Home page for Math 250:1 & 5, spring 2011


Links to other webpages for Math 250:1 & 5

The course syllabus
with suggested homework
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General information
for these sections
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Students in the course |
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Definitions

Things to do and information

Course grades have been entered in the Registrar's computer system on Wednesday afternoon, May 11. A link to the final exam and to how it was graded is below. A brief discussion of how course letter grades were determined is here.

We missed a day during the semester due to snow and some rearrangement is needed as a result. What follows is the schedule for the last meetings of these sections of 250. This is slightly different from the previous schedule.

Day and dateTopic and book section
Monday, April 186.2 Orthogonal Sets of Vectors; Gram-Schmidt Process; QR factorization
Wednesday, April 206.3 Orthogonal Projection; Orthogonal Complements
Monday, April 256.5 Orthogonal Matrices
6.6 Diagonalization of Symmetric Matrices
Wednesday, April 27
Monday, May 2 Catch up and review


Please keep up with the syllabus and suggested homework. Your life will be better in this course if you glance at material ahead of time, before the lectures. You will almost surely be unsuccessful in this course if you don't do most of the homework problems: practice!

Links to other class material

Title
(with PDF links)
What is it?Handed out
or posted
The final exam Here is a version of the final exam, in a somewhat more compact format.
Here is a discussion of the grades and grading.
5/11/2011
The ninth quiz and some possible answers Students were told that they would be "given" a 3 dimensional subspace of R? by specifying one basis of this subspace. They would then be asked to find an orthogonal basis for this subspace. The quiz had ?=4. Also they would need to find the coordinates relative to that basis for a vector in the subspace. The first task is done using Gram-Schmidt and the second one uses dot products.

The version which was distributed had a misprint. The third coordinate of w in the second question should have been –3 not –1. A correction has been made in what's posted here. I apologize for this error.

4/25/2011
Review material for the final exam
To be given Tuesday, May 10, for section 1, and Friday, May 6, for section 5.
4/16/2011
Answers to the second exam Here are detailed answers to version A of the second exam. Please tell me any comments or corrections.
Here is a discussion of the grades and grading.
4/14/2011
The second exam Here is a version of the second exam, in a somewhat more compact format. Graded exams will be returned in class on Monday, April 18.4/14/2011
One version of the eighth quiz and some possible answers;
another version of the eighth quiz and some possible answers
Students were told that they would be asked to find the eigenvalues and bases for the eigenspaces of a "simple" matrix. Some examples were supplied so that students could practice.
Quizzes with two similar-looking matrices were prepared, one with "enough" eigenvectors and one without "enough" for diagonalization. The solutions supplied discuss the reasoning.
4/10/2011
The seventh quiz and some possible answers Here is the seventh quiz and some answers. I told students that I would ask "for the definitions of eigenvector and corresponding eigenvalue. I will ask some questions about eigenvalues and eigenvectors." This is what was done. The computations needed for responding to these questions were not extensive but some understanding of the concepts was necessary. 4/3/2011
Review material for the second exam
To be given Wednesday, April 13.
3/28/2011
The sixth quiz and some possible answers Here is the sixth quiz and some answers. One previous lecture discussed subspaces, and two lectures (including the one given on the day of the quiz!) discussed the definitions and examples of basis and dimension. A homework assignment was given on this material. I don't believe extensive computation was needed to answer these questions, but certainly some understanding was essential. 3/24/2011
The fifth quiz and some possible answers Here is the fifth quiz and some answers. The answers also relate the material of the quiz to the column space and null space of a matrix. This quiz pins down whether or not students can connect "solving" a system of linear equations with some of the abstraction of the course.
There was a 13 in the denominator of one of the fractions in the version of the quiz which was distributed. This was wrong (a typing error by the instructor!) and is corrected in the version published here. Students were not penalized for using the incorrect information nor for using that information with 19 substituted for the 13 (that's the correct version!).
Mr. Battista noticed another misprint (misplaced –'s) which has now been fixed. I thank him for this.
3/11/2011
3/22/2011
Answers to the first exam Here are detailed answers to version A of the first exam. Please tell me any comments or corrections.
Here is a discussion of the grades and grading. Students should read carefully the first section, entitled The future, student performance, exam construction, and course grades.
3/5/2011
The first exam Here is a version of the first exam, in a somewhat more compact format. Graded exams will be returned in class on Monday, March 7.3/5/2011
The zoo for the first exam A copy of this will be given to every student along with the first exam. What's on this page is the output of certain Maple commands. A few entries are slightly strange.
The first exam will still have some row operations and arithmetic, but I hope that students will be able to use the information on this page to answer some questions on the exam and reduce their computational effort!
2/25/2010
The fourth quiz and some possible answers Here is the fourth quiz and some answers. 2/24/2011
Review material for the first exam
To be given Wednesday, March 2.
2/23/2011
The third quiz and some possible answers Here is the third quiz and some answers. Please note that I asked one of six designated definitions. I will ask for definitions on other quizzes and the exams in the course. Practice examples were available here for the other questions. 2/15/2011
Template for the second quiz A template for the second quiz is shown to the right. Practice examples were available here. The matrices which were used on the quiz are here.
Here is a discussion of how I graded, including a warning for students who got low scores or "missed" the quiz.
2/8/2011
The first quiz and some possible answers Here is the first quiz and some answers. Students who did not get full credit in the first problem (asking for a definition of transpose of a matrix) should read this. Actually, maybe all students should read it. I tried to discuss "What is a definition?" and what I expect from such a question. 2/1/2010
Information sheet A form to be passed out on the first day of class. 1/15/2011


Maintained by greenfie@math.rutgers.edu and last modified 1/14/2011.