Course
Syllabus

Math
4853-01W: Introduction to the History of Mathematics

**Instructor:** Dr. David G. Robinson,
Boyd #326, 678-839-4137

E-Mail: davidr@westga.edu

Office
Hours: *MWF*
9:10 Ð 10:00 a.m., 11:15 Ð 12:05 p.m., *M* 3:30 Ð 5:30 p.m.

**Class Meetings: ***Monday *5:30 Ð 8 p.m., Boyd #302

These will consist of a
combination of lectures, question-and-answer sessions, problem presentations,
and general discussions. All reading will be assigned in advance of the meeting
thereon.

**Text/Resources:** Boyer, Carl, *A History of Mathematics*, 2^{nd} ed.,
John Wiley & Sons, 1991

** **

Some good alternative
authors of general histories of mathematics are:

D.M. Burton, F. Cajori, T.L. Heath, M. Kline, D.E. Smith, D.J. Struik, H. Eves, J. Stillwell

** **

**Prerequisites:** Completion
of core math requirements (usually Math 1113 or higher) and English 1102.

** **

**Topics: ***Week 1 (Chs. 1 Ð 3):* Origins of mathematics,
Egyptian and Mesopotamian
arithmetic and geometry

*Week
2 (Chs. 4 Ð 5):*
Pre-Socratic Hellenic math Ð Pythagoras to Zeno

*Week
3 (Chs. 6 Ð 7):*
Golden age of Greek math Ð Plato to Euclid

*Week
4 (Chs. 8 Ð 9):*
Works of Archimedes and Appollonius of Perga

*Week
5 (Chs. 10 Ð 11):* Ptolemaic period, Greek
trigonometry and astronomy, DiophantusÕ algebra and PappusÕ geometry.

*Week
6 (Chs. 12 Ð 13):*
Chinese, Hindu and Arabic mathematics Ð Brahmagupta to Al-jabr

*Week
7 (Chs. 14 Ð 15):*
European math of the middle ages and the renaissance, Fibonacci to Cardan.

*Week
8 (Chs. 16 Ð 17):*
Prelude to Calculus Ð European math of the 16^{th} and early 17^{th}
centuries, Viete, Descartes, Fermat and Pascal.

*Week
9 (Chs. 18 Ð 19):*
Discovery of the Calculus Ð 17^{th} century, Wallis, Newton and
Leibniz.

*Week
10 (Chs. 20 Ð 21):*
Golden age of Calculus Ð 18^{th} century, the Bernouillis to Euler.

*Week
11 (Chs. 22 Ð 23):*
Dawn of modern mathematics - late 18^{th} and early 19^{th}
centuries, Lagrange & Laplace to Gauss and Cauchy.

*Week
12 (Chs. 24 Ð 26):*
Founding of modern mathematics Ð 19^{th} century development of
abstract geometry, analysis and algebra, Riemann to Cayely.

*Week
13 (Chs. 27 Ð 28):*
The modern era Ð 20^{th} century - topology, functional analysis,
universal algebra, computer science, discrete math, fractal geometry and chaos;
Poincare to Mandelbrodt.

** **Besides developing your understanding of the topics
mentioned above, there are some particular skills you should improve upon along
the way in order to be able to apply what you learn in this course to future
courses of study. These include:

á
use
of mathematical terminology and notation

á
mathematical
abstraction

á
mathematical
problem-solving techniques

á
writing
skills Ð both formal and informal

á
appreciation
of the interplay between mathematics and the surrounding culture

**WAC Objectives and Requirements:**

This is a** **Writing Across the Curriculum (WAC) course. Like all
such courses, it *emphasizes writing as a tool for both learning and
communication.* Therefore the writing
assignments for this course are divided into two types according as the main
objective is either Òwriting to learnÓ (WTL) or Òwriting to communicateÓ (WTC).
The specific assignments are as follows. (See the attached schedule for exact
due dates):

** **

**WTL
**

á
*Math autobiography *(1 to 2 pages) informal but neatly written story of
your own personal math history (from birth to present day.)

á
*Problem
solutions/proofs* (six sets of 4
problems) creatively and logically solved and neatly written up, using complete
sentences and proper mathematical notation.

á
*Journal entries *(six installments, 2 to 3 pages each) informal notes,
summaries, observations, questions, etc., based on the current readings and
class discussions

* ***WTC**

á
*Formal Paper* (at least five-pages, type-written) on some aspect of
the *historical development* *of a
specific mathematical topic.* You will
submit this in three stages: (1) One-page description of the topic and the
references to be used (including *at least one book other than our text.*) (2) Rough draft. (3) Final draft. [Note: You may
choose the topic or take it from a list I will provide, but it must be approved
by me before you get too far into the research and writing stages of the
paper.]

á
*Short-answer exam
problems* (two per exam, 1 paragraph
each.)

Your understanding of
the subject material and your progress toward the aforementioned objectives
will be evaluated on the basis of your *written work, as described above,* your performances on
two written *exams*,
and your *class participation *(attendance, preparedness and contributions.)

** **

á
accuracy
of information (including calculations and use of mathematical notation and
terminology)

á
depth
and breadth of solutions

á
logic
and clarity of arguments

á
neatness
and clarity of presentation

á
correctness
of grammar and spelling

á
thoroughness
and timeliness of work

á
intellectual
honesty and creativity

á
achievement
of personal potential

á
difficulty
of the assignment/test

**Grades: **My scale for converting
numerical grades (i.e., percentage points) to letter grades will be as follows:

** **

*89-100* A, *77-88* B, *65-76* C, *50-64* D, *below 50* F

Your
final grade will be based on the following distribution of points:

*Math autobiography* 3
%

* Journal
entries* (six installments) 18
%

*Problem
sets *(six sets of four) 24
%

* Midterm
Exam score* 15
%

* Final
Exam score* 15
%

*Term
paper* (topic report, rough draft and
final draft) 15 %

*Class* *participation* * 10
%

* **Class participation
includes attendance: Missing more than one class meeting *for any reason* will result in a
deduction of 1 point per absence (beyond the first) from the 10 points
available.

**Important**

**Reminders:**

á
Attendance
is important! However, should you find for some reason that you must miss a
class meeting, remember that you are still responsible for any and all material
you may have missed during your absence.

á
Assignments
must be turned in at the prescribed times (see attached schedule) in order to
be eligible for any credit. *All work on these assignments must be your own,
i.e., no help from anyone, without prior permission from the instructor.
Failure to abide by this policy will lead to serious consequences: automatic
zero on the assignment in question, possible expulsion from the class, etc.*

á
Exams
must be taken at the prescribed times (see attached schedule),* except by
prior permission from the instructor, which will only be given under the direst
of circumstances (serious illness, e.g.).* In order for you to obtain such
permission,* I must be notified of your Òdire circumstancesÓ, by e-mail,
phone, or otherwise, before the test is given. Otherwise you will almost
certainly receive a score of zero for that test.*

á
If
you find yourself falling behind in the course, do not delay in seeking out
appropriate help and advice from someone who is competent in the subject area
and who has your best interests at heart!

á
I
assume you will abide by the UWG Honor Code. So will I!