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MATH 8, SECTION 1, WEEK 1 - RECITATION NOTES
TA: PADRAIC BARTLETT
Abstract.
These are the notes from Monday, Sept. 27th’s lecture. Here, we
introduce some basic logical notation, and begin to discuss what it means to
“prove” something.
1.
Administrivia and Announcements
•
Email: [email protected]
•
Website:
www.its.caltech.edu/
∼
padraic
Course notes for every lecture are
posted here, ideally within a day of the lecture.
•
Oﬃce: 360 Sloan
•
Oﬃce Hours: MWF, 3-4 pm, in Sloan 151 / by request!
•
Grading Policy: Math 8 is a 3-credit class that meets for three hours a week.
Accordingly, its grading is strictly attendance-based! Registered students
are required to attend at least 3/4 of the lectures to pass the course –
eﬀectively, this means you’re allowed to miss at most 7 classes over the
quarter. Absences are excused only if they are accompanied by a note from
the Deans or from the Student Health Center; make-up work for missed
classes is not available.
•
Unregistered Students: Unregistered students are more than welcome to
attend as many lectures as they want, and read the course notes online!
2.
Random Question
Every class (that I remember to do this for,) I’ll put up a question or two for
people to think about during lecture; that way, if you’ve seen some of the material
we’re covering before and want something else to ponder, you won’t be bored.
These are random, mostly mathematical puzzles I’ve ran into in my career as a
mathematician that I liked – if you’re interested in any of them or happen to
solve one of them, talk to me! I’m always happy to hear possible solutions or
oﬀer hints. Alternately, if you’re not interested, don’t worry; these are just for the
curious/easily-distracted among you.
Question 2.1.
Can you ﬁnd 4 points in the plane so that the distance between any
two of them is odd?
3.
What is Math 8?
Math 8 is an auxiliary course for Math 1a; where Math 1a is (by design!) a highly
abstract course, Math 8 is a much more hands-on and example-oriented series of
lectures. Speciﬁcally, Math 8’s lectures are designed to serve as a ”how-to” guide
on how to craft clear, well-written mathematical proofs; students who are new to
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TA: PADRAIC BARTLETT
the concept of formal proofs or who are otherwise concerned with meeting the levels
of rigor in Math 1a are encouraged to attend!
Throughout Math 8, we’re going to try to develop four main themes:
(1) The
language
of proofs. Throughout the course, we will continually in-
troduce and deﬁne mathematical symbols and shorthand, so that you can
read and write mathematics ﬂuently.
(2) The
methods
of proof. There are many diﬀerent styles of proof used
throughout mathematics; in this class, we will focus on developing four
speciﬁc styles (construction, deduction, induction, contradiction), discuss
where to use each of these styles, and possibly mention some other more
esoteric methods (probabilistic methods, anyone?)
(3) The

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