MTH 132 (sec 104) Syllabus Fall 2004
MTH 331 (sec 101) Syllabus Fall 2010
CRN 4278
Prerequisites: MTH 300 with a grade of C or higher, fairly recently.
Course Objectives : Methods of solving linear systems, matrices and applications,
vector spaces, linear transformations, eigenvalues and eigenvectors,
inner product spaces and much more.........
Meeting time : M T W R 11 – 11:50 am Room 518 Smith Hall
( 4 credit hours )
Instructor : Dr. Alan Horwitz Office : Room 741 Smith Hall
Phone : (304)696-3046 Email : horwitz@marshall.edu
Text : Linear Algebra with Applications , 4th Edition , Otto Bretscher, Prentice Hall
Grading : attendance 4% (23 points )
surprise quizzes and Mathematica lab assignments 21% (117 points)
at least 3 major exams 54% (300 points)
(if we have 4 exams, then your grade will be based on the three highest scores)
final( comprehensive ) exam 21% (117 points)
Final exam date : Thursday December 9, 2010 from 10:15am -12:15 pm
General Policies :
Attendance is required and you must bring your text and graphing calculator (especially on quizzes and exams ). You are responsible for reading the text, working the exercises, coming to office hours for help when you’re stuck, and being aware of the dates for the major exams as they are announced. The TI-83 will be used in classroom demonstrations and is the recommended calculator, but you are free to use other brands (although I may not be able to help you with them in class).
Exam dates will be announced at least one week in advance. Makeup exams will be given only if you have an acceptable written excuse with evidence and/or you have obtained my prior permission.
I don’t like to give makeup exams, so don’t make a habit of requesting them. Makeups are likely to be
more difficult than the original exam and they must be taken within one calendar week of the original exam date. You can’t make up a makeup exam: if you miss your appointment for a makeup exam, then you’ll get a score of 0 on the exam.
If you anticipate being absent from an exam due to a prior commitment, let me know in advance so we can schedule a makeup. If you cannot take an exam due to sudden circumstances, you must call my office and leave a message on or before the day of the exam!
Surprise quizzes will cover material from the lectures and the suggested assigned homework exercises. Quizzes can be given at any time during the class period. No makeup quizzes will be given, but the 2 lowest quiz grades will be dropped. No Mathematica lab assignment grades and homework grades will be dropped ! The combined sum of your quiz scores ( after dropping the two lowest ) and your lab/homework assignment scores will be scaled to a 117 point possible maximum, that is, to 21% of the 557 total possible points in the course.
The Mathematica lab assignments and homework assignments should be turned in on time and should reflect your own work and thinking , not that of your classmates. If there are n lab assignments which appear to be identical, then I will grade with one score, which will be divided by n to give as the score for each assignment. For example, if three students submit identical assignments and the work gets a score of 9, then each assignment will get a score of 3.
In borderline cases, your final grade can be influenced by factors such as your record of attendance, whether or not
your exam scores have been improving during the semester, and your class participation.
Attendance Policy : This is NOT a DISTANCE LEARNING course !!!!
Attendance is 4% of your grade( 23 points total). If your grade is borderline, these points can be important
in determining the final result. Everyone starts out with 23 points, then loses 2 points for each class missed.
Your attendance score will be graded on a stricter curve than your exam scores.
Having more than 3 weeks worth of unexcused absences (i.e., 12 of 56 lectures ) will automatically result in a course grade of F! Being habitually late to class will count as an unexcused absence for each occurrence. Carrying on conversations with your neighbor could be counted as being absent. Suddenly walking out in the middle of lecture will count as an unexcused absence: if you must leave class early for a doctor’s appointment , etc., let me know at the beginning and I’ll usually be happy to give permission. Absences which can be excused include illness, emergencies, or official participation in another university activity. Documentation from an outside source ( eg. coach, doctor, court clerk…) must be provided. If you lack documentation, then I can choose whether or not to excuse your absence.
MTH 331 (sec 101) Syllabus Fall 2010
( continued )
HEED THIS WARNING:
Previously excused absences without documentation can, later, instantly change into the unexcused type if you accumulate an excessive number ( eg. more than 2 weeks worth ) of absences of any kind, both documented and undocumented : You are responsible for keeping track of the number of times you’ve been absent. I won’t tell you when you’ve reached the threshold. Attendance will be checked daily with a sign-in sheet. Signing for someone other than yourself will result in severe penalties!! Signing in, then leaving early without permission will be regarded as an unexcused absence.
Sleeping in Class :
Habitual sleeping during lectures can be considered as an unexcused absence for each occurrence. If you are that tired, go home and take a real nap! You might want to change your sleeping schedule, so that you can be awake for class.
Policy on Cap Visors :
During quizzes and exams, all cap visors will be worn backward so that I can verify that your eyes aren’t roaming to your neighbor’s paper.
Cell Phone and Pager Policy :
Unless you are a secret service agent, fireman, or paramedic on call, all electronic communication devices such as pagers and cell phones should be shut off during class. Violation of this policy can result in confiscation of your device and the forced participation in a study of the deleterious health effects of frequent cell phone use.
Student Support Services:
0. Office Hours. Schedule to be announced.
1. Math Tutoring Lab, Smith Hall Room 526. Will be opened by the start of 2nd week of
classes
2. Tutoring Services, in basement of Community and Technical College in room CTCB3.
See for more details.
3. Student Support Services Program in Prichard Hall, Room 130.
Call (304)696-3164 for more details.
4. Disabled Student Services in Prichard Hall, Room 120.
See or call (304)696-2271 for more details.
_________________________________________________________________________________
Schedule of Topics
I'm leaving this schedule BLANK because I don't know when we'll get to the topics, or even precisely which ones we will cover. You can fill it in as the semester progresses. The major exams will be roughly on the 4th, 8 th , and 12th weeks, plus or minus one week. Their precise dates will be announced at least one week in advance and the topics will be specified.
|Week |Dates | Sections covered and topics |
| |Fall | |
| |2010 | |
|1 |8/23- | |
| |8/27 | |
|Week |Dates | Sections covered and topics |
| |Fall | |
| |2010 | |
|2 |8/30- | |
| |9/3 | |
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|3 |9/7- | |
| |9/10 | |
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| |Labor | |
| |Day on 9/6 | |
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|4 |9/13- | |
| |9/17 |Exam 1? |
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|5 |9/20-9/24 | |
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|6 |9/27- | |
| |10/1 | |
|7 |10/4- | |
| |10/8 | |
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|Week |Dates | Sections covered and topics |
| |Fall | |
| |2010 | |
|8 |10/11- |Exam 2? |
| |10/15 | |
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|9 |10/18- | |
| |10/22 | |
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|10 |10/25- | |
| |10/29 | |
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| |(Last day | |
| |to drop | |
| |on 10/29) | |
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|11 |11/1- | |
| |11/5 | |
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|12 |11/8- |Exam 3? |
| |11/12 | |
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|Week |Dates | Sections covered and topics |
| |Fall | |
| |2010 | |
|13 |11/15- | |
| |11/19 | |
| | | |
| |Thanks-giving | |
| | | |
| |Break | |
| | | |
| |next week | |
|14 |11/29-12/3 | |
| |Week | |
| |of | |
| |the | |
| |Dead | |
| | | |
| |(12/1-12/7) | |
|15 |12/6- | |
| |12/7 | |
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We may not have the time to cover all the topics listed on the Topics sheet ( below ) and we won’t necessarily
cover the sections in order. In some chapters, we will focus on specific topics, rather than covering everything.
Some topics may be covered with material from outside of the text. Come regularly and you’ll know where we are.
Topics in Textbook
Note: The following topics may be covered in a different order from that below.
In some sections, we will focus on specific topics, rather than covering
everything in the section . We probably won(t be able to cover all of the sections.
1.1 Methods of solving 3 linear equations and 3 unknowns
Dependent and inconsistent systems
Geometric interpretations of systems
1.2 Introduction to matrices
Standard representation of vectors in [pic][pic]
Augmented matrices
Row reduction and row reduced echelon form
1.3 Consistent and inconsistent systems
Rank of system vs. number of solutions to system
Matrix algebra: sums and scalar multiplication
Dot product of vectors
Product of a matrix with a vector
Linear combinations
Writing a linear system as a matrix equation
MTH 331 (sec 101) Syllabus Fall 2010
( continued )
Topics in Textbook
2.1 Encoding a message by using matrix multiplication
Using row reduction to find the decoding transformation
Inverse of a matrix, non-invertible matrices
Linear transformations from [pic]
What the columns of the matrix of a linear transformation represent
Algebraic properties of linear transformations
2.2 [pic] rotation matrix and other rotation matrices
Scaling matrices
Reflection matrices, orthogonal projection matrices
Matrices for combinations of scaling and rotations
Matrices for horizontal and vertical shears
2.3 Matrix products to represent composition of linear transformations
Computing a matrix product
Algebraic properties of matrix products
Multiplying block matrices
2.4 Inverse of a matrix
Using RREF to identify invertible matrices and find their inverses
Solving linear systems with invertible coefficient matrices
Finding the inverse of a product of invertible matrices
Hand computing the inverse of a 2x2 matrix
3.1 Finding the image and kernel of a linear transformation
Algebraic properties of images and kernels
3.2 Definition of a subspace of [pic]
Images and kernels of linear transformations are subspaces
Definition of linearly dependent and linearly independent vectors, properties
Basis of a subspace
Uniqueness of coordinates of a vector with respect to a basis
3.3 All bases of a subspace have the same size
Dimension of a subspace
Using RREF to construct basis of an image and kernel
Rank Nullity Theorem
Using a basis of [pic] to construct an invertible matrix
3.4 Finding coordinates of a vector with respect to a basis
Finding the matrix representation of linear transformations with respect to any basis
Similar matrices
4.1 General definition of a vector space
Examples of vector spaces
Linear independence, basis and coordinates
4.2 General definition of a linear transformation
Isomorphisms between vector spaces
4.3 Finding the matrix representation of any linear transformation
MTH 331 (sec 101) Syllabus Fall 2010
( continued )
Topics in Textbook
5.1 Length of vector, unit vectors
Properties of orthonormal vectors
Formula for orthogonal projection into a subspace
Properties of orthogonal complement of a subspace
Pythagorean Theorem, Cauchy Schwarz inequality, inequality for projections
Computing the angle between two vectors
5.2 Gram Schmidt process of producing an orthonormal basis
Computing a QR factorization
5.3 Examples of orthogonal transformations and matrices
Properties of orthogonal transformations
5.4 Geometric interpretation of least squares solution to an inconsistent linear system
Normal equation of a system
Finding a unique least squares solution
Finding matrix of an orthogonal projection onto a subspace
Fitting an nth degree polynomial to n+1 data points
Least squares fitting of an nth degree polynomial to more than n+1 data points
5.5 Properties of inner products; inner product spaces
Examples of inner products
Example of using a trace to define an inner product on matrices\
Norm and orthogonality
Formula for an orthogonal projection onto a subspace with an orthonormal basis
Fourier coefficients and Fourier approximations
6.1 Ways to compute determinant of 3x3 matrix, including Sarrus Method and
cofactor expansion
Determinants of upper triangular matrices
Effect of switching columns on value of determinant
Column-wise linearity of determinates
Using the “permutation formula” for computing determinants
Determinants of block matrices
6.2 Determinant of a transpose
Column-wise and Row-wise linearity of determinants
Determinant of matrix where two rows are identical
Effect of elementary row operations on determinants
Determinant of a row reduced echelon version of a matrix
Using Gauss Jordan elimination to simplify computation of determinants
Determinant of a product of matrices
Determinants of similar matrices have same value
Determinant of an inverse matrix
6.3 Computing area of parallelogram and volume of a parallelpiped using determinants
Effect of expansion factors on determinants
Cramers Rule for solving linear systems
Computing the inverse of a matrix
MTH 331 (sec 101) Syllabus Fall 2010
( continued )
Topics in Textbook
7.1 Eigenvectors and eigenvalues
Examples of eigenvectors
Applications to discrete dynamical systems
7.2 Using characteristic equation to solve for eigenvalues
Eigenvalues of a triangular matrix
Determinant and trace appearing as coefficients of a characteristic polynomial
Using eigenvalues to compute determinant and trace
Counting the number of real eigenvalues, together with their multiplicities
7.3 Eigenspace associated to an eigenvalue
Finding eigenvectors which correspond to a given eigenvalue
Dimension of an eigenspace
Finding an eigenbasis
Eigenvalues for similar matrices
7.4 Using an eigenbasis to diagonalize a matrix of a linear transformation
Conditions for being diagonalizable
Computing powers of a diagonalizable matrix
Eigenvalues and eigenvectors of any linear transformation: example on an
infinite dimensional space
7.5 Review of complex numbers: rectangular and polar form, Euler's formula,
DeMoivres formula for powers
Examples of diagonalizing matrices with complex eigenvalues: scaling and rotation matrices
Conditions for a complex matrix to be diagonalizable
Trace and determinant from complex valued eigenvalues
8.1 Spectral Theorem on orthogonally diagonalizable matrices and symmetry
Finding an orthogonal matrix to diagonalize a symmetric matrix
Orthogonality of eigenvectors for distinct eigenvalues of a symmetric matrix
Using Gram Schmidt process to orthogonally diagonalize a symmetric matrix
for eigenspaces with dimension greater than one
Symmetric matrices only have real eigenvalues
8.2 Definition and examples of quadratic forms on [pic]
Symmetric matrix of a quadratic form
Using eigenvalues of the symmetric matrix to represent a quadratic form
Positive definite, semidefinite and indefinite quadratic forms
Positive definite, semidefinite symmetric matrices are determined by the eigenvalues
Using principal submatrices to determine if a matrix is positive definite
Level curves and principal axes of a quadratic form in [pic]
Principal axes of a quadratic form in [pic]
8.3 [pic] is always symmetric for any matrix[pic]
Singular values of [pic] are square roots of eigenvalues of [pic]
Finding orthonormal basis vectors whose images under [pic] are orthogonal with
singular values of [pic] as their lengths
How the number of singular values is related to rank of an [pic]matrix
Singular Value Decomposition of any matrix
MTH 331( sec 101) Fall 2010
Keeping Records of Your Grades and Computing Your Score
|Quiz# |1 |2 |3 |4 |
|score | | | | |
Exam Total = sum of three highest exam scores(not including final)
|grade range for |Exam 1 |Exam 2 |Exam 3 |Exam 4 |average of range values |
| | | | | |for all four exams |
| A | | | | | |
| B | | | | | |
| C | | | | | |
| D | | | | | |
Absence # |1 |2 |3 |4 |5 |6 |7 |8 |9 |10 |11 |12 |13 |14 |15 |16 |17 |18 | |Date absent | | | | | | | | | | | | | | | | | | | |Excused? Y or N? | | | | | | | | | | | | | | | | | | | |Attendance Score |21 |19 |17 |15 |13 |11 |9 |7 |5 |3 |1 |0 |0 |0 |0 |0 |0 |0 | |
Attendance Score = 23 – [pic](# of days you were absent or extremely late)
Total % of Points=( Attendance Score
+Adjusted Quiz & Lab/Homework Score
+Exam Total
+Final Exam Score)/557
................
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