Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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MAT102S - Introduction to Mathematical Proofs - Spring 2010 - UTM Problem Set A - TO BE SUBMITTED TO YOUR TA Due : Monday, January 11, in tutorials. ± This assignment must be submitted to your TA at the beginning of the tutorial on the above date. ± Marking scheme : 8 marks for your solutions to the problems assigned (only some of the questions will be marked) and 2 marks for presentation. ± To receive the 2 marks allotted to presentation, you must submit at least half of the problems assigned and pay attention to the following: { Your full name, student number, tutorial section and the name of your TA appear in the top of the ±rst page. { The section and question number (including a,b,c. .. if the question has several parts) are clearly indicated at the beginning of each of your answers. { Your assignment is stapled in the top left corner (if it is more than one page in length). { You are using a clean paper (no ripped paper), that is not folded or rolled.
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Unformatted text preview: { Your writing is clear and organized (use full sentences), and your reasoning is easy to follow. Submit your solutions to the following problems from the textbook: Chapter 1, Exercises 1.2, 1.5, 1.6, 1.7, 1.11, 1.23, 1.25, and 1.28 . DO NOT use calculus to solve 1.28 ! Also submit a solution to the following question: Let x;y;z be nonnegative real numbers such that x + z 2. Prove that ( x 2 y + z ) 2 4 xz 8 y . Determine when equality holds. Note : 1. A hard copy of this document was handed out in the rst lecture. The rest of the problem sets will be posted on the course website ONLY, and you are responsible for downloading them every week (and print them, if you wish). 2. If you have not purchased the textbook yet, you can download the above Exercises from the course website. You are expected to purchase the textbook by the end of the rst week of classes....
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This document was uploaded on 03/25/2011.

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