TAILIEUCHUNG - Proofs and Concepts the fundamentals of abstract mathematics

If the proof of such a trivial consequence of sin2 A + cos2 A = 1 is now reserved only for college-intending students, how does NCTM expect the average high school graduate to understand sec2 A = 1+tan2 A ? To graph (sec2 A) and (1+tan2 A) separately and observe that the two graphs coincide, as suggested in [PEL]? With this in mind, we find it hard to believe that “the mathematics of [the Standards’] core program is sufficiently broad and deep so that students’ options for further study would not be limited” ([N1], ). In education circles, a great merit of the Standards is seen to be. | Proofs and . Concepts the fundamentals of abstract mathematics by Dave Witte Morris and Joy Morris University of Lethbridge incorporating material by P. D. Magnus University at Albany State University of New York Preliminary Version of May 2009 This book is offered under the Creative Commons license. Attribution-NonCommercial-ShareAlike The presentation of logic in this textbook is adapted from forall An Introduction to Formal Logic P. D. Magnus University at Albany State University of New York The most recent version of forall is available on-line at http logic We thank Professor Magnus for making forall freely available and for authorizing derivative works such as this one. He was not involved in the preparation of this manuscript so he is not responsible for any errors or other shortcomings. Please send comments and corrections to or 2006-2009 by Dave Witte Morris and Joy Morris. Some rights reserved. Portions 2005-2006 by P. D. Magnus. Some rights reserved. Brief excerpts are quoted with attribution from copyrighted works of various authors. You are free to copy this book to distribute it to display it and to make derivative works under the following conditions 1 Attribution. You must give the original author credit. 2 Noncommercial. You may not use this work for commercial purposes. 3 Share Alike. If you alter transform or build upon this work you may distribute the resulting work only under a license identical to this one. For any reuse or distribution you must make clear to others the license terms of this work. Any of these conditions can be waived if you get permission from the copyright holder. Your fair use and other rights are in no way affected by the above. This is a human-readable summary of the full license which is available on-line at http licenses by-nc-sa legalcode to .

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