
Math 51 Spring 2013
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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,
- never forget to put your name, your section number and your TA's name on the top of your work;
- 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.
Logistics for Weekly Homework:
Assignments must be turned in to your TA (discussion section leader) -- you will not receive credit for work turned into another section leader.
(If you're unable to turn in your homework in section, slide it under your TA's office door; submission to TA mailboxes is not permissible.)
The deadline is 3:15 p.m. on the given due date, and no late homework will be accepted under any circumstances. (This is as much a courtesy to the grader as an incentive to stay current with the course and not fall behind.)
To accommodate exceptional situations such as a serious illness, your lowest homework score will be dropped at the end of the quarter.
Solutions will be posted on this page by the following morning.
Students are encouraged to pick up their graded homework assignments promptly; please make arrangements with your TA to pick it up outside of class (or via electronic scan if absolutely necessary) if you cannot attend the discussion section on the day the homework is returned. It is ultimately your responsibility to look over your graded assignment while consulting the posted solutions, not only to check your understanding but also to find any grading errors or mis-typed entries in your CourseWork grade record. If you find an error in how an assignment was graded or recorded, please appeal to your section leader (who has final authority on all homework appeals). If more than a week has passed since an assignment was returned in section, your CourseWork score entry for that assignment can no longer be changed.
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| Assignment |
Due |
Exercises |
Extra Problems (Required) |
1
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Apr 9
Solutions
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LA1 # 6, 7, 9
LA2 # 4, 12, 16
LA3 # 3, 4, 9, 13
LA4 # 2abdf, 12, 17, 18, 24
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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.
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2
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Apr 16
Solutions
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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.
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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?
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3
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Apr 23
Solutions
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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."
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[none]
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4
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Apr 30
Solutions
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Click here for all problems
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[see link at left]
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5
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May 7
Solutions
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Click here for all problems
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[see link at left]
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6
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May 14
Solutions
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Click here for all problems
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[see link at left]
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7
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Thu. May 23
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DVC4 # 4, 14, 20
DVC7 # 6, 8, 22, 26, 28, 38
DVC8 # 6, 12, 14, 20
DVC11 # 4, 12, 20
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[none]
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8
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Thu. May 30
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9
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n/a (practice only)
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