MATH 307 (A Condensed Introduction to Analysis)
| DESCRIPTION |
MATH307 is an intensive course which
meets in Winterterm over 3 weeks,
5 days each week, 2 hours each day, and covers a
carefully selected 2/3 of the material of MATH310.
There is a
significant amount of graded homework, which is essential to
developing the ability to write proofs.
The immediate purpose of MATH307 is to prepare
students for Math 410. For many students, it is an appropriate
alternative to MATH310. The general goal of MATH307 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 some important mathematical concepts and results, especially
some which are relevant to MATH410.
Math majors may not use MATH307 for one of their upper
level mathematics requirements.
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PREREQUISITES |
Math 241 is required.
Math240 or 461 is recommended.
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| TOPICS |
Introduction to Sets
Some Logic
Direct proofs
Contrapositive proofs
Proofs by contradiction
Quantifiers
Cardinality
Size of sets
Countability
Bernstein's Theorem
Induction
First principal of finite mathematical
induction
Second principal of finite mathematical
induction (recursive definitions)
Applications
Completeness
Greatest lower bounds
Least upper bounds
Sequences
Convergence
Monotone convergence theorem
Bolzano-Weierstrass theorem
Functions
Injective, Surjective and Bijective functions
Continuous functions with epsilon/delta definition
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| TEXT |
Text(s)
typically used in this course:
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