Mathematics 331 OL Summer, 2007

ON-LINE COURSE
Professor: Dr. E. A. Marchisotto
Office Hours: on-line
Email: emarchisotto@csun.edu

Mathematics Department Office:  Santa Sussana Hall (formerly Faculty Office Building) , first floor
Text: The Mathematical Experience STUDY EDITION. ISBN 0-8176-3739-7. 

Course objectives:  To give students an appreciation of the diversity of mathematics and the spirit in which it is employed in various applications. 

Course description:  The character and origin, as well as historical and modern applications of mathematical concepts. The contributions of various cultures to the field are studied along with the use of mathematical models for physical problems. Prerequisites: Passing score on or exemption from the Entry Level Mathematics Examination; completion of the lower division writing requirement and upper-division standing.

Course Requirements:

Class Assignments:  on-line (email or web posted) reading and writing exercises and problem sets which represent 60% of the grade in the class.   . 

Final Project:   A 12-15 page expository research paper, which represents 40% of the grade that teaches a specific mathematics topic.

Topics for Class Assignments

The Mathematical landscape – what and where is Mathematics?

Characteristics Mathematics shares with other fields

Mathematical ways of thinking: Pythagorean theorem and Pythagorean triples

The course of Mathematical evolution

The role of the individual and the culture in the growth of Mathematics

Conjecture vs. proof

Mathematical ways of thinking: Goldbach’s conjecture, Fermat’s last theorem

Invention vs. discovery in Mathematics

Platonic and Formalist views of the origins of Mathematics

Mathematical ways of thinking: Fibonacci sequences and their applications

The aesthetic appeal of Mathematics.

Mathematicians as pattern finders

Mathematical ways of thinking: Frieze patterns and geometric transformations

Cognitive styles in the learning of Mathematics

Polya’s heuristics
                  Mathematical ways of thinking: Teaching mathematics through art, literature, sports, etc.

Topics for Final Project

The final project involves the selection of a specific topic in mathematics that is connected to a particular field of study. The objective of the expository research paper is to teach its reader the mathematics and demonstrate the connections to the chosen field. Topics include, but are not limited to: similarity in geometry and its use in film; perspective in geometry and its use in art; transformation in geometry and its use in design; fractal geometry and its use in communications; number systems and their developments in different cultures; special numbers (pi, phi, e, zero), their history, and their uses in a variety of fields.

Methods of Evaluation:

The 4 sets of group discussion questions and 5 individual essay assignments will be graded on the basis of 50 points each. Detailed comments will be provided. The total out of 450 points will represent 60% of the grade for the course. The four components (Homeworks I-IV) of the final project will be graded on the basis of 400 points.  Detailed comments will be provided for each component. The final project will represent 40% of the grade for the course. Course grades will be assigned according to the following  scale:  100-90 = A,  89-88 = A-, 87-85 = B+, 84-80 = B, 79- 75 = C+, 74-70 = C, 69-65 = D+, 64-60 = D, 59-55 = D-, and below 55 = F).   No late assignments are accepted.

Class Calendar All reading assignments are from the text:  The Mathematical Experience, Study Edition. ISBN 0-8176-8739-7.   The + indicate reading from an outside source: journal article or book.  Homework assignments are posted on the discussion group pages.

Week	Monday	Tuesday	Thursday	Friday
1: 6-4	Reading Assignment 1: The Mathematical landscape – what and where is Mathematics? Pages 1-30 +	Establish methods of communication and intermediary deadlines within your group for the collaborative work.	Collaboration with groupmates. Email group answer to discussion questions 1 by 8 p.m	Homework 1: Re the characteristics Mathematics shares with other fields. Email individual essay by 8 p.m.
2 : 6-11	Reading Assignment 2: The course of Mathematical evolution Pages 36-37, 59-59, 97-120 +	Collaboration with groupmates. Email group answer to discussion questions 2 by 8 p.m.	Homework 2: Re the role of the individual and the culture in the growth of Mathematics. Email individual essay by 8 p.m.	Reading Assignment 3: Invention vs. discovery in mathematic. Pages 76-97, 356-382,+
3: 6-18	Collaboration with groupmates. Email group answer to discussion questions 3 by 8 p.m.	Homework 3: Re the question of the creation or discovery of Mathematics. Email individual essay by 8 p.m.	Reading Assignment 4: Mathematicians as pattern-finders. Pages 138-195, +	Collaboration with groupmates. Email group answer to discussion questions 4 by 8 p.m.
4: 6-25	Homework 4: Re the aesthetic appeal of Mathematics. Email individual essay by 8 p.m.	Reading Assignment 5: Cognitive styles and the learning of Mathematics. Pages 304 -348, +	Selection of the topic for the final paper:  Email  your selection by 8 p.m.	Homework 5: Re how to teach Mathematics to students with different learning styles. Email individual essay by 8 p.m.
5: 7-2	Homework I: Resources for final paper obtained. Post list by 8 p.m.	Research	Homework II: Detailed outline for final paper. Posted by 8 p.m.	Write
6: 7-9	Homework III: Email Draft of Final Paper as WORD attachment by 8 p.m.	Revise	Revise	Homework IV: Hard Copy of Final Paper DUE in Mathematics Office before 4 p.m.