Mathematics 331 Syllabus

Course Information
Course title: Mathematics 331 OL Fall, 2007: Mathematical Explorations
Course number: 13505R
Course discipline: Mathematics
Course description: Mathematics 331 OL Fall, 2007

Course site:
https://webteach.csun.edu

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

Text: The Mathematical Experience STUDY EDITION. ISBN 0-8176-3739-7. Available only at the Matador Book Store.

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

II. Course Content: The course focuses on explorations of 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.

III. Course Format: With the exception of obtaining books for the final paper, and viewing three videotapes in the Oviatt library, the course is conducted entirely on-line (but NOT in real-time). Students must complete assignments (individual and group) posted on WEB CT by due dates listed in a course calendar.

IV. Course Requirements

A. Class Assignments: Nine individual on-line (email or web posted) reading and writing exercises and problem sets. Six sets of group discussion questions. See Class Calendar on WEB CT for due dates.

B. Final Project: A 12-15 page expository research paper. See Final Project page on WEB CT for details.

V. Topics for Class Assignments

Theme 1: The Mathematical landscape – what and where is Mathematics?
Characteristics Mathematics shares with other fields
Mathematical ways of thinking: Pythagorean theorem and Pythagorean triples

Theme 2: 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

Theme 3: Invention vs. discovery in Mathematics
Platonic and Formalist views of the origins of Mathematics
Mathematical ways of thinking: Fibonacci sequences and their applications

Theme 4: The aesthetic appeal of Mathematics. Mathematicians as pattern finders Mathematical ways of thinking: Frieze patterns and geometric transformations

Theme 5: Cognitive styles in the learning of Mathematics
Polya’s heuristics
Mathematical ways of thinking: Teaching mathematics through art, literature, sports, etc.

Theme 6: Mathematical Reality
Fractals
The Fourth Dimension

VI. Description of Final Project: The final project is an expository research paper that explores a specific topic in mathematics that is connected to a particular field of study. The objective of the paper is to teach the reader the selected mathematical topic and demonstrate its 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.

VII. Methods of Evaluation: The 6 sets of group discussion questions and 9 individual essay assignments will be graded on the basis of 50 points each for a total number of classwork points of 750. Detailed comments will be provided.
The three components of the final project will be graded on the basis of 500 points (Homework I [outline] 100 points; Homework II [final paper] 200 points; Homework III [revised final paper] 200 points). Detailed comments will be provided for each component.
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.

VIII. Student Learning Objectives
As a course that fulfills the General Education requirement in Section A: Basic Subjects, Subsection A.3 (Mathematics), Mathematics 331 attempts to address the goals that involve basic skills in the following areas: ANALYTIC READING AND EXPOSITORY WRITING (RW) and MATHEMATICS. In particular, it addresses following Student Learning Objectives (SLO’s) that have been established by the University and the Mathematics Department:

RW SLO 1 Develop and clearly define ideas through writing;
RW SLO 2 Ethically integrate sources of various kinds into their writing;
RW SLO 3 Compose texts through drafting, revising, and completing a finished product.
RW SLO 4 Express ideas through writing by posing questions, making original claims, and coherently structuring complex ideas
RW SLO 5 Revise writing for greater cogency and clarity.
RW SLO 6 Utilize adopted communication modes and documentation styles of specific disciplines (MLA, APA, Chicago, CBE, etc) where appropriate
MATH SLO 1 Represent, understand and explain mathematical information symbolically, graphically, numerically and verbally.
MATH SLO 2 Develop mathematical models of real-world situations and explain the assumptions and limitations of those models.
MATH SLO 3 Use models to make predictions, draw conclusions, check whether the results are reasonable, and find optimal results using technology where necessary and appropriate.
MATH SLO 4 Demonstrate an understanding of the nature of mathematical reasoning including the ability to prove simple results and/or make statistical inferences.

Course date: Thursday, August 23, 2007 through Monday, December 10, 2007
Prerequisite(s): Passing score on or exemption from the Entry Level Mathematics Examination; completion of the lower division writing requirement and upper-division standing.

Mathematics 331 Spring Calendar of Assignments

 

Week

Monday

Tuesday

Wednesday

Thursday

Friday

 

0

Jan 20

 

-Buy your book

-Review the Course Syllabus and contents of the Class Guidelines

Post your introduction to your groupmates using the Go to Discussion Forums link on Theme 1

-Reading Assignment 1: The Mathematical landscape – what and where is Mathematics? Pages 1-30 +

Complete Self-Test in Theme 1 on Reading Assignment

Post individual answers to Discussion Questions 1 using the Go to Discussion Forums Link on Theme 1

1

Jan 27

Collaborate with groupmates on Discussion Questions 1 and formulate a group response

-Select one member to email to Instructor by 8 p.m. the group response to DQ 1 as a word documen

-Review Instructor's emailed comments on the graded DQ 1 assignment

-Email Essay Homework 1 to Instructor as a word document by 8 p.m.

Reading Assignment 2: The course of Mathematical evolution Pages 36-37, 59-69, 97-120 +

 

2

Feb 3 

-Complete Self-Test in Theme 2 on Reading Assignment 2

Post individual answers to DQ 2 using the Go to Discussion Forums Link on Theme 2

Collaborate with groupmates on DQ 2 & formulate a group response

-Select one member to email to the instructor by 8 p.m. the group response to DQ 2 as a word document

-Read Instructor's emailed comments on the graded DQ 2 assignment

 

3

Feb 10

-Email Essay Homework 2 to Instructor by 8 p.m. as a word documen

-Read Video Assignment A on Theme 2 and go to the Oviatt this week to view the video

 

 

 

Email to Instructor by 8 p.m. as a word document the Essay on Video A

4

Feb 17

-Reading Assignment 3: Invention vs. discovery in Mathematics. Pages 76-97, 356-368,+

Complete Self-Test in Theme 3 on Reading Assignment 3

--Post individual answers to DQ 3 using the Go to Discussion Forums Link on Theme 3

Collaborate with groupmates on DQ 3 & formulate a group response

Select one member to email to the instructor by 8 p.m. the group response to DQ 3 as a word document

-Read Instructor's emailed comments on the graded DQ 3 assignment

5

Feb 24

-Email Essay Homework 3 to Instructor by 8 p.m. as a word document

-Reading Assignment 4: The Aesthetic Appeal of Mathematics - Pages 138-195 +

-Complete Self-Test in Theme 4 on Reading Assignment 4.

Post individual answers to DQ 4 using the Go to Discussion Forums Link on Theme 4

-Collaborate with groupmates on DQ 4 & formulate a group response

 

6

Mar 2

-Select one member to email to the instructor by 8 p.m. the group response to DQ 4 as a word document

-Read Instructor's emailed comments on the graded DQ 4 assignment

 

-Email Essay Homework 4 to Instructor as a word document by 8 p.m.

-Read Video Assignment B on Theme 4 and Go to Oviatt to view the Video

 

7

Mar 9

 

 

 

Email to Instructor by 8 p.m. Essay on Video B

. Reading Assignment 5: Cognitive Styles & the Learning of Mathematics, pages 304-348 +

 

8

Mar 16

Spring break

 

 

 

 

 

9 Mar 23

-Complete Self-Test in Theme 5 on Reading Assignment 5

-Post individual answers to DQ 5 using the Go to Discussion Forums Link on Theme 5

-Collaborate with groupmates on DQ 5 and formulate a group response

Select one member to email to the instructor by 8 p.m. the group response to DQ 5 as a word document

-Read Instructor's emailed comments on the graded DQ 5 assignment.

 

10

Mar

30

-Email Essay Homework 5 to Instructor as a word document by 8 p.m.

-Read Video Assignment C on Theme 5 and go to the Oviatt this week to view the video

 

 

 -Email to Instructor by 8 p.m. Essay on Video C

 

11

April 6

-Reading Assignment 6: Mathematical Reality, pages 233-240, 405-453 +

Complete Self-Test in Theme 6 on Reading Assignment 6

 

-Post individual answers to DQ 6 using the Go to Discussion Forums Link on Theme 6

 -Collaborate with groupmates on DQ 6 and formulate a group response 

 

12

April 13

-Select one member to email to Instructor by 8 p.m. the group response to DQ 6 as a word document

-Read Instructor's emailed comments on the graded DQ 6 assignmen

 Email Essay Homework 6 to Instructor as a word document by 8 p.m.

-Email to the Instructor your topic for your final paper and proposed list of resources by 8 p.m.

. Read Instructor's email comments on your resources.

Go to the Oviatt and secure approved resources for your final paper 

13

April 20

Do your research and formulate a plan for your paper.

 

 

 

Homework I: Email to Instructor as a word document by 8 p. m. the Detailed Outline of Final Paper

 

14

April 27

-Review detailed comments by Instructor on your outline for your final paper

Begin writing your final paper

 

 

 

 

15

May 4

-Homework II: Email to Instructor as a word document by 8 p.m. your Final Paper

 

 

 

Review detailed comments by Instructor on your final paper

 

16

May 11

-Make Revisions on Final Paper this week

 

 

 

 

 

17

May 18

-Homework III: Revised Final Paper + graded paper (hardcopies) due by 4 p.m. in Math Office SSH 114