Math 105: Math As A Liberal Art

Fall, 2005 TTh  10:00 -11:25

ROOM: Fowler 112 

(Last Revised on 09/1/2005 )

Math 105                          COURSE INFORMATION                          M.Flashman
Math As A Liberal Art                                                               Fall, 2005
TTh  10:00 - 11:25                                                   ROOM: Fowler  112

OFFICE: Fowler 325                                    PHONE:  (323) 259- 2555
Hours (Tent.): M-F  11:30-12:30 AND BY APPOINTMENT or chance!
E-MAIL:                 WWW:


TEXTS: REQ'D.:Mathematics: The Science of Patterns by K.Devlin.
Flatland: A Romance of  Many Dimensions by E. Abbott.

Catalog description:

Introduction to mathematical thinking. Investigation of mathematical patterns in counting, reasoning, motion and change, shape, symmetry, and position. Not open to seniors.


Core classes ask students to engage as thoroughly as possible in analytic and creative thinking: posing questions from various points of view, solving problems, formulating hypotheses, gathering evidence to support claims and arguments, drawing appropriate conclusions, and expressing ideas clearly. These classes are designed to ask the large liberal arts questions, questions which we believe all students must address in order to participate fully in their academic careers, their vocations, their lives, questions such as, “how do different societies at different historical times define and represent justice, beauty, the natural world, the self, the sacred, and truth?” Students are asked to examine previously held ideas in the context of new and challenging ones, to experiment as imaginatively as possible, to articulate similarities and differences, and to revise both ideas and written work.

SCOPE: In this course we will explore topics in mathematics that have arisen from attempts to define and explain the visual aspects of experience, such as number, motion, symmetry, space dimension, and surface. Limitations, unexpected consequences and applications resulting from the development of these concepts illustrate the power of mathematics to measure, to translate, to transform, and to classify. Lectures will discuss topics not covered in the text as well as those treated in the text.
Readings and materials will be from the assigned texts and materials linked to the course on the world wide web as appropriate.

Course Objectives (taken from prior Math 105's):  The following are some of the objectives I hope we can accomplish together through this course this semester.
    * Read expository mathematics with understanding and appreciation.
    * Appreciate the breadth of what mathematics is and the beauty of it as a subject of inquiry and as a tool for explaining phenomena in the world.
    * Articulate mathematical ideas in both oral and written forms.
    * Work together on mathematics in small groups.

Blackboard.  We will use Blackboard as one of the learning and feedback tools in this class.  In addition to keeping you updated with class assignments and expectations and making announcements as needed, I will post regular class notes that will address both issues brought up in the readings and from in-class and at-home activities.

The first thing you must do is enroll yourself into this course on Blackboard.  To do so, follow these steps:

    * Logon to Blackboard (at
    * Click on the COURSES tab
    * Select the MATHEMATICS department from the course catalogue list
    * On the list of courses available, find MATH  AS A LIBERAL ART, and …
    * … you will see an ENROLL button
    * Select it and this should enroll you in the course

You should then take some time to explore the site to see where I will post various things, including the daily assignments and “quizzes.”  Again, it is important for you to check Blackboard regularly – I would advise at least twice a week – and keep up with the assignments and expectations as posted there.

Assignments: There will be graded assignments usually consisting of  3 to 5 problems, essays, or activities. Other problems, assigned in class, will be a source for class discussions and activities and will be used to indicate satisfactory class participation. Course materials, including this description, and returned assignments and class activities should be kept in a binder, forming the basis for an assignment as part of a final review of your work at the end of the course.
The Portfolio: Each student will organize a portfolio which should contain entries related to the content of this course but not discussed extensively in the lectures. No particular format or topics for entries are required, but each entry must have some substantial (as opposed to purely subjective) content. A minimum of 4 entries are required to achieve a grade of C. The portfolio (quality and quantity) will be used for determining letter grades above the C level.

A preliminary portfolio entry should be submitted for preview feedback and advice no later than September 23rd.
A second entry is due for review no later than October 14th.
A third entry is due for review no later than November 18th.
A fourth and any more entries are due for review no later than December 2nd.
*The entire complete and revised portfolio is due by Monday, December 5th  before 5 pm.
[Note change from wednesday!]

A portfolio entry can report on the content of  reading, illustrate it by examples, and/or follow up on it with an individual response and creativity.

The content of the portfolio entry should relate specifically and directly to some visual mathematics. Personal observations, philosophical musings, and aesthetical judgments are not adequate connections to something visual by themselves to qualify as mathematical content.

Suggested resources for the entries may be found on the Assignment and Reading List.
Portfolios will be due for grading on Monday, December 5th before 5 P.M.

Academic Honesty:  I expect the highest level of academic honesty from all of my students.  You should read the appropriate sections of the Student Handbook that discuss the “Spirit of Honor” and Academic Honesty.  Any instance of plagiarism or cheating will be dealt with strictly and in accordance with the procedures found in the Handbook.  Copying someone’s homework or problem set solutions is considered cheating.  Including other sources in your papers without appropriate quotes and citations is considered plagiarism.  You may discuss ideas and problems as appropriate, but what you ultimately write and submit must be your own work, written up independently of others.

The Project. Each student will participate in a course project as a part of a team. Each team will have three or four members. These projects will be designed with assistance from myself and the course assistants. The quality of the project will be used for determining letter grades above the C level. Ideas for projects will be discussed during the third week.
Click here for Project Proposal Guidelines and Suggestions

Preliminary Project Proposals should be submitted for first review by 5 p.m., October  7th.
Projects should be submitted for grading by Wednesday, December 7th before 5 P.M.

A Project Fair will be organized for displays and presentations during the last day of class. Details will be discussed later.

ADVICE: I am available during office hours and by appointment to consult with individuals or partnerships on particular portfolio entries and/or project ideas. Don't be shy!


Technology: The computer offers a very useful tool to enhance visual and computational understanding as well as a powerful device for discoverying and presenting resources on the world wide web. An optional lab time will be organized that will be devoted to a number of different projects as well as working with mathematical software tools, such as Wingeom, Winplot, Windisc. (The software we use is all  freeware  available from the www site of Rick Parris or from me.) A short list of world wide web sites for further reading will be organized on a weekly basis with materials specifically related to the course topics.

GRADES: Four or more absences without extenuating circumstances may be justification for a grade of F.

Otherwise final grades will be determined by taking into consideration the quality of work done in the course as evidenced primarily by work on in-class activities, assignments, projects, and portfolios.

**Only the letter grades of A, B, C, D, and F will be given.  (No + or -'s)

Minimum Standards:
** For the grade of C or CR a student must at least
     (1) have satisfactory attendance and participation,
     (2) have a satisfactory record on the assignments and class activities (about 80%  +'s),
     (3) have participated responsibly on a satisfactory group project,
and (4) have submitted a portfolio with at least 4 entries.

** For the grade of B (or A) a student must at least
       (1) be qualified for a grade of C,
and  (2) submit a portfolio with at least 3 (or 6) entries beyond the work submitted for grade of C.
The portfolio's quality will be used also to determine the final grade .

      Students wishing to be graded with either CR or NC should make this request using the on-line registration web site.

Tool Kit: You should have assembled for possible use at each class the following items:
a computer disc to keep course computer software [Wingeometry, Winplot?] and files.
a deck of playing cards
colored pencils or pens (6+)
fastener of some kind (stapler, tape, or glue stick)
rubber bands (at least 2)
string (at least a meter)
one dozen staws
one dozen pipe cleaners.

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Last updated:8-31-05