Penn State University - University Park
Math 220, Matrices
Spring 2008

INSTRUCTOR: Sergey Orshanskiy

SECTIONS: 3 and 5 - Italicized font is for sections 3 and 5 only!, everything else is for all sections.

CATALOG DESCRIPTION: Systems of linear equations; matrix algebra; eigenvalues and eigenvectors; orthogonality and least squares.

PREREQUISITE: Math 110 or 140

TEXT BOOK: "Linear Algebra and its Applications", third edition update, by David Lay, published by Pearson/Addison Wesley.

CALCULATORS: No calculators are allowed on the midterm and final examinations. Permitted during quizzes, but not recommended.

COURSE FORMAT: There are two 50-minute lectures each week. The sections covered in these lectures are listed below.

TUTORS AND MATH CENTER:  Free mathematics tutoring is available at the Math Center located in 220 Boucke Building. More information can be found at: Math Center.  If you need additional help, a (paid) tutors list is maintained by the Mathematics Department Undergraduate Office,  http://www.math.psu.edu/ug/PrivateTutorList.htm.  

LATE-DROP: Students may add/drop a course without academic penalty within the first ten calendar days of the semester. A student may late drop a course within the first twelve weeks of the semester but accrues late drop credits equal to the number of credits in the dropped course. A baccalaureate student is limited to 16 late drop credits. The late drop deadline for Spring 2008 is April 11, 2008.

EXAMINATIONS: A 75-minute evening examination will be given during the semester and a comprehensive final examination will be given during the final examination period. NO books, notes, or calculators may be used on the examinations. Cellphones or any electronic device must be turned off during the exams. You must bring your University ID card to all exams.

Midterm Examination I: Wednesday, March 5, 2008 from 6:30 to 7:45 PM.

Rooms for the examinations will be announced by your instructor at a later date.

Conflict Exam: For the midterm examination, there is a conflict examination from 5:05 to 6:20 PM on the same night as the regular examination. 

Who may take the Conflict Exam?  If you have a valid conflict with the regular examination time, such as a class or other scheduled activity, you may sign up for the conflict exam.

Students are responsible for knowing the room and time of the conflict examination.  Students must bring their University ID to the conflict examination. The ID will be checked by the proctor. Although the conflict examination will end at 6:20 PM, no student will be permitted to leave the examination room before 6:25 PM. Any student who leaves before 6:25 PM will receive a grade of zero on the examination and will not be allowed to retake it.

How and when to sign up for the Conflict Exam.  Students must sign up for the Conflict Exam in class, with your instructor, on a pink form.  The student is responsible for knowing the room and time of the conflict examination.  This information is on  top of the pink form. Your instructor must turn in the pink form 2 class days prior to the examination date. If you have not signed up with your instructor, you will not be allowed to take the conflict exam. 

Makeup Exam:  A makeup exam will be given two days after the regular midterm exam.

Who may take the makeup exam?  Students who have a valid documented reason, such as a class conflict or illness, during both the conflict and regular examination times are permitted to schedule a makeup examination with no penalty. You must be prepared to verify the reason for taking the makeup. Students who do not have a valid reason for missing the examination, such as forgetting the date, time, or room of an examination, are  permitted to schedule the makeup, but 30 points will be deducted from their score. Students who have taken either the regularly scheduled examination or conflict examination are not permitted to take the makeup examination. Students who have not signed up for the makeup with their instructor will not be allowed to take the exam. The makeup examination will be given on

March 7, 2008 from 6:30 to 7:45 PM

How and when to sign up for the Makeup Exam.  Students must sign up for the Makeup Exam in class, with your instructor, on a yellow form, as soon as possible following the regular exam date.   The student is responsible for knowing the room and time of the makeup examination. This information is on top of the yellow form.  Your instructor must turn in the yellow form 2 class days prior to the examination date. If you have not signed up with your instructor, you will not be allowed to take the makeup exam.

Students are responsible for knowing the room and time. Students must bring their University ID to the makeup examination.  The ID will be checked by the proctor.

What if a student misses both the regularly scheduled exam and the makeup exam?  If a student misses both the regularly scheduled examination and the scheduled makeup due to a valid, verifiable reason, it maybe possible to take a makeup examination by appointment. All such makeup examinations must be scheduled through the instructor with the approval of the course coordinator and must be completed no later than ten days after the scheduled makeup  examination.

FINAL EXAMINATION: The final examination will be given during the week, May 5 - 9, 2008. The final examination may be scheduled on any day during the final examination period. Do not plan to leave University Park until after Friday, May 9, 2008. There are two types of conflict examinations, direct and overload. Direct conflicts are two examinations scheduled at the same time. Overload examinations are three or more examinations scheduled within a fifteen hour period, from the beginning of the first examination to the beginning of the third examination. Students may elect to take the three or more examinations on the same day if they wish or request a conflict final examination. Students may access their final exam schedule Monday, February 18, through their e-lion account.  Notification of conflicts is given on the student's final exam schedule.  A student must take action to request a conflict exam through e-lion between February 18 - March 2.  Conflict final examinations cannot be scheduled through mathematics department, and there will be no sign up sheet in 104 McAllister for the final conflict examination.

Students who miss both the regular and conflict final examinations due to a valid and documented reason, such as illness, may be allowed to take a makeup final examination. If the student does not have a valid reason, at least a 30 point penalty will be imposed. All such makeup examinations must be scheduled through the instructor with the approval of the course coordinator and students should contact the instructor within 24 hours of the final examination. Students who have taken the original final examination are not permitted to take a makeup examination.

GRADING POLICY:  Grades will be assigned on the basis of 300 points distributed as follows:
          75 points for homework and quizzes
        100 points for the midterm exam
        125 points for the final exam

More specifically: 30 points for homeworks and 45 for quizzes and take-home quizzes. Typically, I will grade the quizzes and take-home quizzes and the grader will grade the homeworks. At least 3 homework grades and approximately half of the in-class quiz grades will be dropped.

The exact point requirements for each letter grade will be decided at the end of the course. 

A typical distribution follows:
Grade %-score
A, A- 100-90
B+, B, B- 89-80
C+, C 79-70
D 69-60
F 59-0

 NOTE: Your grade will be based EXCLUSIVELY on the midterm examinations, homework and/or quizzes and final examination. There is no "extra-credit" work. However, if specifically announced, in some cases there may be an option of re-doing a quiz or a homework.


LATE HOMEWORK: the penalty for late homework is 10% for up to 24 hours and 20% for up to 48. Late homework can be left in the mailbox, submitted during the office hours or after the next class or in person (if I am not busy). There is no penalty for at most five hours after the homework is due and such homework is not considered late. Otherwise you must write the word ''LATE'' on your homework as well as the time and the date when you are leaving it. When slipped under the door, I reserve the right to count it as late as when I find it (but you must still time and date it). When leaving in the mailbox, it is your responsibility to leave it in my mailbox and not someone else's. I am not responsible for any adversarial third party, stealing or altering homeworks left in my mailbox. .

HOMEWORK by EMAIL:homework by email is not accepted. If you have a documented reason that e.g. you are sick and cannot come to campus, late homework may be accepted and is preferred to prompt homework by email.

MAKEUP QUIZZES: if you need to make-up an in-class quiz before or after the actual quiz, I will do my best to accommodate such requests. No guarantee is given regarding the difficulty of such quizzes. For example, if you are taking a make-up quiz before the actual quiz, I might want to simplify the actual quiz after seeing your performance on it without any compensation for you taking a more difficult version. If you are taking a make-up quiz after the actual quiz, I will make a conscious effort to make it more difficult than the actual quiz, for the sake of fairness. If solution(s) to the quiz have been published or distributed, the make-up is still possible, but it may be substantially more difficult than the actual quiz.

ACADEMIC INTEGRITY regarding homeworks and take-home quizzes: Collaboration is permitted, unless otherwise stated for some specific assignment. Asking for hints or even the answer is permitted. Using a complete or incomplete solution from the solution manual, from another student or any online or another outside source is not permitted. Reading is considered using. (In other words, if you have seen a solution before finishing your work on a given problem, you are not allowed to submit a solution to this problem, unless you have seen this problem in a different course or some other context.) Penalty: 0 points for the whole assignment (e.g. homework). In this case, all accessible past and future work of this student will be checked for general academic integrity violations, as defined by the University (see below). The student has the right to question the evidence of a violation. If the conflict is not resolved in person (possibly, with the course coordinator), the student has to claim in writing that no violation as defined above has taken place. Then this is either considered sufficient evidence that indeed no violation has taken place or can be used in an official investigation of this academic integrity issue.

ACADEMIC INTEGRITY: Academic integrity is the pursuit of scholarly activity in an open, honest and responsible manner. Academic integrity is a basic guiding principle for all academic activity at The Pennsylvania State University, and all members of the University community are expected to act in accordance with this principle. Consistent with this expectation, the University's Code of Conduct states that all students should act with personal integrity, respect other students' dignity, rights and property, and help create and maintain an environment in which all can succeed through the fruits of their efforts.


Academic integrity includes a commitment not to engage in or tolerate acts of falsification, misrepresentation or deception. Such acts of dishonesty violate the fundamental ethical principles of the University community and compromise the worth of work completed by others.

"Academic dishonesty includes, but is no limited to, cheating, plagiarizing, . . ., facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with academic work of other students. . . . A student charged with academic dishonesty will be given oral or written notice of the charge by the instructor. If students believe that they have been falsely accused, they should seek redress through informal discussions with the instructor, the department head, dean or campus executive officer. If the instructor believes that the infraction is sufficiently serious to warrant the referral of the case to Judicial Affairs, or if the instructor will award a final grade of F in the course because of the infraction, the student and instructor will be afforded formal due process procedures." From Policies and Rules, Student Guide to the University Policy 49-20.

Based on the University's Faculty Senate Policy 49-20, a range of academic sanctions may be taken against a student who engages in academic dishonesty.  Please see the Eberly College of Science Academic Integrity homepage for additional information and procedures.

QUESTIONS, PROBLEMS, OR COMMENTS: If you have questions or concerns about the course, please consult your instructor first. If further guidance is needed, you may contact the course coordinator.

COURSE COORDINATOR: Dr. Aissa Wade (wade@math.psu.edu)


COURSE OUTLINE:
(The number after each section is the approximate number of class periods).

I. LINEAR EQUATIONS IN LINEAR ALGEBRA
    1.1 Systems of Linear Equations (1.5)
    1.2 Row Reduction and Echelon Forms (1.5)
    1.3 Vector Equations (1)
    1.4 The Matrix Equation Ax=b (1)
    1.5 Solution Sets of Linear Systems (1)
    1.7 Linear Independence (1)
    1.8 Introduction to Linear Transformations (1)
    1.9 The Matrix of a Linear Transformations (1)

II. MATRIX ALGEBRA
    2.1 Matrix Operations (1)
    2.2 The Inverse of a Matrix (1)
    2.3 Characterizations of Invertible Matrices (1)
    2.8 Linear Subspaces (1.5)
    2.9 Dimension and Rank (1.5)

III. DETERMINANTS
    3.1 Introduction to Determinants (1)
    3.2 Properties of the Determinants +Cramer's rule from 3.3 (1)

V. EIGENPROBLEMS
        5.1 Eigenvalues and Eigenvectors (1)
        5.2 The Characteristic Equation  (1)
        5.3 Diagonalization (1)
        5.5 Complex Eigenvalues (1)

VI. ORTHOGONALITY AND LEAST SQUARES
        6.1 Inner Product, Length, and Orthogonality (1)
        6.2 Orthogonal Sets (1)
        6.3 Orthogonal Projections (1)
        6.4 The Gram-Schmidt Process (no Factorization) (1)
        6.5 Least-Squares Problems (1)

VII. SYMMETRIC MATRICES
        7.1 Diagonalization of Symmetric Matrices. (1)