MATH 274, Spring 2009
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Course title: History of Mathematics
Class time: TuTh 2:003:15
Class location: J.M. Patterson Building, Room 1202
Textbooks:

History of Mathematics, An Introduction,
Victor Katz, 3rd edition

Math through the Ages, A Gentle History
for Teachers and Others,
William P. Berlinghof and Fernando Q. Gouvea
Prerequisite: MATH 140 or MATH 220
Instructor: Professor Mike Boyle
(mmb@math.umd.edu)
Office: 1105 Math
Phone: 3014055056
Office hours: Monday 10, Friday 11, appointment
(You're welcome to drop by unannounced,
but I won't always be in or free to help.)
Syllabus:
Primarily, we will read most of the book of Katz.
Most of the course will be organized like a reading course.
There will be reading assignments and lecture/discussion.
You are reponsible for keeping up with the reading in Katz
and the parallel (easy) reading in Berlinghoff.
There will be homework, not collected (most answers are in the
text).
There will be "reading exams" every two weeks or so to check up on
people doing the reading and homework  I expect it will be
useful to do the homework to succeed on these.
I will also ask you to write a report on a topic of interest
to you, and to read a math/historical book (or approved part, if that is long
and hard enough) and write a 35 page book report on it.
You can suggest reports and books or choose from my suggestions.
You can propose alternatives.
Grading:
Roughly, grading will be
 45% the reading exams
(I will drop your worst exam score and base this on the rest.)
 15% final exam MONDAY MAY 18, 10:30 12:30.
 20% report on a topic (due: April 21)
 You can propose to follow up some topics in depth.
Our Katz text itself has a lot of material, in some cases
plenty for a topic. I may ask you to
do a bit more on some.
 You can propose to read some original sources.
 You need approval from me for your proposal.
 Try to think of something you could find interesting!
 20% book report (due: March 31)
 For this, read a historicalmathrelated book,
or (for hard books) suitable parts, and write a 35 page report.
 Click here for some possibilities.
But, you can choose a different book (subject to my approval).
E.g. there are books referenced in Katz on various topics,
in the footnotes at the ends of chapters.
You can also propose parts of books for which a complete reading
would be too much.
 You can propose to follow up some topics in depth as on p. xii
of Katz (not calculus  we will all do that one). I may ask you to
do a bit more on some.
 You can propose to read some original sources.
 There will be some opportunities for extra credit work
(! this is not
an ordinary math class). If you have historicalmath related
reading or projects you are interested in, you can propose
them for extra credit (e.g. some in the previous list).
I encourage you to follow your
interests.
There may be some opportunities for extra credit work
(! this is not
an ordinary math class). If you have historicalmath related
reading or projects you are interested in, you can propose
them for extra credit, if it is not late in the semester.
I encourage you to follow your
interests.
Homework
(Don't turn it in; some questions close to
or directly from homework will be part of
the reading/homework exams.)
 Ch. 1: 3, 9, 19, 24, 30, 36
 Ch. 2: 4, 18, 19,20
 Ch. 3: 6, 9, 15, 16, 19, 21, 36
(For #36, you may use the facts that (2^n 1) can only
be prime if n is prime; (2^{11} 1) is not prime; and
(2^{13}1) is a prime number.)
 Ch. 4: 2, 11, 14
 Ch. 5: 20,22 (For #22, one method is enough.)
 Ch. 6: 22,23
 Ch. 7: 5,7,16,17,26
 Ch. 8: 2,6,10,35
 Ch. 9: 22, 23, 25a; [extra credit: 30, 31, 35]
 Ch. 10: 28, 42
 Ch. 12: 18, 19, 30,39
 Ch. 13: 17, 18
 Problem L: Leibniz in 1702 asserted (incorrectly)
that the conclusion of the fundamental theorem of algebra
was false. His mistake was to claim that for a positive real number
t, the polynomial P(x) = x^4 + t^4 could never be written as a
product of two real quadratic factors. An example is the polynomial
q(x) = x^4 + 1. Factor q as a product of quadratics.
(Hint: you can easily find 4 roots of q on the unit circle
in the complex plane. If w and w' are complex conjugate roots,
then multiply out (xw)(xw') to get a real quadratic divisor of q.)
 Ch. 14: 7 (just do the two parts involving the sum of the roots and
the sum of the squares of the roots), 29,30,31,41
 Ch. 15, 16; Sec. 22.1 lightly;
Sidebars 22.1 (p.768), 22.2 (p.770) and 22.3
(p.783) (only reading, no problems assigned)
 Included for final, from Berlinghof and Gouveia: pp.3746, and
Sketches 11,14,16,17,19
TESTBANK:
Online archive of math department exams (with answers to
our exams).
Disabilities.
If you have some disability related to testing under the usual timed,
inclass conditions, you may contact the office of Disabled Students
Services (DSS) in Shoemaker. If they assess you as meriting private
conditions and/or extra time, then you may arrange to take your tests
at DSS, with extra time as they indicate. You must arrange this well in
advance of a test (in particular: no retakes). Click to
Disability Support Services for further information.
The honor pledge; academic integrity; what constitutes cheating
EMAIL:
I will send the class email
with a course reflector to
email addresses officially registered with the
University. Students are responsible for
maintaining a correct address. If your
official email address
is not correct, then click
here to update it. If this doesn't work, just email
me your email address to add manually.