MA350 History of Mathematics

for SP 2010

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MA 350 History of Mathematics


SP 2010 HO


Smith, Charlie L.


Associate Professor of Mathematics


Ph.D., University of Missouri-Kansas City, 2002
M.A., University of Kansas, 1983
B.A., William Jewel College, 1981

Office Location

Science Hall, Room 308

Office Hours

Monday & Wednesday 3:00-4:00 pm; Tuesday & Thursday 9:00 am to 12:00 p.m. or By Special Appointment

Daytime Phone



Semester Dates

January 11, 2010 - May 7, 2010

Class Days


Class Time

1:30 - 2:45 PM



Credit Hours


There is no required textbook.  I may order an optional textbook for those who want full detail.

Additional Resources:
Linda Hall Library
5109 Cherry
Kansas City, MO
(816) 363-4600

McAfee Memorial Library - Online information, links, electronic databases and the Online catalog. Contact the library for further assistance via email or at 800-270-4347.
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Course Description:
MA350 Mathematics in Civilization (MLL): An introduction to the history of mathematics with emphasis on contributions of the many and diverse cultures which have influenced the development of the discipline. Cultures studied include: the Egyptians, Babylonians, Greeks, Romans, Arabs, medieval Europeans, and Renaissance Europeans. Topics include the Pythagorean Theorem, perfect numbers, classic construction problems, the golden ration, noteworthy mathematicians and current trends. One field trip is required. 3:0:3 It is strongly recommended that the student has passed MA131 or its equivalent.

Educational Philosophy:
A famous old adage says that mathematics is not a spectator sport.  In order to learn mathematics, students must attempt a significant number of problems.  Drill and practice are essential in order to succeed.  In addition, the material should not be covered too quickly.  Student comprehension always takes priority in the educational process.

Learning Outcomes:
  Core Learning Outcomes

  1. Analyze mathematical concepts from the aesthetic point of view.
  2. Answer historical and mathematical questions pertaining to: the ancient Egyptians, the ancient Babylonians, the Pythagorean School, the three classic construction problems of ancient Greece, Euclid's elements, Archimedes, Diophantus, the University and library of Alexandria, the medieval Europeans, and the Renaissance Europeans
  3. Write a term paper on a famous mathematician or mathematical concept.
  4. Present a summary of the term paper in class.

Core Assessment:
  • Participation in a field trip
  • Class attendance
  • Class participation
  • Reaction papers
  • Periodic assignments
  • Major term paper
  • Oral presentation
  • Comprehensive final exam

Class Assessment:
1. Class Participation (10%)
    (1) Attendance
    (2) Response to questions in class
    (3) Participation in class discussions
    (4) Attending mandatory field trip

2.  Problem Assignments (30%)
    You will be solving mathematical problems which have been selected from actual historical sources.  They are representative of the various branches of mathematics, cultures, and time periods that we will study.  You are encouraged to work together in groups on these problems if you wish.
    These problems will require usage of the mathematical skills which are taught in MA 131 College Algebra.  If you are not familiar with the necessary mathematics, then you will have to learn it as part of the course.
    You may also be asked to write reaction papers and reports relating to films, videos, speaker presentations, and field trips.
    Other types of assignments may be given also.

3.  Major Term Paper (40%)
    You will write a major term paper on a topic chosen from one of the 4 following options.
    (1)  The life and works of a famous mathematician, chosen from the List of Famous Mathematicians on page 8.
    (2)  An investigation of a significant mathematical concept from a historical perspective, chosen from the List of Topics on page(s) 8-9 of the syllabus.
    (3)  An investigation of a topic of current relevance in mathematics, possibly related to underrepresented groups in the discipline.  The topic MUST be approved by the instructor.  Modifications of the scope and extent of the topics may need to be negotiated with the instructor.
    (4)  Be original and creative.  Design your own topic.  The topic MUST be approved by the instructor.  Modifications of the scope and extent of the topics may need to be negotiated with the instructor.

    The major term paper MUST be at least 10 pages in length, typed and double-spaced.  If a student's paper is LESS THAN 10 pages long, then the score for that paper will be reduced by 1 letter grade.  You MUST use a minimum of 8 sources.  At most 40% of your sources may be taken from the Internet.  NO WIKI!!  ALL Internet sources MUST be approved by the instructor.
    DO NOT PLAGIARIZE.  Any final version of the major term paper containing plagiarized material will automatically receive a score of ZERO, and furthermore, the Chairman of the Mathematics Department and the Dean will be notified for further disciplinary actions.  You MUST use some type of referencing system.  Use whatever system you are familiar with, be consistent with this system throughout the paper.  Include a title page and a bibliography page.  (These do not count toward the total number of pages).  Pictures and diagrams, while strongly encouraged, do not count toward the total number of pages.
    Two students may not write on the same topic.  Only the first student to declare a choice for a topic can write a paper on that topic.

Important Deadlines:
    You MUST have your topic selected and approved by the instructor no later than Wednesday, January 20, 2010
    The paper must be submitted to me no later than Monday, March 15, 2010.
    Then each student will meet individually with the instructor, who will make corrections and recommendations for improvement.  The student will be given an opportunity to rewrite the paper in an attempt to earn a higher score.  The timeline for the second chance will be individually negotiated with each student.  Important Rule:  The second chance rewrite can raise your score by a maximum of 1 letter grade.

Competition for the J. Malcolm Good Award
    Presented for the best research paper in mathematics.  Includes a generous cash prize.  Winner announced at the Honor's Convocation in Spring Semester 2010.

Summary Report on the Major Term Paper
    Near the end of the semester, those students submitting the best 6 papers will present a report to the class.  In this report they will summarize the important themes and main ideas of their papers; they will tell the class what aspects of their research discoveries they found to be most significant, fascinating, surprising, and inspiring.  Then they will respond to questions from their classmates, as well as from their instructor.
    Summary Report:                     15 minutes
    Question and Answer Period:   10 minutes

Guidelines for Writing the Major Term Paper
    If you choose the biographical option (1), then attempt as best you can to address the following concerns when writing your paper.  If you choose option (2), (3), or (4), and you need some direction in the writing of the paper, please consult with the instructor.  These items are intended to be general guidelines and suggestions, not a mandatory checklist to be followed rigorously.
    1.  Basic biographical data.
    2.  What educational institutions was he/she associated with?  (In what capacity? Student, professor, researcher...?)
    3.  What were his/her major achievements, discoveries, theorems, contributions in the field of mathematics?
    4.  What were his/her most significant works and publications? (Books, journal articles, treatises, dissertations...?)
    5.  Was he/she the founder of any new branches of mathematics?
         Was he/she the founder of a new school of thought or movement?
         Did he/she belong to any school or thought or movement?
    6.  Did he/she contribute significantly to any other disciplines besides mathematics?  How?
    7.  Where does he/she rank on the all-time list of great mathematicians? To what extent are modern mathematicians indebted to him/her?
    8.  Mathematics and natural science majors must include a significant amount of actual mathematical detail: formulas, theorems, examples, proofs, and so on.  Others are encouraged to include specific mathematical content.

Of course, you are not bound exclusively to this list.  Allow your research to lead you naturally in directions that interest you, wherever that may be.

4.  Final Examination (40%)
     Date: Wednesday, May 5, 2010 from 1:00-3:00 p.m.

     The final exam will contain the following type of problems: True or False, Multiple Choice, Matching, Short Answer, Fill in the Blank, Mathematical Calculations, Mathematical Problem solving, Definitions, and State the Theorem. (NO Proofs!!)

     The final exam will cover both historical and mathematical material, and will be comprehensive in nature.  The final exam will be a CLOSED REFERENCE test, meaning that you are NOT allowed to use any books, notes, or handouts.  You will of course be required to bring a calculator.  You will need to study very hard in order to be adequately prepared for the Final.   You will be given a Study Guide-Practice Test to work in order to prepare for the Final Examination.  This will be reviewed in class on the last day of regular classes, Friday, April 30, 2010.

5.  Possible Special Activities

    1.  Films and Videos: Donald Duck in Mathemagic Land; The Theorem of Pythagoras; The Story of Pi; N is a Number: The Story of Paul Erd ös; The Proof (Andrew Wiles and Fermat's Last Theorem); possibly others.

    2.  Possible reading and discussion of classic writings, including "The Nature of Mathematics" by A.N. Whitehead, "A Mathematician's Apology" by G.H. Hardy.

    3.  Possible optional visits to UMKC Undergraduate Lecture Series. (Extra Credit for attending designated lectures).


90-100%     A     Class Participation          10%
80-89%       B     Problem Assignments      30%
70-79%       C     Major Term Paper          40%
60-69%       D     Final Examination            20%

Late Submission of Course Materials:

Homework assignments MUST be turned in on the announced due date.  LATE PAPERS WILL NOT BE ACCEPTED.  You will either turn in an assignment on the date that it is due, or you will not turn it in at all.  An assignment MUST be received by class time on the announced due date.  If it is not received by this time, then a score of ZERO will be recorded for that assignment.  NO EXCEPTIONS.  NO EXCUSES.  Athletes who are traveling out of town with a Park University team must turn in the assignment before departure.

Classroom Rules of Conduct:

EXPECTATIONS:   What are the things that the student needs to do in order to succeed in this course?

1.  Regular attendance is ESSENTIAL.

2.  PLEASE bring your textbook to every class session.

3.  Listen carefully and pay attention.

4.  Take thorough, accurate class notes.  For better retention, review your notes as soon as possible after each

     class session.  Review your notes regularly throughout the semester. 

5.  VOCABULARY, TERMINOLOGY, and NOTATION are extremely important in learning mathematics.

6.  ASK QUESTIONS DURING CLASS whenever you need more explanation.

7.  Read your textbook over and over until you understand the material completely.

8.  Consult with the instructor if you are having ANY DIFFICULTY WHATSOEVER. 

     That's why they pay me the big bucks.

9.  Tutoring assistance is available through the Academic Support Center, Mabee Underground Room 406, phone 6330.


Behavior:  Show respect for the instructor.  Show respect for your classmates.  Disruptive behavior will not be tolerated.

Responsibility:  The student is entirely responsible for obtaining and learning any material missed because of absence.  Get handouts and assignments from instructor.  Get class notes from another student in the class.

Calculator:  Each student will need a scientific (not statistical or business) calculator.  Graphing calculators will not be needed.  Try not to spend more that $15 or so.  You can probably find one on sale somewhere.  Most students use Texas Instruments, Casio or a comparable brand name.

Miscellaneous: What materials are you responsible for understanding?  EVERYTHING.  Of course, it would be impossible for you to reproduce everything or demonstrate total knowledge on homework and tests, but you are expected to strive for excellence in everything that we cover, so that you will be prepared for anything.  As Park University students, any effort on your part less than this cannot be considered satisfactory.

Computers make writing and revising much easier and more productive.  Students must recognize though that technology can also cause problems.  Printers run out of ink and hard drives crash.  Students must be responsible for planning ahead and meeting deadlines in spite of technology.  Be sure to save copies of your work to a disk, hard drive, and print out copies for backup purposes.

The instructor reserves the right to make changes in the syllabus due to time constraints, speed of coverage, or other factors.

Course Topic/Dates/Assignments:

 Week 1:      Syllabus, Pythagoras

Week 2:       Pythagoras

Week 3:       Classic Constructions of Ancient Greece

Week 4:       Euclid

Week 5:       Euclid

Week 6:       Archimedes

Week 7:       Archimedes

Week 8:       Diophantus

Week 9:       Spring Break

Week 10:     Fermat's Last Theorem

Week 11:     The Commentators

Week 12:     Medieval Europe

Week 13:     The Cubic Controversy

Week 14:     Renaissance Mathematics

Week 15:     Student Presentations

Week 16:     Review for Final Exam

Week 17:     Final Exam

Academic Honesty:
Academic integrity is the foundation of the academic community. Because each student has the primary responsibility for being academically honest, students are advised to read and understand all sections of this policy relating to standards of conduct and academic life.   Park University 2009-2010 Undergraduate Catalog Page 92

Plagiarism involves the use of quotations without quotation marks, the use of quotations without indication of the source, the use of another's idea without acknowledging the source, the submission of a paper, laboratory report, project, or class assignment (any portion of such) prepared by another person, or incorrect paraphrasing. Park University 2009-2010 Undergraduate Catalog Page 92

Attendance Policy:
Instructors are required to maintain attendance records and to report absences via the online attendance reporting system.

  1. The instructor may excuse absences for valid reasons, but missed work must be made up within the semester/term of enrollment.
  2. Work missed through unexcused absences must also be made up within the semester/term of enrollment, but unexcused absences may carry further penalties.
  3. In the event of two consecutive weeks of unexcused absences in a semester/term of enrollment, the student will be administratively withdrawn, resulting in a grade of "F".
  4. A "Contract for Incomplete" will not be issued to a student who has unexcused or excessive absences recorded for a course.
  5. Students receiving Military Tuition Assistance or Veterans Administration educational benefits must not exceed three unexcused absences in the semester/term of enrollment. Excessive absences will be reported to the appropriate agency and may result in a monetary penalty to the student.
  6. Report of a "F" grade (attendance or academic) resulting from excessive absence for those students who are receiving financial assistance from agencies not mentioned in item 5 above will be reported to the appropriate agency.

Park University 2009-2010 Undergraduate Catalog Page 95

Disability Guidelines:
Park University is committed to meeting the needs of all students that meet the criteria for special assistance. These guidelines are designed to supply directions to students concerning the information necessary to accomplish this goal. It is Park University's policy to comply fully with federal and state law, including Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, regarding students with disabilities. In the case of any inconsistency between these guidelines and federal and/or state law, the provisions of the law will apply. Additional information concerning Park University's policies and procedures related to disability can be found on the Park University web page: .

Additional Information:

List of Famous





















Al- Khowarizmi































































Bernoulli, Daniel 









Bernoulli, James









Bernoulli, John









The Bernoulli Family









Bolyai, John









Bolyai, Wolfgang


































































Hippocrates of Chios











































































Von Neuman



De Moivre









De Morgan






























































List of Topics

1.      The
History of Euclid’s Elements

2.      The
History of Pascal’s Triangle

3.      The
History of Imaginary and Complex Numbers

4.      The
History of the Number Pi

5.      The
History of the Number e

6.      The
History of Fibonacci Numbers

7.      The
History of the Golden Ratio

8.      The
History of Fermat’s Theorem

9.      The
History of the Four Color Theorem

10.  The History
of the Fundamental Theorem of Algebra

11.  Mathematics
and Physics

12.  Mathematics
and Computer Science

13.  Mathematics
and Engineering

14.  Mathematics
and Chemistry

15.  Mathematics
and Biology

16.  Mathematics
and Elementary Education

17.  Mathematics
and Middle School Education

18.  Mathematics
and High School Education

19.  Mathematics
and College Level Education

20.  Mathematics
and Art

21.  Mathematics
and Music

22.  Mathematics
and Architecture

23.  Mathematics

24.  Ancient
Babylonian Mathematics

25.  Ancient
Egyptian Mathematics

26.  The Seven
Sages of Ancient Greece

27.  Alexandria: The
University and the Library

28.  The

29.  Chinese

30.  Arabic

31.  Hindu

32.  The

33.  Mathematics
in the Dark Ages

34.  Medieval

35.  Renaissance

36.  Women in

37.  The Search
for Prime Numbers


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Last Updated:1/8/2010 3:59:37 PM