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)