138-16-FALL-WEEK1-Sept.12,16-H1.pdf

138-16-FALL-WEEK1-Sept.12,16-H1.pdf - UNIVERSITY OF TORONTO...

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UNIVERSITY OF TORONTO DEPARTMENT OF MATHEMATICS MAT138H1 - INTRODUCTION TO PROOFS – FALL 2016 WEEK #1 (SEPTEMBER 12 AND 16) Part 1. BASICS ON “PROBLEM SOLVING” . - Topic: The Polya/Schoenfeld problem-solving scheme. I. Understand the problem (Analysis) 1. What are the unknowns? 2. What are the relevant hypotheses and data? 3. Could the problem be conveniently represented by a figure, a diagram, a table, etc.? Could suitable notations be introduced for the variables and other elements in the problem? 4. Are there any easy special or extreme cases for the problem? Can we identify any pattern in the problem? 5. Are there any symmetries or circularities that could simplify the problem? What are the most convenient units to be used in the problem? II. Devise a plan (Exploration) 1. Could the problem be converted to an equivalent but easier problem? 2. Could we start by solving some particular cases of the problem? 3. Could we solve a simplified version of the problem and then generalize our solution?
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  • Winter '15
  • Math, 1 cm, 30 cm, Department of Mathematics, 12 cm, rectangular printed area

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