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MATH 310 (Introduction to Analysis)
| DESCRIPTION |
The immediate purpose of this course is to prepare students
for Math
410. Its general goal is to develop the student's ability to construct
a rigorous proof of a mathematical claim. As a side benefit, the
student
is made aware of various mathematical results that are of interest to
those
wishing to analyze a particular mathematical model.
Math majors may not use this course for one of their upper level
mathematics
requirements. |
| PREREQUISITES |
Math 141 with Math 241 as a corequisite. |
| TOPICS |
Some Logic
Direct proofs
Contrapositive proofs
Proofs by contradiction
Set Relations
Equivalence relations
Discussion of "modulo"
Cardinality
Size of sets
Countability
Bernstein's Theorem
Induction
First principal of finite mathematical
induction
Second principal of finite mathematical
induction
Applications
Recursive Equations
Problems expressible as a difference equation
Verification of solutions using induction
Pigeonhole Principle
Problems which can be solved by utilizing
partitions
Completeness
Greatest lower bounds
Least upper bounds
Sequences
Convergence
Monotone convergence theorem
Bolzano-Weierstrass theorem
accumulation points
Contraction mapping principle |
| TEXT |
Text(s)
typically used in this course. |
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