math Lab located in MC-84. Calculators: No graphing calculators are allowed on the exams. Regular scientific calculators are okay. Homework (10%): Homework is a very important part of math learning process. Homework assignments are collected at the start of every meeting. Homework assignments are checked for completeness, neatness, format and accuracy. Late homework is not accepted. Exams (60%): Three exams are given. Makeup exams are not given for any reason. Dates of exams are preset, so mark your calendar! Final Exam (30%): The final exam is cumulative. So, prepare for it throughout the semester. Grading Policy (NonNegotiable!): Drop Policies: 90-100% = A; 80-89.9% = B; 70-79.9% = C; 50-69.9% = D; 0-49% = F I consider dropping anyone with more than 2 days of absence or tardiness. Every student is personally responsible to find out about drop deadlines of school. Math 13 Room: MC-67 Spring 2016 Calendar of Events DATE 2-17-16 2-22-16 2-24/3-7 3-9/3-21 3-23-16 3-28-16 3-30/4-6 4-11/4-16 4-18/4-20 4-25-16 4-27-16 5-2/5-11 5-16/5-25 5-30-16 6-1-16* 6-6-16 6-8-16 CHAP Intro, 1.1 1 2 3 4 ♪♪♪♪ 4 ☺ 4 ♪♪♪♪ 5.3 6 7 ☺ ♪♪♪♪ 7 ♫♫♫♫♫ DESCRIPTION Introduction, read 1.1 Gauss-Jordan Elimination Matrices Determinants Vector Spaces Exam #1, Chap. 1, 2, 3, 4 (partial) Vector Spaces Spring Break (try not to forget everything!) Vector Spaces Exam #2, Chap. 4 Gram-Schmidt Process Linear Transformations Eigenvalues and Eigenvectors Memorial Day (Legal Holiday) Exam #3, Chap. 5.3, 6, 7 Eigenvalues and Eigenvectors Final Exam (Note the time: 6:45 – 9:45 pm)