Learn how to write proofs...

• Innovative proof-writing software makes it easy to learn how

• Simply point and click to invoke the rules of logic, each line verified as you enter it

• Interactive, self-study tutorial introduces standard methods of proof using examples from the simpler domains of formal logic, set theory and elementary number theory

Free full-version download     Last updated:  2009-03-25

"Well conceived, carefully planned and remarkable in its pedagogy and content."
–Brendan Kelly Ph.D., Ed.D.,  Emeritus Professor of Mathematics and Mathematics Education, OISE/University of Toronto

"What impressed me most about this teaching software is that it seems to focus on ensuring that logic is stripped to its bare essentials, and these simplest concepts are taught very thoroughly indeed, with full cross referencing between practice and theory."
– Stephen Simmons, Clinical Director, National Health Service, UK

"A better tool for learning about proofs in the way that mathematicians usually do them."
–Norman Megill, creator of "Metamath" 
 

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Contents

1. What is DC Proof?

2. Features

3. Sample Proofs

4. System Requirements
 

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What is DC Proof?

• Proof-writing software that enables the user to write formal arguments and proofs using convenient pull-down menus to invoke the rules of logic and set theory
   
• A proof checker that verifies each line of proof as it is entered, making it impossible to enter even one invalid line of proof
   
• An aid to critical thinking using the methods of formal logic and proof
   

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Features

• Includes fully interactive, self-study tutorials that can serve as an introduction to symbolic logic and set theory at the high school, college or university levels (view table of contents and excerpt)
   
• Tutorial introduces the user to:
   
  • Direct proof
     
  • Indirect proof, or proof by contradiction
     
  • Proof by contrapositive
     
  • Proof by cases
     
  • Proof by induction
     
  • Manipulation of universal and existential quantifiers
     
  • A simplified set theory (functions, subsets, power sets, Cartesian products, etc.)
     
  • Use of formal definitions (in elementary number theory)
     
• Color-coded variables (in predicate logic) indicate at a glance what kind of generalizations can be made, and when conclusions may be drawn
   
• View proofs at various levels of detail, hiding or revealing details as required ─ absolutely indispensible for writing longer proofs!
   
• User comments (in blue) and meaningful variable names (of unlimited length) facilitate both the reading and writing of proofs
   

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Sample Proofs

Samples of proofs in the easy-to-read DC Proof format:

• Sun, cloud and rain (propositional logic)
   
• Dolphins, mammals and fish (predicate logic)
   
• The composition of functions (set theory)
   
• Resolution of Bertrand Russell's The Barber Paradox (predicate logic)
   

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System Requirements

DC Proof is a PC-based program that requires the following software to run:

• PC users require Windows 95 or later
   
• Mac OS X or Linux users require a Windows emulator or the equivalent. Recommended are:
   
  • Wine 1.0.1
     
    • Free download
    • Limited tech support
    • No need to install Windows
       
  • CodeWeavers Crossover
     
    • 30 day free trial, reasonably priced
    • Makes using Wine 1.0.1 easier
    • Tech support included
    • No need to install Windows
       
• MS Internet Explorer, Version 4 or later
   
  • DC Proof uses components of IE
     
  • IE must be installed on your computer
     
  • IE need not be your default browser, and need not be running or active at any time
     
  • Free download of latest version of IE available from Microsoft
     

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Copyright © 2007 Dan Christensen