ma8_wk1_monday_notes_2010

ma8_wk1_monday_notes_2010 - MATH 8 SECTION 1 WEEK 1...

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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 1

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2 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?)
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