MATH 2002, Number Systems: An Introduction to Higher Mathematics
Dr. Markus Pflaum
Introduces the concepts of mathematical proofs using the construction of the real numbers from set theory.
Topics include basic logic and set theory, equivalence relations and functions, Peano's axioms, construction
of the integers, the rational numbers and axiomatic treatment of the real numbers.
The main intention of this course is to provide a bridge between the more computationally oriented
Calculus courses and the more abstract upper division Mathematics courses like MATH 3001 Analysis 1 and
MATH 2135 Linear Algebra.
It serves as a prerequisite for these courses and can be taken as an alternative to MATH 2001.
Homework assignments will be given on the course homepage on a bi-weekly basis.
It is the student's responsibility to get these assignments in the event of an absence from class.
Homework will be graded. Late turn-ins will not be accepted.
Your grade will be determined from the graded project paper and the presentation.
Elliott Mendelson: Number Systems and the Foundations of Analysis,
Dover Books on Mathematics, Dover Publications, Inc. (required).
Sergei Ovchinnikov: Number Systems: An Introduction to Algebra and Analysis,
Pure and Applied Undergraduate Texts, American Mathematical Society (optional).
Steven Krantz: The Elements of Advanced Mathematics,
Chapman and Hall/CRC (optional). Short Notes in Mathematics (required).