Department of Mathematics

Writing Resource Center

Writing Resource Center Welcome to the on-line writing resource center for the Department of Mathematics. This site aims to provide support for students who are learning to read and write mathematical arguments.

Here is a summary of the main features to look for when first approaching proofs:

• How to read a mathematical proof

Introduction to Some Common Proof Structures

• Direct Proof
• Proof by Contradiction
• Proof by Contraposition
• Proof by Counterexample
• Proof by Induction
  • Further examples of proof by induction
• Distinguishing between logical structures

Resources for Writing Mathematical Ideas

• Glossary of mathematical terms
• Style guide for writing mathematics
• A markers' list of features found in a well-written proof
• Common mathematical symbols
• A more comprehensive list of math symbols (from Wikipedia)
• Dr. L.W. Cusick's proof-writing page

Resources for Teaching Reading and Writing Skills

• In-Class Activity Worksheets
  • Proof that there are infinitely many prime numbers
  • A variation of the Triangle Inequality
  • Proof that one can count the rational numbers
  • What is wrong with this false proof by induction?
• Further examples of proof by induction
• Bloom's Taxonomy in the context of mathematics
• A handout on Bloom's Taxonomy for mathematics
• A handout on how to read math proofs(as listed above)
• Suggested elements of acceptable style for written mathematics(as listed above)
• A markers' list of features found in a well-written proof(as listed above)

All questions and comments pertaining to the content of this site may be directed to writing@math.toronto.edu This includes requests for the solution sets to any activities listed above.