Introduction to Mathematical Proofs

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• This is the syllabus for the class.

Worksheets

• Worksheet 1
• Worksheet 2
• Worksheet 3 (Hints and selected solutions)
• Worksheet 4 (Hints) (Solutions)
• Handout on Induction
• Worksheet 5 (Hints) (Solutions)
• Handout on Strong Induction
• Worksheet 6
• Peano Arithmetic Handout
• Set Theory Handout
• Worksheet 7 (Sample solutions) (Solutions)
• Worksheet 8 (Solutions)
• Worksheet 9
• Worksheet 10 (Solutions)
• Worksheet 11 (Solutions)
• Worksheet 12
• Worksheet 13

Exams

• Take-home midterm exam
• In-class midterm exam

Projects

• Peano arithmetic: multiplication
• Challenging induction problems (aka worksheet 6)
• Inequalities
• Absolute value and distance between rational numbers (we hadn't built the real numbers at this point)
• Elementary number theory
• The pigeonhead principle
• Exercises on set theory
• Elementary classification of equivalence relations
• Elementary classification of chains
• Infinite Ramsey Theory
• An explicit bijection between the set of natural numbers and the set of positive rational numbers