MAA 4211, Section 7222 (Groisser)
Fall 2019
Miscellaneous handouts

• Taking notes in a college math class
• 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.
• Sets and Functions
• Difference Between Inverse Functions and Inverse Images
• Equivalence Relations
• 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.
• The cardinality of the set of real numbers.
• Interiors, Closures, and Boundaries
• The Extended Reals
• Continuity, Images, and Inverse Images
• 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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