Polytechnic Institute of New York University
Mathematics
Course Outline for MA2012 Linear Algebra
Fall 2011
All Sections
Course Coordinator: Dr. Lindsey Van Wagenen
Contact Information: Office: RH305D
Email: vwagenen@poly.edu
Phone: 718-260-3737
Office Hours: Monday & Wednesday 3:00—5:30PM
Thursday 12:00—1:00PM
Course Website: www.math.poly.edu
Course Pre-requisites: You are expected to have mastery of the concepts and
skills covered in MA0914, MA1024/1324, and MA1124/1424.
Course Description: Linear algebra is central to modern mathematics. The
concepts in linear algebra have the power to explain fundamental principles and
simplify calculations in engineering, computer science, mathematics, physics,
biology, statistics, digital media and economics. In this course you will learn the
basic concepts and skills of linear algebra that are needed for later math courses,
such as differential equations, multivariable calculus, and by other courses needed
for your major. The course combines abstract thinking with elementary
calculations. The abstract concepts you will learn in linear algebra are as important
as the computations.
Course Objectives: Students are expected to:
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Formulate, solve, apply, and interpret systems of linear equations in several
variables using Gaussian elimination;
Learn the properties of matrices and apply them to the solutions of systems
of linear equations;
Understand the notions of vector spaces and basis, and apply their
understanding to the solution of problems;
Develop an understanding of linear transformations and be able to apply
that knowledge;
Learn to calculate eigenvalues and eigenvectors, and be able to use them in
context.
Course Structure: The 2-credit, half semester course meets for lecture twice a
week for 110 minutes each class. You are also expected to study outside of class, a
good ‘rule of thumb ‘ is three hours of study for each hour of class.
Course Requirements: (The grading policy is detailed in a section below).
 Twice Weekly Lecture
 WileyPLUS Online Homework—WileyPLUS is free for Fall 2011.
 Midterm Exam M/W sections, 9/28; T/Th sections 9/27 in class.
 Final Exam M/W sections, 10/26; T/Th sections 10/25 in class.
Examinations: One 105-minute midterm given during class time, and a 105-minute
cumulative Final during class time (in the first half of the semester) and during
finals week (in the second half of the semester). The only calculator permitted is
the TI-30, no substitutions.
Textbook The required text for the course is:
Elementary Linear Algebra by Howard Anton. Wiley and Sons, 2010.
ISBN 978-0-470-45821-1.
New copies are on sale in the bookstore, and new and used copies of previous
editions are available online. We will be using the online homework system,
WileyPLUS for homework this semester. WileyPLUS is FREE for this course for
the Fall 2011 semester, and WileyPLUS homework assignments will count towards
your final grade. WileyPLUS contains many helpful study tips and resources and has
an e-book associated with it. You will want to spend some time to become
acquainted with WileyPLUS and this can be done by viewing the online introductory
tutorials.
WileyPLUS
To log in to WileyPLUS go to www.wileyplus.com, go to the student’s section on the
first page, lower right, click on next, identify your institution, Polytechnic
Institute of NYU, and then select Math 2012 (2010) and follow the instructions.
(The folks at Wiley made an error and they are calling the class MA2010/2012, it
is the same MA2012 course—all Linear Algebra courses will use this section unless
otherwise directed by your instructor.)
If you have any problems with WileyPLUS you can email either, Dr. Van Wagenen at
vwagenen@poly.edu or Luciano Medina at lmedin02@hotmail.com.
Grading Policy
Course Grade: Final grades will be calculated according to the rules below. The
course grade is determined by the best of your course averages using the table
below.
Average 1 Average 2
Midterm
35%
15%
Final Exam 50%
80%
Homework 15%
5%
Information about the grading scale conversion to letter grades can be found on
www.math.poly.edu.
Course Lecture Syllabus (The sections are quoted from the 10th edition of
Anton.)
Lecture 1
 Section 1.1 Introduction to Systems of Equations
 Section 1.2 Gaussian Elimination & Applications Problems
Lecture 2
 Section 1.3 Matrices and Matrix Operations
 Section 1.4 Inverses and the Algebraic Properties of Matrices
 Section 1.5 Elementary Matrices and Finding the Inverse of a Matrix
Lecture 3
 Section 1.6 More on Linear Systems and Invertible Matrices
 Section 1.7 Diagonal, Triangular, and Symmetric Matrices
Lecture 4
 Section 2.2 Evaluating Determinants by Row Reduction
 Section 2.3 Properties of Determinants
Lecture 5
 Section 2.1 Determinants by Cofactor Expansion
 Section 4.1 Real Vector Spaces
Lecture 6
 Section 4.2 Subspaces
 Review
Lecture 7
Midterm Examination
Lecture 8
 Section 4. 3 Linear Independence
Lecture 9
 Section 4.4 Coordinates and Basis
 Section 4.5 Dimension
Lecture 10
 Section 4.6 Change of Basis
 Section 4.7 Row Space, Column Space, and Null Space
Lecture 11
 Section 4.8 Rank, Nullity and the Fundamental Matrix Spaces
 Section 4.9 Matrix Transformations ( until the rotation operations) &
Examples from Section 8.1
Lecture 12
 Section 5.1 Eigenvalues and Eigenvectors
 Section 5.2 Diagonalization
Lecture 13
 Section 5.2 Diagonalization
 Review
Lecture 14 Comprehensive Final Exam—Includes all material covered in the
course.
Additional Learning Resources:
General Evening Math Workshops
Days
Hours
Monday-Thursday 6PM-9PM
Location
JAB373
Room 2C
General Math Workshops
Days
Hours
Location
Friday
9AM-6PM
RH315
Saturday 10AM-2PM
RH707
Internet Resources
Math Department Website: www.math.poly.edu. This comprehensive website has
the course policies as well as old exam and practice materials for both the midterm
and final exam.
http://web.mit.edu/18.06/www/Video/video-fall-99.html
http://tutorial.math.lamar.edu/ Paul’s Online Math Notes,
Choose Class Notes and then the course you want.
Important: General Exam Policies
Valuables (especially your laptop!):
Please do not bring your laptop or any other valuable items to the exam. You are
required to leave your bags and books at the front of the exam room.
Time and Place:
It is your responsibility to consult the web site to know when and where an exam is
being held. You will not receive any special consideration for being late or missing
an exam by mistake.
Identification:
You are required to bring your Polytechnic ID to the exam. If for any reason you
are unable to do so, another photo ID, such as a drivers license, is acceptable.
Before the Exam:
You must wait outside the exam room before the start of an exam. You must sit
only in seats where there is an exam for your course. You must not move the exam
to a different seat.
Neatness and Legibility:
You are expected to write as neatly and legibly on your exam. Your final answer
must be clearly identified (by placing a box around it). Points will be deducted if
the grader has difficulty reading or finding your answer.
Missed Exams:
If you missed an exam due to a medical reason, then University policy requires you
to provide written documentation to the Office of Student Development (JB158).
It is University policy that the Mathematics Department may not give make-up
exams without prior authorization by the Office of Student Development.
Academic Integrity:
Any incident of cheating or dishonesty will be dealt with swiftly and severely. The
University does not tolerate cheating. (There is no such thing as "a little bit of
cheating.") During an exam you are not allowed to borrow or lend a calculator;
borrowing or lending a calculator will be considered cheating.
TI-30 is the only calculator allowed! No Exceptions