MAA 4211, Section 7222 (16732)
Fall 2020
Instructor: David Groisser
Miscellaneous handouts

• Proof-writing quiz
• What is a proof? Ignore the references to the textbook; this handout was originally written for a linear algebra class (MAS 4105).
• Mathematical grammar and correct use of terminology. Same comment as above.
• Book of Proof, by Richard Hammack. This is the textbook now being used for MHF 3202 (Sets and Logic).
• One-to-one and onto: What you are really doing when you solve equations. This was written for a more elementary class, but you may still find it useful.
• Difference Between Inverse Functions and Inverse Images
• Some mistakes and/or misleading items in Section 1.1
• The cardinality of the set of real numbers.
• The Extended Reals
• Logarithms and Exponentiation
• The handouts in the group below have more to do with the foundations of arithmetic than with advanced calculus, but every student of mathematics should have an idea of which properties of arithmetic can be proven and which need to be assumed.
  • Peano Axioms for the Natural Numbers
  • Establishing some familiar properties of the natural numbers
  • Constructing Z from N
  • Constructing Q from Z
  • Constructing R from Q: Dedekind-cut approach

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