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Class Details |
Fall 2009
Wednesdays, 10.00 – 13.00 hrs
Location to be confirmed. |
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Prerequisites |
Pre -calculus and High School Geometry |
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Class
Description |
This is an introductory course in the theory of linear transformations
and abstract vector spaces. It is
designed to familiarize students with the basic concept of a vector
space and its algebraic properties and
the manipulative techniques necessary to use matrices and determinants
in solving applied problems.
The course supports many applications in engineering, science,
statistics and operations research .
The course is delivered through lectures and discussions. The amount of
material to be covered does not
allow for complete proofs to be given in class of all the results that
are important. The instructor is
responsible for choosing a representative sample of proofs that
illustrate the most common techniques .
Students are expected to understand other proofs through careful reading
of the text. |
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Desired
Outcomes |
At the end of this course, students will be able to:
• Understand the dimension of a vector space, rank of a matrix and basis
for a vector space
• Reduce a matrix using Gauss-Jordan reduction, find the inverse of a
matrix and solve a system of n
equations and m variables
• Use the LU decomposition to solve systems of linear equations
• Understand the concept of spanning sets, linear independence , linear
transformation and
determinants
• Find eigenvalues and eigenvectors, and diagonalize matrices. |
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Assessment
Components |
There will be weekly assignments, a midterm exam and a final exam.
Assignments will be given at the
end of each lecture, except for the last lecture. These assignments must
be completed on a weekly basis
and submitted at the beginning of the following lecture. Late submission
of assignments is not
permitted. The breakdown of marks will be:
Weekly assignments = 30%, Mid- term Exam = 30% and Final Exam = 40%
Failure to submit or fulfill any required course component results in
failure of the class. |
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Assessment
Expectations |
Grade A: A=94-100, A-=90-93
Grade B: B+=87-89, B=84-86, B-=80-83
Grade C: C+=77-79, C=74-76, C-=70-73
Grade D: D+=67-69, D=65-66
Grade F: F=below 65 |
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Required
Text(s) |
Linear Algebra , A Modern Introduction (2nd Edition), Brooks-Cole
Publishing Company, 2006. By
David Poole. ISBN: 0-534-99845-3/0-534-40596-7 |
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Supplemental
Texts(s) (not
required to
purchase as
copies are in
NYU-L Library)
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1. Elementary Linear Algebra, McGraw-Hill, Inc., 1988. By William L.
Perry, ISBN:0-07-049431-2
2. Linear Algebra and Its Applications, Thomson Brooks/Cole., 2006. By
Gilbert Strang, ISBN:
0534422004
3. Matrix Theory and Linear Algebra, Macmillan Publishers, 1988. By I.N.
Herstein and David J.
Winter, ISBN: 0023539518 |
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Internet
Research
Guidelines |
N/A
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Additional
Required
Equipment |
A scientific calculator
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Session 1
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Vectors: The Geometry and Algebra of Vectors (1.1), Length and Angle:
The Dot Product (1.2).
Exercises 1.1 and 1.2 |
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09-09-09 |
Assignment due on Wednesday 16th September 2009 |
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Session 2
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Systems of Linear Equations : Introduction to Systems of Linear Equations
(2.1) and Computer lab.
Exercises 2.1 |
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16-09-09 |
Assignment due on Wednesday 23th September 2009 |
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Session 3 |
Systems of Linear Equations: Direct Methods for Solving Linear Systems
(2.2). Exercises 2.2 |
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23-09-09 |
Assignment due on Wednesday 30th September 2009 |
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Session 4 |
Systems of Linear Equations: Spanning Sets and Linear Independence
(2.3). Exercises 2.3 |
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30-09-09 |
Assignment due on Wednesday 7th October 2009 |
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Session 5 |
Systems of Linear Equations: Applications (2.4) and Computer lab.
Exercises 2.4 |
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07-10-09 |
Assignment due on Wednesday 14th October 2009 |
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Session 6 |
Matrices: Matrix Operations (3.1) and Matrix Algebra (3.2). Exercises
3.1 and 3.2 |
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14-10-09 |
Assignment due on Wednesday 21stOctober 2009 |
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Session 7 |
Matrices: The Inverse of a Matrix (3.3) and The LU Factorization (3.4).
Exercises 3.3 and 3.4 |
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21-10-09 |
Assignment due on Wednesday 28th October 2009 |
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Session 8
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Revision and a two hour midterm exam
(No assignment) |
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28-10-09 |
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Session 9 |
Matrices: Subspaces, Basis, Dimensions, and Rank (3.5). Exercises 3.5 |
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30-10-09 |
Assignment due on Wednesday 4th November 2009 |
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Session 10 |
Matrices: Introduction to Linear Transformations (3.6) |
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04-11-09
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Eigenvalues and Eigenvectors: Introduction to Eigenvalues and
Eigenvectors (4.1).
Exercises 3.6 and 4.1
Assignment due on Wednesday 18th November 2009 |
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Session 11 |
Eigenvalues and Eigenvectors: Determinants (4.2). Exercises 4.2 |
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18-11-09 |
Assignment due on Wednesday 25th November 2009 |
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Session 12
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Eigenvalues and Eigenvectors: Eigenvalues and Eigenvectors of nXn
matrices (4.3).
Exercises 4.3 |
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25-11-09 |
Assignment due on Wednesday 2nd December 2009 |
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Session 13 |
Eigenvalues and Eigenvectors: Similarity and Diagonalization (4.4).
Exercises 4.4 |
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02-12-09 |
Assignment due on Wednesday 9th December 2009 |
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Session 14 |
The General Vector Spaces: Vector Spaces and Subspaces (6.1). Exercises
6.1 |
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09-12-09 |
No Assignment |
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Session 15 |
The final examination will last two hours and thirty minutes. |
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16-12-09 |
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Classroom
Etiquette |
Eating is not permitted in any classrooms in 6 Bedford Square or at
Birkbeck College. Please kindly
dispose of rubbish in the bins provided. |
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Required Co-curricular |
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