MA320 History of Mathematics Spring 2010
Instructor
Dr. James Rauff, Professor of Mathematics Shilling Hall 203J Office Phone: 424-6249
Office
Hours: TTHF
Textbooks
Math Through the Ages: A Gentle History for Teachers and Others. Expanded Edition by Berlinghoff/Gouvea (Oxton House Publishers, 2004) 0-88385-736-7
Mathematics
Elsewhere by Marcia Ascher (
Catalogue Description
A study of major developments in the history of mathematics and in the mathematical contributions of non-Western cultures. The interplay between mathematics and culture is emphasized. Prerequisite: Mathematics 140.
Assessment
Your grade will be based upon written assignments, class participation, and your semester paper (see below). Written assignments and class participation have variable point value. Your semester paper will be worth 200 points. Written assignments are due every Monday. They cover material for the previous week. Class participation includes discussion, Q/A, group activities, and quizzes. Your grade will be computed as a percentage of total possible points earned. A: 90 -100%, B+: 86-89%, B: 80-85%, C+: 76-79%, C: 70-75%, D+: 66-69%, D: 60-66%, F: below 60%.
Assignments are due by class time on their due date. If an assignment is turned in late it receives and automatic 50% deduction (No foolin' ... no exceptions). Assignments will be graded on mathematical accuracy, quality of exposition, grammar and spelling. Essays should be typed.
Schedule of Assignments:
Last Updated
on May 5, 2010
The exercises address material over a whole
week of readings. It may be advantageous to you to work these exercises
as you go along rather than waiting until the night before they are due.
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Date |
Reading: |
Written Assignment Due (pages/ numbers in |
Other Events of Note |
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Jan. 20 |
none |
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Jan. 22 |
MTAS1 |
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Jan. 25 |
MTAS2 |
p.71 #1,2,3 |
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Jan. 27 |
MTAS3 |
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Jan. 29 |
MTAS4, complete
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Quiz 1 |
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Feb. 1 |
MTAS5 |
p.77-78 #1,2,6; p.83-84 #4,5; p.91 #1,4,5 |
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Feb. 3 |
MTAS6 |
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Feb. 5 |
MTAS7 |
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Feb. 8 |
MTAS8 |
p.99 #3; p.111 #1,2a,4 |
Project Lottery |
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Feb. 10 |
MTAS9 |
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Quiz 2 |
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Feb. 12 |
MTAS10, complete |
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Feb. 15 |
MTAS11 |
p.119 #1,2; p.125 #1,3; p.131 #2 |
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Feb. 17 |
MTAS12 |
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Feb. 19 |
MTAS13 |
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Quiz 3 |
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Feb. 22 |
MTAS14 |
p. 137 #1,2; p.145 # 1,4; p.153 #1ac |
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Feb. 24 |
MTAS15 |
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Feb. 26 |
MTAS16, complete |
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Mar. 1 |
MTAS17 |
p. 161 #2, p.176
project #1abc |
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Mar. 3 |
MTAS18 |
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Quiz 4 |
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Mar. 5 |
MTAS19 |
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Mar. 8 |
MTAS20 |
p.183 #1; p.192 project #1abc |
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Mar. 10 |
MTAS21 |
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Mar. 12 |
MTAS22 |
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Quiz 5 |
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Mar.13-21 |
none |
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Spring Break-no class |
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Mar. 22 |
MTAS23 |
p.205 #6; p.213 #1abcde |
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Mar. 24 |
Eves pp.379-397 |
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Mar.26 |
Eves pp.397-406 |
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Mar. 29 |
none |
Eves: Problem Study 11.6a on p.410 |
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Mar. 31 |
MTAS24 |
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Apr. 2 |
none |
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Easter Holiday-no class |
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Apr. 5 |
none |
Easter Holiday-no class |
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Apr. 7 |
MTAS25 |
P.243 #2abde |
Quiz 6 |
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Apr. 9 |
First draft
of semester project due 11:00 a.m. |
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Apr. 12 |
ME 5-38 |
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Apr. 14 |
1. Construct the final tableau for the mother-sikidy assigned to you in class on Apr. 12. (attach the slip depicting your mother-sikidy) 2. Classify each of the columns in your final tableau by region and rank. Is your tableau sikidy-unique? |
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Apr. 16 |
ME 59-74 |
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Apr. 19 |
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Apr. 21 |
ME 75-88 |
1. Bird-Jaguar was a ruler of
Yaxchilan, Mexico. He was born on 8 Oc 13 Yax and was seated as Lord of
Yaxchilan on 11 Ahau 8 Tzec. How old was he when he was seated? 2. Kan Xul was a ruler of Palenque, Mexico. He was seated as ruler on 5 Kan 12 Kayab. We are told that this was 1.19.6.16 days after he was born. What was Kan Xul’s Calendar Round birth day? 3. An inscription at Quirigua, Guatemala gives the Long Count date 9.16.10.0.0. What is the Calendar Round date for this inscription? 4. Find the complete designation of the day that
comes 8.11.3 days after 9.0.9.0.4 2 Kan 12 Yax. |
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Apr. 23 |
none |
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Celebration of Scholarship
Day – no class |
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Apr. 26 |
none |
Hand in your completed Tika
assignment that was given to you on April 21. |
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Apr. 28 |
ME 128-142 |
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Quiz 7 |
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Apr. 30 |
ME 142-159 |
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May 3 |
1. Basque system. If there are ten households and household H1 has the role of "woman of the house" on May 11, find the household that will have the role of "guardian of lambs" in 30 days. 2. Tongan system. Consider the following (hypothetical) Tongan family. In each case , M indicates male and F indicates female. Kanokupolu (M) married Salote (F). They had three children. The first was Moungamotua (M), the second was Ha'api (F), and the third Ngata (M). Finau (M) married Kuini (F). They also had three children. Their oldest was Sinifu (F), then Fefine (F) and their youngest was Kainga (M). Ngata married Sinifu and they had three children. Their oldest was Pilinisi (M), then Pelehake (M) and their youngest was Fokonofo (F). For each of the following pairs decide who has the higher kinship rank. a. Moungamotua, Fokonofo b. Kanokupolu, Kuini c. Pilinisi, Kainga d. Ha'api, Pelehake
3. Borana system. Mr. Achwe's makabasa is sabbaka. It is the current gada. a. What is the next gada? b. What is the makabasa of Mr. Achwe's grandson? c. What is the makabasa of Mr. Achwe's great-grandfather? d. Olomo is in the Raba grade. What is his makabasa? |
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May 5 |
Weil’s Appendix to The Elementary Structures of Kinship |
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Quiz 8 |
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May 7 |
none |
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May 11 (T) |
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Semester Paper Due: 1:00 pm (SH203J) |
SEMESTER PAPER
Your semester paper must
be selected from the list below. Papers
should be a minimum of 6 pages in length.
Use MLA style for citations. On February
8 we will have a lottery on class for topics. I will call on you to pick your
topic. The order of selection will be
determined by my TI-83 random number generator.
Please have a list of 3-5 topics in order of preference ready by this
day.
Paper Topics (all pages are
in
A. P.62 #12
B. P. 62 #14 (Include philosophical trends)
C. P.64 #21 (at least 4 mathematicians; include
historical setting)
D. P. 72 #3
E. P.78 #1 (Read the book cited and write an extended
book review)
F. P. 84 #1 (go deep into the contrasts;
explore 0/0, elsewhere_files/image003.gif){kind=small}
, 0!)
G. P.92 #2 (Include context of Liber Abbaci & bio of Fibonacci)
H. P.100 #1 (Read the book cited and
write an extended review)
I.
P.106
#1 (in addition, write this exercise as
a lesson plan for elementary school)
J.
P.
112 #1 (apply his technique yourself; include context and bio of Archimedes)
K. P.120 #1 (include a lesson plan that implements your
method)
L. P.126 #3
M. P.162 #1
N. P.162 #2 (Read the book cited (NOT Alice in Wonderland)and write an
extended book review)
O. P.184 #2 (also write a lesson plan
based on this)
P. P.200 #2
Q. P.206 #1
R. P.236 #2
S. Trace the development of the concept
of the limit from Newton to Maclaurin to d'Alembert. How do their formulations
agree or disagree? How do they compare with the modern formulation of this
concept?
T. Describe Eudoxus' method of
exhaustion. Implement the method in at least three contexts.
U. Who was Claude Levi-Strauss? What is
structural anthropology and why is it relevant to mathematics?
V. Who was Bourbaki? Discuss the impact of his work on modern
mathematics.
W. Who is Grothendieck? Where is he? How did he
get there? What was his role in 20th century mathematics?
X. Compare and contrast the numeral
systems of Lakota, Navaho, Ojibwa and Nahuatl.
Y. Discuss some aspect of the
ethnomathematics of the Vedas.
Z. Discuss some aspect of the
ethnomathematics of the Warlpiri.
AA. Discuss some aspect of the
ethnomathematics of basket making.
BB. Discuss some aspect of the ethnomathematics
of the Quechua.
CC. Report on the Ishango Bone and other
paleolithic objects that may be mathematical in content.
DD.Describe the lo shu and its
relationship to Chinese culture and Chinese mathematics.
EE. Discuss the sea island problem from the Haidao
Suanjing and compare modern and ancient methods of solution.
FF. Discuss the relationship between
bilingualism and mathematics teaching and learning.
Learning Goals - This course addresses the following goals for applied mathematics and mathematics - secondary teaching majors.
Applied Mathematics Goal 2: The applied mathematics major will be able to express and interpret mathematical relationships from numerical, graphical and symbolic points of view.
Applied Mathematics Goal 3: The applied mathematics major will be able to read and construct mathematical proofs in analysis and algebra.
Mathematics- Secondary Teaching Goal 1: A mathematics education major will be able to pass the Illinois high school mathematics certification exam. Specifically, this course addresses the following content distribution areas for mathematics of the Illinois State Board of Education: 1A, 1C, 4C, 4E, 8C3, 9E6.
Mathematics- Secondary Teaching Goal 2: A mathematics education major will know in broad terms the history of calculus, algebra, and probability.
NCTM Standards (2003): 1.1, 1.3, 1.4, 2.1-2.4, 3.1,3.2, 4.1-4.3, 9.7, 9.10, 10.6, 11.1, 11.2, 11.5, 11.8, 12.5, 13.4, 14.8, and 15.4
Academic Honesty Policy
All students are expected to uphold professional standards for academic honesty and integrity in their research, writing, and related performances. Academic honesty is the standard we expect from all students. Read the Student Handbook for further details about offenses involving academic integrity at: http://www.millikin.edu/handbook/. Staley Library also hosts a web site on Preventing Plagiarism, which includes the complete university policy. It is located at: http://www.millikin.edu/staley/services/instruction/Pages/plagiarism-faculty.aspx. Visit and carefully read the Preventing Plagiarism web site.
The Faculty has the right and the responsibility to hold students to high ethical standards in conduct and in works performed, as befits a scholar at the university. Faculty members have the responsibility to investigate all suspected breaches of academic integrity that arise in their courses. They will make the determination as to whether the student violated the Academic Integrity Policy. Should the faculty member determine that the violation was intentional and egregious, he or she will decide the consequences, taking into account the severity and circumstances surrounding the violation, and will inform the student in writing, forwarding a copy of the letter to the Registrar and to the Dean of Student Development.
This letter will be destroyed when the student graduates from the University unless a second breach of integrity occurs, or unless the first instance is of sufficient magnitude to result in failure of the course, with an attendant XF grade recorded in the transcript. If an XF is assigned for the course, the faculty letter of explanation becomes a permanent part of the student’s record. If a second violation occurs subsequent to the first breach of integrity, the Dean of Student Development will begin disciplinary and judicial processes of the University, as outlined in the Student Handbook.
If a
student receives an XF for a course due to academic dishonesty, this remains as
a permanent grade and cannot be removed from the transcript. However, students
may repeat the course for credit toward graduation. Some programs and majors
have more explicit ethical standards, which supersede this Policy, and
violation of which may result in dismissal from some programs or majors within
the University. If you have difficulty with any assignment in this course,
please see me rather than consider academic dishonesty.
Disability Accommodation Policy
Please
address any special needs or special accommodations with me at the beginning of
the semester or as soon as you become aware of your needs. If you are seeking
classroom accommodations under the Americans with Disabilities Act, you should
submit your documentation to the Office of Student Success at