Longwood University
Department of Mathematics & Computer Science
MATH 245 (History of Mathematics, Spring 2011)
Instructor:
Dr. Wendy Hageman Smith
Email: smithwh@longwood.edu
Office: 346 Ruffner; Phone 395-2992 Math Office: 395-2194, 395-2865(fax)
Class Time: Lecture: M,W
Room 350 Ruffner
Dr. Hageman Smith – OFFICE HOURS
Dr. Hageman Smith – OFFICE HOURS
Monday; 1:00-3:30
Wednesday; 1:00-3:30
Thursday; by appointment
Friday: 10:00-11:30
Text: The History of Mathematics by David Burton 7th ed.
Recommended Supplies: TI-83 or TI-84 graphing calculator.
Course Content and Goals:
This class is designed for the future secondary school teacher and provides the background for the
foundation of the mathematics students learn in the public schools. In order to provide a broad background
for the foundations of the body of mathematics taught in the public schools, this class will address the
historical foundations of mathematics and practice in doing mathematics as it was formulated through
history.
During the semester, come to class prepared to explore and refine your knowledge of chapter content as the
accompanying schedule dictates. “Prepared” means you have read the chapter before coming to class. You
have already seen/learned much of the mathematics in this book. However, this class is not about simply
“doing the math problem”, but developing a deeper knowledge of the structures and history that give rise to
the mathematics we will do in class. So then, the course has three primary goals:
1) To re-examine the mathematics that you will teach and improve your math skill.
2) To help you become more effective teachers by providing the background for the subject you teach.
3) To introduce the idea that mathematics is a human endeavor, that it has a history just as human
civilization does, and that the two grow together symbiotically, and mathematics is still growing and
changing and has relevance now as it has through history. Discussions will include whole-class
participation and small group participation.
Course Requirements:
1. There will be two tests. Each test will be worth 20% of your final grade. Tests will consist of computation
problems and essay problems about the history and contributions of mathematics in the sections assigned.
This means that if you have not read the sections assigned, you probably won’t do well on the test.
2. You will have four quizzes throughout the semester; the quizzes are worth 10% of your final grade.
Quizzes will be a reduced format version of tests. Quizzes will be designed so that if you have done the
required homework and read the sections in the textbook, the quiz will take no more than 15 minutes.
3. Attendance is mandatory. Each student is expected to actively participate in all group work and class
discussions. Group work for any day cannot be made up if class is missed – group work is worth 1 pt.
4. Class assignments and homework combined will constitute 15% of your final grade.
5. Homework: I will collect homework each week. Homework will consist of problems from the
textbook.
6. A research project will be assigned on April 18th and due on the day of the final. The project will
constitute 20% of your final grade. Specifics will be provided when the project is assigned to the class.
7. In lieu of a final test, your final for this class will consist of a presentation that will last 15 minutes. The
topic will be chosen by you from a list I will provide to the class. Specifics will be provided when the
project is assigned to the class. Your final presentation is worth 15% of your grade.
8. Absences are excused only for illness, college sponsored activities, and recognizable emergencies. You
must assume full responsibility for all material covered during your absence. A grade of "0" will be
assigned for all work missed due to unexcused absences.
9. Make-up tests will be given only when the reason for missing the test meets the criteria for an excused
absence. Make-up tests will always be more difficult then regularly scheduled tests.
10. I expect you to conform to the Longwood College Honor Code as contained in the Student Handbook. All
assignments and tests must be pledged.
General Grading Overview
Course Grades will be calculated using a 10 point scale as follows:
A = 90 ~ 100
B = 80 ~ 90
C = 70 ~ 80
D = 60 ~ 70
F = 0 ~ 60
Plus and minus grades are given at the discretion of the instructor.
In general, the achievement of a student in a course indicates the following:
A: Superior work
B: Above average work
C: Average work
D: Below average
So I will award a grade of A only to a student who meets every standard of learning in the course, and
who in addition consistently exhibits excellence in their work. Absent consistent excellence, I award a B to
the student who meets every standard. I award a C to the student who has met most of the standards of
learning, but continues to struggle in acquiring some key skills or concepts. I award a grade of D to a
student who is capable but appears, based on their performance and effort, unable to commit themselves to
achieving a minimum acceptable standard. I reserve a failing grade only for those students who do not
meet minimum standards of learning, and who seem unable to do so at the level of the course. This
indicates that the student must, if he or she is to continue to pursue the same educational goals, be prepared
to repeat coursework and – most critical – thoughtfully reexamine their goals and priorities with an eye
towards reinventing themselves as a student.
Your Instructor: Please do not hesitate to come and get help if you need it. I am here to help facilitate
your learning mathematics. The most important thing to remember is that I am available to help, that is my
job, so do not wait until problems reach critical mass. He who hesitates is lost, so don't hesitate. You are
responsible for everything that happens in class. I am of course willing to help you, but I am not willing to
re-teach the course in my office. If you miss class, get the notes from someone, try the problems, and then
come get help.
If you have specific physical, psychiatric, or learning disabilities and require accommodations, please
let me know early in the semester so that your learning needs may be appropriately met. You will need to
provide documentation of your disability to the Disability Services Office.
ADDITIONAL INFORMATION
Students are responsible for checking the ANNOUNCEMENTS in Blackboard in advance of each class
period as there will be, from time to time, important information regarding assignments, due dates, items
that must be brought to the next class session, etc. Since announcements trigger an email message, check
email before class to see if there are nay announcements. Also, students are responsible for downloading
all needed course documents from Blackboard, printing them if hardcopies are desired, and knowing the
information contained therein.
Class Attendance: Students are expected to attend all classes. Work missed because of illness or other
excused absences may be made up if you advise me of the absence with attendant paperwork. If you miss
an exam or are late with an assignment you may be asked to provide proof that you had a legitimate reason
(such as illness, certain college-sponsored activities, or recognized emergencies). When possible, you
should notify the instructor in advance of assignments you expect to miss because of legitimate absences.
Note:
 A grade of “0” or “F” may be given on work missed because of unexcused absences
 A course grade of “F” may be assigned when the student has missed a total (excused and
unexcused) of 25 percent of the scheduled class meeting times (more than 7 absences)
 Acceptable excused absences (as listed in the Longwood catalog) will be taken into consideration
for missed tests; however, except in VERY EXTREME circumstances, be sure to make PRIOR
arrangements.
Longwood’s Honor System: A strong tradition of honor is fundamental to the quality of living and
learning in the Longwood community. The Honor System was founded in 1910, and its purpose is to create
and sustain a community in which all persons are treated with trust, respect, and dignity. Longwood affirms
the value and necessity of integrity in all intellectual community endeavors. Students are expected to abide
by the Longwood College Honor Code. Assignments should be pledged, but the provisions of the Honor
Code are assumed to apply to all work, pledged or not. Students are encouraged to study together and to
seek help from the instructor or tutors when needed, but receiving unauthorized help or copying will be
graded is a violation of the Honor Code.
The Longwood Honor Code applies to all work for the course as follows:
 Any out-of-class practice work or hand-in assignment can include using text information, discussion
with other class members, and/or discussion with instructor BUT, the final product handed-in for
the grade must be the student’s own work.
 All tests are to be completed individually. Please sign the honor code on all exams indicating that:
“I have neither given nor received help on this work, nor am I aware of any infraction of the Honor
Code.”
Class Schedule:
Note: This schedule is tentative, small changes may be made to this schedule through the semester,
according to how the class progresses, and will be announced in class before any changes are initiated.
Week
Jan 19
Jan 2426
Jan 31Feb 2
Feb
7-9
Feb
14-16
Chapter/Sec
Introduction
Text: 1.1, 1.2
BBC Film
Text: 1.3
Text: 2.1, 2.2, 2.3,
2.4
Weekly Content
1.1: Tally Systems, Peruvian
1.2: Egyptian, Greek
1.3: Babylonian, Chinese
Feb 2123
Text: 4.1, 4.2, 4.3
Feb 28Mar 2
Film: Archimedes
Text: 4.4, 4.5
2.1/2.2/2.3 Egyptian Arithmetic and Rational Numbers
2.4: Circle Area and Truncated Pyramid Volume
2.6: Pythagorean Triples
3.1: Thales
3.2: Pythagoras Triangular and Square numbers and Zeno
3.3 Pythagorean Theorem and Incommensurables
4.1/4.2: Euclid’s Elements and Euclidean Geometry
4.3 Euclidean Algorithm and Fundamental Theorem of
Arithmetic
4.4 Sieve of Eratosthenes and Ptolemy
4.5: Archimedes method of exhaustion
Mar
7-9
Mar
14-18
Mar
21-23
Mar
28-30
Apr
4-6
Apr
11-14
BBC Film
Text: 5.1, 5.3, 6.1
5.1, 5.3: Diophantine equations
6.1: Transmission of Arabic knowledge
Apr
18-20
Apr
22-27
May
2-6
Text: 2.6
Text: 3.1, 3.2, 3.3
Assessment
Quiz 1
Test 1
Quiz 2
Spring Break
Text: 6.2, 7.1, 7.2
Film: Galileo
Text: 8.1
Text: 8.2, 8.3, 8.4
BBC Film
Text: 9.1, 9.3
6.2: Hindu-Arabic Numerals and Fibonacci
7.1/7.2: Tartaglia and Cardano
8.1: Galileo
8.2: Descartes Cartesian geometry and perspective
8.3/8.4: Newton and Leibniz
10.1 Origins of probability
9.3 Bernoulli:
Text: 10.2, 10.3
10.2 Fermat and Euler: Number Theory
10.3 Gauss: Congruence Theory
Text: 11.3, 12.2
11.3 Cauchy, Weierstrass, and Hilbert
12.2: Poincare’ and Cantor
Finals Week
Final May 5 11:30-2:00
Quiz3
Test 2
Quiz 4
Final
presentation
assigned
Final