MATH 2002, Number Systems: An Introduction to Higher Mathematics

Spring 2023

Instructor:

Dr. Markus Pflaum

Course Contents:

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.

Syllabus

Lecture Hours and Venue:

MWF 9:05 am - 9:55 am, CLRE 302.

Assignments:

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.

Homework	Due Date	Homework	Due Date	Homework	Due Date
Set 1	01/27/2023	Set 2	02/06/2023	Set 3	02/24/2023
Set 4	03/10/2023	Set 5		Set 6
Set 7		Set 8

Exams:

An in class midterm exam will be held on Monday, March 17th

The final exam will be held on TBA.

Course Grading:

Your grade will be determined from the graded homework and the exams.

Textbooks:

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).