MAA 4211, Section 16G0 (Groisser)
Fall 2016
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.
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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