Mathematics for Computer Science
6.042J/18.062J
http://courses.csail.mit.edu/6.042
WELCOME!
Prof. Albert R. Meyer
Albert R. Meyer, 2009
September 9, 2009
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Quick Summary
1. Fundamental Concepts of
Discrete Mathematics (sets,
relations, proof methods,… )
2.Discrete Mathematical
Structures (graphs, trees,
counting…)
3.Discrete Probability Theory
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Vocabulary
Quickie:
What does “discrete” mean?
( “discreet”)
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Online Tutor Problems
TP1:
•Course Registration asap
•Diagnostic Questionnaire
by Friday, 5pm
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September 9, 2009
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Reading Assignment
• Courseinfo on web page asap
• Class Notes Chapt 1--3
• Comments by Mon 10AM
-- using online system NB
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September 9, 2009
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Course Web site
http://courses.csail.mit.edu/6.042
• announcements
• class schedule
• notes, slides,…
• course organization
• grading info
Albert R. Meyer, 2009
September 9, 2009
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Lecture & Team Problems
Three 1.5 hour class sessions:
•1/2 hour overview lecture,
•then team problem-solving.
Team participation counts
20% of final grade
Teams assigned next Monday
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Active Lectures
Say “hello” to your
neighbors –you’ll be
working with them
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September 9, 2009
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Active Lectures
Quickie question:
Where was your
neighbor born?
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Getting started:
Pythagorean theorem
c
b
a
2
2
2
a +b = c
Familiar? Yes!
Obvious? No!
Albert R. Meyer, 2009
September 9, 2009
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cc
A Cool Proof
c
b
a
Rearrange into:
(i) a cc square, and then
(ii) an aa & a bb square
Albert R. Meyer, 2009
September 9, 2009
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A Cool Proof
c
c
c
a
b
c
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September 9, 2009
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A Cool Proof
a
b
a
a
b-a
b
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September 9, 2009
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A False Proof:
Getting Rich By Diagram
1
1
1
10
11
1
1
1
1
1
10
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September 9, 2009
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A False Proof:
Getting Rich By Diagram
1
10
11
1
1
1
10
11
1
1
Albert R. Meyer, 2009
September 9, 2009
Profit!
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Getting Rich
The bug:
1
1
1
1
are not right triangles!
So the top and bottom line of the
“rectangle” is not straight!
10
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September 9, 2009
1
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1 = -1 ?
1 = 1 = (-1)(-1) = -1 -1 =
2
 -1 
= -1
Moral:
1. Be sure rules are properly applied.
2. Calculation is a risky substitute for
understanding.
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Consequences of 1= 1
½ = ½
2=1
(multiply by
(add
3
2
½)
)
“Since I and the Pope are clearly 2,
we conclude that I and the Pope are 1.
That is, I am the Pope.”
-- Bertrand Russell
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Consequences of 1= 1
Bertrand Russell (1872 - 1970)
(Picture source: http://www.users.drew.edu/~jlenz/brs.html)
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September 9, 2009
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Team Problems
Problems
1 3
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