Miscellaneous handouts

MAA 4211, Section 3045
Fall 2014

• Taking notes in a college math class
  
• 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.
• Proof-writing quiz
  
• Dr. McCullough’s notes. Please remember that while you’re welcome to use these excellent notes as source-material to supplement the textbook, your class notes, and my own handouts on various topics, Dr. McCullough’s notes are not an “official” set of notes for our section. There may be topics that I cover that Dr. McCullough does not, and vice-versa. On the topics that we both cover, there may be some (generally minor) differences in definitions.
• Notation-difference chart . Notational and terminological differences among Rosenlicht, Dr. Groisser, and
  Dr. McCullough. (May be updated occasionally.)
• 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.
• 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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