To develop the students' ability to construct a rigorous proof of a mathematical claim. Students will also be made aware of mathematical results that are of interest to those wishing to analyze a particular mathematical model. Topics will be drawn from logic, set theory, structure of the number line, functions, sequences and continuity.
Credit will be granted for only one of the following: MATH 310 or MATH 307.
Math majors may not use this course for one of their upper level mathematics requirements.
Math141 is a prerequisite. Math241 and Math240/461 (or Math340 and 341) are pre/co-requisites.
Introduction to Sets
De Morgan's Law
Proofs by contradiction
Impact of change of quantifiers, order of quantifiers and negations on meaning of statements
Proof techniques applied to:
Real number properties
Size of sets
First principle of finite mathematical induction
Second principle of finite mathematical induction
Definition of limit
Monotone convergence theorem
Greatest lower bounds
Least upper bounds
Injective, Surjective and Bijective functions
Continuous functions with sequence definition
Continuous functions with epsilon/delta definition