Download NYIT Mathematics Department

http://iris.nyit.edu/~asilvers/310s16.htm
INFORMATION SHEET -- MATH 310 — Spring 2016
INSTRUCTOR Dr. Anna Silverstein
OFFICE Room 214, Schure Hall
PHONE (516) 686-1092
INSTRUCTOR WEB PAGE http://iris.nyit.edu/~asilvers/
E-MAIL ADDRESS [email protected]
OFFICE HOURS
Mon..
Noon to 1:30 pm, 4:30-6 pm
Tue.
9:30 am to 12:30 pm
Wed.
Noon to 1:30 pm
Thur.
10:30 am to 1:30 pm
PREREQUISITE The prerequisite for Linear Algebra is Calculus II (Math 180). It is recommended that those
students requiring Calculus III (Math 260) take Math 260 before this course if possible so that the vector space
concepts will seem less abstract.
STUDENT CONFERENCES You are invited to meet with me at any time to discuss any concerns you may
have. These would include discussing the specific goals of the course, going over material you missed when
absent, discussing a special situation which affects you, assessing progress in the course, and many other
issues. It is always a good idea to make an appointment if you have to miss a class for any reason.
MATHEMATICS RESOURCE CENTER
The Math Center, located in Harry Schure Hall, room 214, provides tutoring assistance for all math
classes at NYIT. All instruction is by experienced and caring NYIT math faculty. Math can cause much anxiety;
the Center is set up to help you deal with that anxiety and get the most out of your class. Any student can
stop by to schedule regular assistance or to get immediate help. The Center is open daily Monday to Thursday.
Call for more information at 516-686-1092.
TEXT Elementary Linear Algebra, 9th Ed., Bernard Kolman, Prentice Hall, 2008 (ISBN 0-13-229654-3). There
is also an excellent student study guide available for this text; I recommend it highly.
CALCULATOR You must have a TI-84, TI-83 or TI-89 calculator for quizzes and tests within the first two
weeks. The calculator will save many repetitive steps in transforming matrices (row reduction), finding
inverses, and determinants. Class demonstrations on the TI-84 will illustrate calculator techniques so you will
be able to easily follow the steps.
TOPICS TO BE COVERED The course is organized by exam into two major units. The final will cover these
two units plus some additional topics, as specified below.
I. Systems of Linear Equations, Matrix Operations and Properties, Echelon Form, Inverse of a Matrix,
Elementary Matrices, Definition of Determinant (Text Sections 1.1-1.5, 2.1-2.3, 3.1) EXAM DATE Wed., Feb.
24
II. Properties of Determinant, Cofactors, Applications of Determinant, Vector Spaces, Subspaces, Spanning,
Linear Independence (Secs. 3.2-3.4, 4.1-4.5) EXAM DATE Wed., March 30
III. Basis and Dimension, Homogeneous Systems, Rank of a Matrix, Linear Transformations, Range and
Kernel, Coordinates and Isomorphisms, The Matrix of a Linear Transformation, (Secs. 4.6-4.9, 6.1-6.3) EXAM
DATE Wed., April 27
The final exam will cover all of the above, plus Eigenvalues and Diagonalizaiton (Secs. 7.1-7.2). FINAL EXAM
WEEK May 16-20
STUDENT RESPONSIBILITIES You should complete the text assignment given on the course outline after
each lesson. It is not necessary to hand in solutions to these assignments, although it is expected that you will
keep them together in convenient form for reference before quizzes and tests. You should check all answers
to odd-numbered problems in the back of the text; if you have any questions about the solutions, this can be
brought up at the next class.
There will be three hourly exams (see dates above). In addition, there will be a quiz each week, except
during the same week as an exam. Be sure to go over the quiz problems thoroughly before each exam,
including the final, as many of the quiz problems will be similar to those on the exam. For all four exams there
will be two parts. The first part is to be done without a calculator; on the second part a calculator is permitted.
The first quiz will be on Wed., Jan. 27.
The final exam will be departmental and cumulative. The final exam grade itself must be higher than 40,
regardless of the computed average, for you to pass the course. No one will be exempted from the final.
EXAM POLICIES
1) No cell phones or other interruptions are allowed during exams. (Visit the rest room before taking the
test!)
2) No notes or books may be used.
3) No makeups of exams or quizzes are permitted.
ABSENCE POLICY
You are not permitted to miss more than 20% of the class meetings (6 or more classes). You may be
automatically dropped from the class if you are absent 6 or more times.
WITHDRAWAL FROM THE COURSE
Please be aware of the current policy at NYIT on withdrawals. You may not receive an official withdrawal (W)
from any course more than 8 weeks into the semester unless you are passing the course at the time of
withdrawal and fill out the appropriate forms. After 8 weeks, if you are not passing but stop attending, you
receive a WF. Even if you stop attending within the first few weeks, NYIT now requires that a drop form be
filled out and signed by the student and instructor. If the form is not filed during the semester, the grading
system has no provision for a faculty member to fill in a W at the end of the semester. This semester the eighth
week ends on March 17.
BREAKDOWN OF THE COURSE GRADE
Hourly exams
60%
Final Exam
25%
Quizzes (best 6)
15%
COURSE LEARNING OUTCOMES – MATH 310
Upon successful completion of this course, students will be able to:
1. Use Gaussian elimination to solve a system of m equations in n unknowns.
2. Find the inverse of a nonsingular matrix using Gauss-Jordan reduction.
3. Decompose a nonsingular matrix into a product of elementary matrices.
4. Determine if a subset of a vector space V is a subspace by checking closure under addition and
scalar multiplication.
5. Determine if a set of vectors is linearly independent.
6. Write a vector in a dependent set T as a linear combination of the other vectors in T.
7. Determine if a set of vectors spans a given vector space V.
8. Given a basis S for a vector space V, write any vector in V as a linear combination of vectors in
S.
9. Find the dimension of a vector space S.
10. Find a basis for a subspace of Rn.
11. Apply all vector space procedures to polynomial spaces, matrix spaces, column spaces and row
spaces.
12. Determine if a mapping between two vector spaces is a linear transformation by checking the
addition and scalar mpultiplication properties.
13. Find the kernel and range of a linear transformation.
14. Determine if a given linear transformation is one-one or onto.
15. Find the representation matrix for a given linear transformation relative to arbitrary bases for the
domain and codomain spaces.
16. Find the eigenvalues and corresponding eigenvectors of a square matrix A.
Math 310 Syllabus