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 co-requisite. |
| TOPICS |
Introduction to Sets
Set operations
De Morgan's Law
Some Logic
Direct proofs
Contrapositive proofs
Proofs by contradiction
Quantifiers
Impact of change of quantifiers, order of quantifiers and negations on meaning of statements
Disproving statements
Proof techniques applied to:
Divisibility
Real number properties
Set equalities
Equivalence relations
Cardinality
Size of sets
Countability
Bernstein's Theorem
Induction
First principal of finite mathematical
induction
Second principal of finite mathematical
induction
Applications
Sequences
Definition of limit
Convergence
Monotone convergence theorem
Bolzano-Weierstrass theorem
Completeness
Greatest lower bounds
Least upper bounds
Cauchy sequece
Functions
Injective, Surjective and Bijective functions
Continuous functions with sequence definition
Continuous functions with epsilon/delta definition
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| TEXT |
Text(s)
typically used in this course:
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