## Math 51 Spring 2013

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### Weekly Homework Policy

Completing homework assignments is an integral part of this course. Problems are designed to reinforce concepts covered in lecture as well as to encourage students to explore implications of the results discussed in class. Very few students will be able to go through the entire course without struggling on many problems, so do not be discouraged if you do not immediately know how to solve a problem. In confronting difficult questions you should consider how the problem at hand connects to topics, definitions and/or theorems discussed in class.

When you have worked on a problem for a while and remain stuck, you are encouraged to ask for hints from your instructor or TA. Students may also discuss problems with one another, but must write solutions on their own. In particular if you have taken notes while discussing homework problems with friends or instructors, you must put these notes away when writing your solution. The Honor Code applies to this and all other written aspects of the course. Be warned: watching someone else solve a problem will not make homework a good preparation for tests. Don't get caught in the trap of relying on others to get through homework assignments.

Students are expected to take care in writing their assignments. For instance,

• assignments should be written neatly;
• assignments should contain clear, complete solutions; and
• completed assignments which contain multiple pages should be stapled for easy grading -- one point will be deducted for not doing this.

Partial progress toward solutions on problems will be awarded partial credit, but simply writing answers down without justification will receive zero credit. Please note that usually only a portion of each week's problems will be scored; the selection of problems chosen to be graded will not be announced in advance.

Assignment Due Exercises Extra Problems (Required)
1
Apr 9
Solutions
LA1 # 6, 7, 9
LA2 # 4, 12, 16
LA3 # 3, 4, 9, 13
LA4 # 2abdf, 12, 17, 18, 24
Suppose you manage a mutual fund that invests in one thousand companies. Let S be the vector in R1000 whose ith component is the number of shares of company i that you have today. Let P be the vector in R1000 whose ith component is today's price per share of company i's stock. Express the total value of your holdings in terms of vector operations.
2
Apr 16
Solutions
LA5 # 2, 14
LA6 # 2, 15
LA7 # 1, 2
LA8 # 1, 4, 13, 18, 20, 24
LA9 # 3*, 4abc, 5, 12

*NOTE: For #3 above, your answer should be one or more linear relations involving the entries of b.
There are 6000 undergraduate students at Stanford. Let M be the 6000 x 6000 matrix whose ij entry is 1 if student i and student j are Facebook friends and 0 if they are not. (Here we assume that Facebook does not permit a person to be a friend of themselves, so all the diagonal entries of M are zero.) Let u be the vector in R6000 each of whose entries is 1. What does the vector Mu represent?
3
Apr 23
Solutions
LA10 # 11, 12, 21, 22, 23
LA11 # 4, 8, 10, 15
LA12 # 1, 3, 7, 13acd*
LA13 # 2, 6, 8, 18, 22

*NOTE: For each designated part of #13 above, either briefly explain why the statement is "true," or give a counterexample if the statement is "false."
[none]
4
Apr 30
Solutions
5
May 7
Solutions
6
May 14
Solutions
7
Thu. May 23
DVC4 # 4, 14, 20
DVC7 # 6, 8, 22, 26, 28, 38
DVC8 # 6, 12, 14, 20
DVC11 # 4, 12, 20
[none]
8
Thu. May 30

9
n/a (practice only)

Spring 2013 -- Department of Mathematics, Stanford University