Credits:
Course Description:
This course is intended to cover those aspects of mathematics that form a foundation for the study
of advanced mathematics. In particular, it will cover such basic concepts as set theory,
propositional and predicate logic, relations, functions and cardinality. In studying these
concepts, the emphasis will be not only on the subject matter, which forms the core of
knowledge needed to pursue more advanced mathematical courses, such as abstract algebra
and real analysis, but also on how one reads and writes mathematical proofs. What constitutes
a proof and various means of proving statements will be examined in detail during the course.
As time permits we will then apply these topics and methods to specific areas, such as the
study of calculus (the epsilondelta definition of limit, continuity, differentiation,
sequence and series), group theory (binary operations, fundamental properties of
groups, subgroups, isomorphic groups) and linear algebra.
PreRequisites:
MATH 260  Linear Algebra
Note: this special topics course will serve as a 300level mathematics elective for mathematics majors
or minors. In the future, if the course, or a modified version of it, is approved by the department
and university governance, then it may become a required course for the mathematics major and be a
prerequisite for courses like
MATH 360  Abstract Algebra Iand
MATH 450  Real Analysis. It should not be taken after MA 360 or MA 450.
Frequency:


Current Textbook:
Mathematical Proofs: A Transition to Advanced Mathematics,
Second Edition, by Chartrand, Polimeni and Zhang, published by Pearson Addison Wesley in 2008.
Check with your instructor to make sure this is the
textbook used for your section.
Fall 2011 Schedule:
Topics
 0. Communicating mathematics (how to read and write mathematics)
 1. Sets
 2. Logic
 3. Direct proof and proof by contradiction
 4. More on direct proof and proof by contradiction
 5. Existence and proof by contradiction
 6. Mathematical induction
 7. Prove or disprove
 8. Equivalence relations
 9. Functions
 10. Cardinalities of sets
 11. Proofs in calculus
 12. Proofs in group theory
The order of presentation of the contents of this syllabus,
exams, and grading policies are entirely at the discretion of the
individual instructor.
