tailieunhanh - Metamath A Computer Language for Pure Mathematics

While a little bit of group learning and guiding-on-the-side is good in the classroom, too much poses an obstruction to effective dialogue between teacher and students as well as to the efficient transfer of knowledge from teacher to students. In such a climate, gone is the possibility that the teacher can share with students his or her insights or warn them against pitfalls, or that students can learn enthusiastically from their teacher in class and do the mental construction at home — with or without a group of friends. Right now all the learning must take place instantly in school. But can any substantive mathematics be learned this. | Metamath A Computer Language for Pure Mathematics Norman Megill Public Domain This book has been released into the Public Domain by Norman Megill on March 10 2007 per the Creative Commons Public Domain Dedication http licenses publicdomain . The public domain release applies worldwide. In case this is not legally possible the right is granted to use the work for any purpose without any conditions unless such conditions are required by law. Several short attributed quotations from copyrighted works appear in this book under the fair use provision of Section 107 of the United States Copyright Act Title 17 of the United States Code . The public-domain status of this book is not applicable to those quotations. Any trademarks used in this book are the property of their owners. ISBN 978-1-4116-3724-5 Lulu Press Morrisville North Carolina USA Norman Megill 19 Locke Lane Lexington MA 02420 E-mail address nm@ http Contents Preface . vii 1 Introduction 1 Mathematics as a Computer Language. 4 Is Mathematics User-Friendly . 4 Mathematics and the Non-Specialist. 12 An Impossible Dream . 14 Beauty. 15 Simplicity. 16 Rigor . 18 Computers and Mathematicians. 20 Trusting the Computer . 21 Trusting the Mathematician. 22 The Use of Computers in Mathematics . 24 Computer Algebra Systems. 24 Automated Theorem Provers. 25 Proof Verifiers . 27 Mathematics and Metamath. 29 Standard Mathematics. 29 Other Formal Systems. 29 Metamath and Its Philosophy. 30 A History of the Approach Behind Metamath. 30 Metamath and First-Order Logic. 31 2 Using the Metamath Program 33 Installation . 33 Your First Formal System. 34 From Nothing to Zero. 34 Converting It to Metamath. 36 A Trial Run . 40 Some Hints for Using the Command Line Interface . . 45 Your First Proof. 46 A Note About Editing a Database File. 53 .

• Toán học
• ferreted out
• difference between
• Brazilian rainforest
• species becomes
• constant flux
• project reroutes
• Ferraris
• apart and reassemble
• rainforest
• rainfores