MATHEMATICS 231
Foundations of Mathematics
Dr. Mel Friske
Office:  S147 (Science Building)
Office Phone: 443-8836
E-mail: mfriske@wlc.edu
Homepage: http://faculty.wlc.edu/friske
Office Hours:  1:30 MTWRF; 10:30 MWF (WU); 10:00 T (WU); 11:30 R; other times by appointment

Text:  Friske, Mel. Concept and Proof: An Introduction to the Foundations of Mathematics. Text manuscript provided at cost of printing.



Catalog Description. Foundations of Mathematics. 3 cr. A transitional course to prepare students for upper-level courses in mathematics. Logic, proof techniques, set theory, functions, countable and uncountable sets, finite induction, equivalence relations. Selected topics. Prereq: MAT 222 or permission of the instructor.

Objectives. (1) To develop a rigorous understanding of the fundamental definitions and concepts of higher mathematics, and (2) To develop an ability to read and write mathematical proofs.

Course Content. The course will cover Chapters 1-6 of the text. Chapter 6 will provide you with an opportunity to use what you have learned to study an assortment of topics.

Methodology. Reading material and homework exercises will be assigned almost every time the class meets. Homework exercises will not be collected. It is your responsibility to ask questions about any difficulties encountered in these assignments. However, discussion of homework in class will be less than you may be accustomed--this is a higher-level course and you will assume more responsibility for learning. You should come prepared to participate in class discussion and may anticipate being "called on" every time the class meets. Please note that class participation is a major component of the final grade.

Assignments. There will be approximately 6 - 10 problem assignments, each consisting of several problems (usually proofs). Due Dates: each assignment will have a specified due date. Late work will not be accepted unless, in the judgment of the professor, there are legitimate extenuating circumstances. Unacceptable late work will receive a grade of 0.

Exams. There will be two in-class exams plus a final exam. Exam 1 will cover the first third of the course. Exam 2 will cover the second third of the course. The final exam will be cumulative.

Final Grades. The final average (AVE) will be computed as follows:

C = class participation (20%)

P = problem assignment average (20%)

E1 = score on Exam 1 (20%)

E2 = score on Exam 2 (20%)

F = score on Final exam (20%)

AVE = (C + P + E1 + E2 + F)/5

The grade for the course is determined by the value of AVE: A: 100-93, AB: 92-88, B: 87-83, BC: 82-78, C: 77-73, CD: 72-68, D: 67-60, F: below 60. The professor reserves the right to lower the grade ranges (e.g. the bottom of the B range might be lowered from 83 to 82). The grade ranges will not be raised. The professor also reserves the right to exercise discretion in raising your grade if he feels that the value of AVE does not properly reflect the quality of your work (e.g. because of one low exam score). This does not imply in any way that the lowest test score necessarily will be dropped. The professor will not use discretionary judgments to lower your final grade.

Attendance Policy. Attendance at each class is expected. If your judgment is so misguided that you choose to cut this class, you will bear the consequences of a reduced class participation grade and poor performance on exams.


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SELECTED BIBLIOGRAPHY

The nature of mathematics

Courant, Richard and Herbert Robbins. What is Mathematics? London: Oxford UP, 1941.

Eves, Howard. Foundations and Fundamental concepts of Mathematics. 3rd. ed. Boston: PWS-Kent, 1990.

Kershner, R.B. and L.R. Wilcox. The Anatomy of Mathematics. New York: Ronald Press, 1950.

MacLane, Saunders. Mathematics: Form and Function. New York: Springer-Verlag, 1986.

Wilder, Raymond L. Introduction to the Foundations of Mathematics. 2nd ed. New York, Wiley, 1965.

Proof writing

Knuth, Donald. Mathematical Writing. Washington, D.C.: Mathematical Association of America, 1996.

Krantz, Steven. A Primer of Mathematical Writing: Being a Disquisition on Having Your Ideas Recorded, Typeset, Published, Read & Appreciated. Providence (RI): American Mathematical Society, 1997.

Solow, Daniel. How to Read and Do Proofs. 2nd ed. New York: Wiley, 1990.

Set theory

Halmos, Paul R. Naive Set Theory. Princeton: Van Nostrand, 1960.

Hrbacek, Karel and Thomas Jech. Introduction to Set Theory 3rd ed. New York: Marcel Dekker, 1999.

Kamke, E. Theory of Sets. Trans. from 2nd German ed. by Frederick Bagemihl. New York: Dover, 1950.

Suppes, Patrick. Axiomatic Set Theory. Princeton: Van Nostrand, 1960.

Vilenkin, N. IA. Stories about Sets. Trans. by Scripta Technica. New York: Academic Press, 1968.


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