GST 1510: History and Concepts of Mathematics

**Time & Place**: Wednesday, 6-8:45 p.m., 0334 Cohn.

**Instructor’s Work Address**: Moti Nissani, Interdisciplinary
Studies Program, 2nd floor, 5700 Cass, Wayne State University, Detroit,
MI 48202

**Home Address**: 28645 Briar Hill, Farmington Hills, MI 48336

**E-mail**: moti.nissani@wayne.edu

**Tel**.: 248.427.1957 (h) (12 p.m. every day<calling hours<10
p.m every day)

**Internet Homepage**: http://www.cll.wayne.edu/isp/mnissani/

**Class Internet Address**: :
http://www.cll.wayne.edu/isp/mnissani/pagepub/math/gst1510

**Office hours:** By appointment.

**Materials**: TI-36X solar calculator (must be brought to every
session of this class).

**Text**: *Coursepack* (mandatory, $5). Note: my approach is
based on explaining principles on the chalkboard in class, on you
writing them down in your *Math Principles Folder* (see below),
followed by a concrete illustration. Supplementary sources such as the
internet or books are recommended but not required.

**Internet**: By now, the internet—if you know how to use it—is just
as good a resource as any math textbook you might purchase on your own.
Indeed, some of the best instructional material, nowadays, is on the
internet—for free:

Sample MPE with Answers: http://www.cll.wayne.edu/olmt/welcome.htm

The Math Forum Home Page: http://forum.swarthmore.edu/

Dave's Math Tables: http://www.sisWeb.com/math/tables.htm

Math World (for mathematicians, but still worth visiting): http://mathworld.wolfram.com/

Measurement Units Translation: http://www.ur.ru/~sg/transl/

But perhaps even more important and useful is a simple search of
whatever you are doing at the moment. If you have *Netscape*, for
instance, and are tackling a concept, you can do so by going to the
address on top and typing the concept in quotes, e.g., "greatest common
divisor"

**Grading**: Your grade will be based on:

*Performance*on the MPE (40%)*Attendance*(30%). Attendance will be graded as follows: Above-the-call-of-duty: A+. Full and punctual: A. A portion of one session missed: A-. One session missed: B. Two sessions missed: C-. Three or more sessions missed: E.*Math Principles Folder*(20%): Here and then during class discussions, I shall pause and ask you to write down one math principle, and one illustration thereof, in a special section of your math binder—one principle and illustration per page. This journal will be submitted to me for review several times during the semester and on the day you take the*MPE*.*Turned-in Weekly Assignments*(10%)

Course Objectives

- Prepare participants for WSU's math proficiency exam (
*MPE*). - Review the historical roots of modern mathematics.
- Explore the influence of mathematics on scientific, technological, and cultural developments.
- Show that math can be as fun-filled and interesting a subject as literature, sports, or history.
- Impart basic quantitative skills. The importance of such skills can't be overemphasized. You should be able to go over your bank statement, have a clear perception of the meaning of a 4% raise in your salary when inflation is at the 7% level, and decide whether the 200-by-51-ft plot of land you are about to buy is larger than the adjacent circular lot, also for sale, whose diameter = 110 feet. You should, for that matter, know what a diameter is. If you plan to visit Mexico, France, Canada, or Spain, you might want to have some idea of what the people there mean when they talk about kilometers, kilograms, and centigrades. The point is obvious: it's about time you become comfortable with everyday math.

Instructional Philosophy

The instructional approach—possibly for the first time in your career—will stress comprehension, not memorization of dates, names, formulas and computational routines. Although we will occasionally have formal lectures, for the most part we will tackle our subject in a somewhat unconventional way—by solving problems and by exploring their underlying principles. The key to your success will not be buying and reading $100 texts—you have done that before—but attending all classes, joining a study group, doing all assignments, and working as hard as you can in and out of class.

You are almost certainly unaccustomed to this approach, so it (and I) might seem odd for a while. But, I can assure you, it works. So please suspend disbelief for one term, think it possible that math is fun and that it can be taught in ways that you have never experienced before, and try to enjoy this class!

A Word of Advice

To do well in this class, try to discard any negative opinions you might
have about
numbers and figures. Approach the subject with a "can do" attitude. Form a
study
group. Think and live math for one term. Do your assignments diligently.
Attend all
sessions and come prepared for class. Ask questions whenever you don't
understand
anything: don't be inhibited, you are among fellow strugglers. Take an
active part in
class discussions. If you follow this advice, by late April you are almost
certain to know
and understand math better than ever before. The most important thing for
you to remember
is this: *The harder you work, the more likely you are to pass the MPE.*

Another critically important factor is English proficiency. To pass the
MPE, your
reading comprehension must be pretty good. If it isn’t, drop the class for
now, read *fifty
*children classics, take English classes, take and pass the English
Proficiency
Examination, and only then re-register for this class. To help you make
this decision,
this class will start with a brief English comprehension diagnostic test.

*MPE* Information

The Math Proficiency Examination (*MPE*) lasts 90 minutes and
consists of 45
multiple choice questions. The *MPE* is administered by WSU's
testing service
(313-577-3400). Calculators are permitted (e.g., TI-36X solar
calculator—about $17 at
*Target*). We shall all take this test collectively at the end of
this term. To take
the test, students must pre-register at the begining of the term and bring
a picture ID,
student ID, and calculator to the test.

Passing score is 44.4%. Let's explore the meaning of this. 47% of 45 =
21; that is, you
need to answer correctly 21 questions to pass this test. Let's say you
don't know what
they are talking about in 20 questions, so you simply guess the answers.
With four answers
to each question, this would net you, on average, 5 correct questions. To
pass, you need
16 more correct answers out of the 25 questions that you are familiar
with. But let's play
it safe and say that only two of your guesses were correct. You now need
to answer
correctly 19 out of the 25 familiar questions to pass. So, if you WORK
VERY VERY HARD, and
if you read plenty of books when you were a child, chances are that you
WILL pass the *MPE*.
Another important lesson from these calculations is this: You don't need
to know all the
material that would appear on the test; if you know well about half, you
would comfortably
pass.

We can learn something from the experience of other ISP students. Of the
10 people in
my one before last class who attended all (or almost all) sessions and who
worked hard,
eight passed and two failed. On the other hand, only one person out of the
four with
patchy attendance and homework record passed the *MPE*.

In my last class, only 45% passed. The scores were: 13, 14, 15, 16, 17,
20, 21, 27, 27,
28, 32. The lowest three tried very hard and still failed. They were, and
are, unlikely to
pass this test, no matter what they do—their best hope of meeting the *MPE*
requirement is taking MAT 0991. The next two had a patchy attendance and
work record. Had
they worked harder, they might have passed. The 20 score was definitely
avoidable with a
bit more work. The next two (21, 27) did not over-exert themselves, but
nonetheless did
study and attend enough to improve considerably in one semester. The next
two (27, 28)
performed at chance level at the beginning of the class, but *they are
both readers*,
they worked hard, enjoyed math, and attended all classes. The top scorer
might have just
passed without taking the class. The class helped to improve his potential
score by about
50%.

To give yourself every chance of passing, you may wish to avail yourself
of the free
private tutor *attached *to this class.

If all fails, and only after you have flunked the *MPE* twice, you
can still
graduate from Wayne State. In that case, you will need to take and pass
the not-for-credit
class *MAT O910*. For example, a student of mine who failed the *MPE*
*six*
times has just comfortably passed *MAT 0910*. So, if there is a
will, there is a way!