cais - Preparing Students for the College Mathematics...

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Preparing Students for the College Mathematics Experience (A Personal Wish List) By Andrew J. Bernoff Professor of Mathematics Harvey Mudd College
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Who am I ? Andrew Bernoff's Homepage I’ve spent time in departments of Math, Physics and various flavors of Engineering. “Math lives and breathes through its applications.”
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Who is Harvey Mudd ? Harvey Mudd College is located in Claremont, California. Specializes in Mathematics, the Sciences and Engineering. Roughly 700 students (all undergraduate) and 80 faculty. Median SAT score 1470 -- 25% HS valedictorians. Roughly half our students obtain graduate degrees.
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Part I: Communicating Mathematics. “No one would talk much in society if they knew how often they misunderstood others” -Goethe Part II: Different styles of teaching and learning. Part III: Tools and technology.
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Neatness Counts!! HMC Homework Template Students tend to be better at copying an existing format than creating their own. Part I: Communication Give students a template to work from.
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Honing Writing Skills Style points: Let 5% of the credit for every assignment be for presentation, including neatness. Homework rewrites for credit: Let students resubmit corrected assignments for up to half the points lost. Extra Credit: Mathematical text processing LaTeX - Microsoft Equation Editor j = n ( n +1) 2 j =1 N å Part I: Communication Real mathematicians use LaTeX !!!!
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Writing Math Teach students to write. Mathematically. In whole sentences. Proposition: Show M=n 2 -1 is not prime for n an integer greater than 2. Proof: n 2 -1 = (n-1)(n+1). n>2 so (n-1),(n+1)>2. M is the product of two numbers greater than 1 so M is composite. Part I: Communication
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Writing Math Teach students to write mathematically in whole sentences. Proposition: Show M=n 2 -1 is not prime for n an integer greater than 2. Proof: Note that M can be written as the product of two factors, M = n 2 -1 = (n-1)(n+1). As n is greater than 2, both factors of M, namely (n-1) and (n+1), are greater than 1, which implies M is composite. Part I: Communication
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The Art of Proof Like a Zen garden . . . Succinct. Clear. Complete. Part I: Communication
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Proof Templates For example, here is a template for induction: To prove: Proposition -- show A(n) is true for n=1,2,3 . . . . Proof: We wish to show A(n). Base Case (n=1):
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cais - Preparing Students for the College Mathematics...

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