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MATH
12 MATHEMATICAL EXCURSIONS , not offered this semester
Reminder:
CREDIT GIVEN ONLY FOR ONE OF MATH 12 AND MATH 16.
Instructor:
Dr. David Knee, Office: 100B Adams, Phone: x3-5072
Hours: Mon & Wed 9:35-10:05 AM, e-mail: MATDIK@Hofstra.edu
Textbooks
(both are paperbacks):
"Strength in Numbers by Sherman Stein, Wiley
"The Code Book by Simon Singh, Anchor Books
Our
two primary themes this semester are Secret Codes
and Mathematics in Popular Paperbacks. In recent
years the great number of well-written popular math books
published has been astonishing-- consider the works of John
Paulos, Simon Singh, Martin Gardner, Theoni Pappas, Ian Stewart,
A.K. Dewdney, Ivars Peterson, Rudy Rucker, William Dunham,
Paul Hoffman, Sherman Stein and Keith Devlin for starters.
These are serious books written for the well-educated and
curious layperson on a variety of novel subjects. They are
not text books, they have no exercises, they are not expensive.
Often in paperback, they are written to entice, amuse, and
share a mathematician 's love for his/her art with a serious
reader. This trend began with "Number, The Language of Science
written in the 1930 's by Tobias Dantzig. This book dealt
with the story behind the dry techniques that were usually
taught as being all there was to mathematics. Einstein found
this revolutionary little book to be "beyond doubt the most
interesting book on the evolution of mathematics that has
ever fallen into my hands, and in his preface, Dantzig describes
his effort as pioneering and it was just that; it is what
we would today call a work of "Humanistic Mathematics".
Many of the mathematics topics he wrote about were unusual
in a popular work: infinity, number theory, the ideas of calculus,
other bases for numeration.
Other
works in a similar spirit appeared soon thereafter: E.T. Bell
wrote "Queen of the Sciences and "Men of Mathematics
in the 30’'s, "Mathematics for the Million
by Lancelot Hogben also appeared in the 30’'s and "Mathematics
and the Imagination by Edward Kasner and James Newman in
the 40’'s. In England W.W. Sawyer’'s "Mathematician’
' s Delight became available in the 40’'s too. At
a higher level, "What Is Mathematics by Courant and
Robbins (another Math book that Einstein praised), and published
in 1941, it recognized that "The teaching of mathematics
has sometimes degenerated into empty drill that does not lead
to real understanding or greater intellectual independence.
The goal is genuine comprehension of mathematics as an organic
whole.
What started as a trickle in the 30’'s is now an avalanche!
Of the many marvelous, accessible, well-written Math books
presently available for the general public we have picked
two and in this course we will fill in the gaps they leave
as we go along, to give the student a deeper understanding
than a cursory reading would allow. In the process we’'ll
be touching on: Number Theory, Probability, Codes, Geometry,
Sequences and Series, Infinite Sets, Math History, Popular
Math Literature, Pedagogy and Applications.
Students
will be expected to participate to a great degree: taking
notes, solving & discussing problems, summarizing class
discussions, interpreting reading assignments and presenting
problems & solutions at the board. Attendance is taken
at every class, is extremely important for success in this
course, and counts in your term grade. You’'ll need
a cheap scientific calculator for this course. Save all your
notes, HW, returned tests and handouts. When attending office
hours, please bring all this material.
Tests:
A half-hour quiz is worth 50 points; two will be given. Two
100 point full period exams will also be given. The Final
Exam is worth 150 pts. Preparing for exams and taking them
when they are scheduled is extremely important for the student’
' s and the class’' progress. Missed exams count as
0. Normally, no make-ups are given. If you know that you will
need to miss some exams or that you’'ll need to be absent
frequently, it would be wise to switch sections now.
Students
will volunteer each day to summarize and comment on the assigned
reading (boil down/explain/question/admit ignorance/remember
Math from High School or elsewhere that is relevant/agree
or disagree, etc.) and dialogue with the instructor and classmates
in that process. The student stands or sits in front of the
class and puts a short outline of the reading on the blackboard.
He or she then gives an overview with explanations. Don't
read from the book but you may use notes and refer to figures
in the text. Feel free to use the board to help explain.
Homework
problems will appear in the instructor’'s handouts or
emerge from class discussions.Students will be invited to
present solutions at the board. After the middle of the semester,
pairs of students (or you can work solo if you prefer) may
volunteer to collaborate on reports about popular math books
(some are mentioned above)-- a list of further suggestions
will be distributed.
Grades
a) 2Quizzes, 2 full-period exams, Final: Total = 450 points.
b) Class Participation: i) Pair Report on a Popular Math Book,
3 pages: 25 points;
i) Summaries of Reading Assignments or of your Report on a
Popular Math Book:15 points each; iii) HW problems at the
board :6 points each; iv) Special Hand-In HW assignments:
8 points each. Total = 50
points.
There will be an optional review class on a reading day .
Exemptions from the Final may be possible
for those of you who miss no exams, achieve a B or higher
average (at least 83) on all the exams, complete all assignments,
have good attendance, participate abundantly in the class
work, and show proficiency in the material covered after the
last quiz.
Averages:
Except for exemptees (where only one quiz grade will be dropped),
your lowest 100 points on any exam(s) will be dropped (i.e.
2 quizzes or a full-period exam). Numbers are turned into
letter grades thus, [80, 83) = B-, [83, 87) = B, [87, 90)
= B+, etc.
HW
Assignments:
For the earlier material we’'ll cover approximately
20 pages/day, 2 students volunteer to summarize 10 pages each.
We’''ll cover less per day as the material gets harder.
Weeks
1, 2 & 3: Part I of Stein @ 3 chapters per day
Quiz #1
Weeks 3, 4 & 5: Chaps. 1, 2 & 3 up
thru p.124 of Singh
Weeks 6, 7 & 8: Part II of Stein
Full-period
exam #1
Weeks 9 ,10 and 11: Chaps.3 (from p.124)
, 4 & 5 up thru p. 217 of Singh
Submit choice of Book Report partner and book
Full-period Exam #2
Week 12 , 13 & 14: selections from Part
III of Stein and Chaps. 6, 7 & 8 of Singh
Book Report due
Quiz #2
Official last day of classes , with optional extra day
Final
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