Fall 2007, Math 220.
Instructor:
Sergey Orshanskiy
(Italicized font means this information is for sections 5 and 10 only.)
Course Coordinator: Misha Guysinsky (guysin_m@math.psu.edu)
Course Description: Systems of linear equations; matrix algebra; determinants; eigenvalues and eigenvectors; orthogonality and least squares.
Prerequisite: Math 110 or 140.
Textbook: Linear Algebra and its Applications, third edition update, by David Lay, published by Pearson/Addison Wesley.
Midterm: A 75-minute evening examination will be held on (TBA), 2007 at 6:30.
Final Exam:
A comprehensive final examination, covering all the content of the
course, will be given. The final examination period will start on
Monday, December 17 and will end on Friday, December 21. Students should not make plans to leave University Park before Saturday, December 22. Students must bring their student ID cards for all exams.
Conflict and Makeup Exams:
Only students with official University conflicts, or a valid,
documented excuse, will be permitted to schedule the conflict or makeup
exams. Students must sign up for conflict or makeup exam at least 48
hours in advance of the exam date.
Homeworks and Quizzes:
At least 3 worst homework grades and at least 2 quiz grades will be dropped.
The remaining will be averaged. There may or may not be partial credit for
quiz problems. It is determined before the quiz but not announced. No makeup
quizzes after the quiz in class, even with a University recognized reason.
Every person has a right for one makeup quiz before the quiz in class without
any reason or explanation (equal difficulty is not guaranteed).
If the section average for the quizzes (after dropping at least 2 grades) is
below 60%, quiz grades shall be curved (increased) uniformly to fix it.
No other curving of quiz/homework grades shall be done.
Typically, not all problems will be graded. It is then guaranteed that homework
problems to be graded will be chosen randomly. Homeworks are graded by the grader
(but may occasionally be graded by the instructor to check the work of the grader).
All quizzes are graded by the instructor.
Late Homework:
The homework is due the end of class.
Always indicate (on the top of the front page) the exact time & date of the moment
when you leave a late homework.
If you write the wrong time that is earlier than when you actually left
the homework (in a mailbox or under the door), the homework will not be graded.
If the time is not indicated, it is the time when I find it. Early homework is OK.
Leave it in the mailbox in McAllister bldg (1st floor) or give me in class!
(Exception: when the mailbox is full, indicate it on the homework and slide it under
the door of the office - 418, McAllister.)
If you slide the homework under the door or bring it to my office not during the office hours,
it is considered at least 6 hours late.
In all circumstances, homework sent by email is considered 24 hours late. Homework
sent by email later than 24 hours after the class will not be graded.
If you mail your homework (by regular mail), make sure it is delivered within
50 hours from the moment it is due.
To ask for an exception, (not provided by other University policies),
you shall first bring or mail at least one official document serving as
an explanation or a note from a parent/guardian with an address and a phone
number.
If the homework is at most 5 hours late, there is no penalty.
If the homework is at most 25 hours late, the penalty is -10%.
If the homework is at most 50 hours late, the penalty is -20%.
Not graded if 50 hours late.
Grading Policy: Grades will be assigned on the basis of 300 points distributed as follows:
50 points for homework and quizzes
35 for homework and 15 for quizzes
100 points for the midterm exam
150 points for the final exam
Final grades will be assigned as follows:
A 275-300
A- 265-274
B+ 255-264
B 245-254
B- 235-244
C+ 225-234
C 210-224
D 190-209
F 0-189
Academic Integrity: The following is the required academic integrity statement for
this course: During QUIZZES and EXAMS, the use of books,
calculators or notes of any sort is not permitted and
communicating with anyone or copying anything from anyone
is not permitted. Cell phones must be turned OFF.
Also see the Student Guide to the University, Policy 49--20.
Collaboration on homeworks is permitted, but not encouraged. Using solution manuals
is permitted, but not encouraged. If the collaboration is significant, you MUST idenify
your collaborators before the solution of each problem on which you collaborated (or give a list in
the beginning). You MUST write down the solution on your own.
You MUST identify if you have seen the solution in the solution manual or a similar
source before the solution of each problem to which it applies, even if you have not used
the solution from the solution manual at all!
However, if you fail to do so, the penalty will not exceed getting 0 points for
all homeworks in the course.
The number of points you get for one homework will never exceed 3 times the number of
points you get for the problems solved on your own, with no collaborators and without
using any solutions. (That is, do at least 33% on your own.)
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)