MA350 History of Mathematics

for SP 2008

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MA 350 History of Mathematics


SP 2008 HO


Smith, Charlie L.


Associate Professor of Mathematics, and Chairman of the Mathematics Department


Ph.D. in Mathematics, UMKC, 2002
M.A. in Mathematics, University of Kansas, 1983
B.A. in Mathematics, William Jewell College, 1981

Office Location

Science Hall 308

Office Hours

Monday, Friday 9:00-10:00; Tuesday/Thursday 9:30-11:30 and Wednesday 9:00-11:00

Daytime Phone



Semester Dates

January 14 - May 9, 2008

Class Days


Class Time

11:00 - 12:15 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:
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 7 of the
      (2)  An investigation of a significant mathematical concept from a historical prospective, chosen from the List of Topics
            on page 7 of the syllabus.
      (3)  An investigation of a topic of current relevance in mathematics, possibly related to under-represented groups in the
            discipline.  The topic MUST be approved by the instructor.  Modicfications 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 topic may need to be negotiated with the instructor.
      The major term paper MUST be 12-18 pages in length, typed and double-spaced.  If a student's paper is LESS THAN 12 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.  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 action.  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 no later than Friday, January 25, 2008.
      The paper must be submitted to me no later than Monday, March 17, 2008.
      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 2008.
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 the 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 your 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 of 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:  formuas, 
           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 (20%)
     Date:  Monday, May 5, 2008 from 10:15 a.m. to 12:15 p.m.
      The final exam will contain the following types 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.  This is a very challenging and difficult test.  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, May 2, 2008.
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 Erdös; 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 to the UMKC Undergraduate Lecture Series.  (Extra credit for attending designated lectures.)


90-100%   A               Class Preparation         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 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 the student needs to do in order to succeed in this course?)
      1.  Regular attendance is ESSENTIAL.
      2.  PLEASE bring your calculator 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.  Consult with the instructor if you are having ANY DIFFICULTY WHATSOEVER.  That's why they pay me the
           big bucks.
      Show respect for the instructor.  Show respect for your classmates.  Disruptive behavior in any form will not be tolerated.
      The student is totally responsible for obtaining and learning any material missed because of absence.  Get handouts an dassignments from the instructor.  Get class notes from another student in the class.
      Each student will need a scientific (not statistical or business) calculator.  Graphing calculators will not be needed.  Try not to spend more than $15 or so.  You can probably find one on sale somewhere.  Most students use Texas Instruments, Casio, or a comparable brand name.
      What material 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 recongnize thought 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, Egyptians, Babylonians, 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 2007-2008 Undergraduate Catalog Page 85-86

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 2007-2008 Undergraduate Catalog Page 85

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.
  3. Work missed through unexcused absences must also be made up within the semester/term of enrollment, but unexcused absences may carry further penalties.
  4. 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".
  5. A "Contract for Incomplete" will not be issued to a student who has unexcused or excessive absences recorded for a course.
  6. 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.
  7. 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 2007-2008 Undergraduate Catalog Page 87-88
Attendance will be recorded daily.  Any student who accumulates 4 CONSECUTIVE absences will be automatically withdrawn from the course by the institution.

No distinction will be made between excused and unexcused absences.  In fact, these terms do not exist: you are either present or absent.  If you are not in class FOR ANY REASON, then you will be counted absent.  It is the student's responsibility to sign the attendance sheet or else be counted absent.

There will be a mandatory field trip.  Early in the class we will visit the Linda Hall Library.  We will receive a library orientation, learn how to use the library to gather research material for the major term paper, learn the locations of the mathematical history resources, and tour the Rare Book Room.  The date for this field trip is TBA.

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 Mathematicians:

Abel, Agnesi, Al-Khowarizmi, Apollonius, Archimedes, Aristarchus


Babbage, Banach, Barrow, Daniel Bernoulli, James Bernoulli, John Bernoulli, The Bernoulli Family, John Bolyai, Wolfgang Bolyai, Bolzano, Bombelli, Boole, Borel, Brahe, Brahmagupta,Brouwer


Cantor, Cardano, Cauchy, Cayley, Chebyschev, Copernicus


D'Alembert, Dedekind, De Moivre, De Morgan, Descartes, Diophantus, Dirichleet


Einstein, Eratosthenes, Erdös, Euclid, Eudoxus, Euler


Fermat, Fibonacci, Fisher, Fourier, Frege


Galileo, Galois, Gauss, Germain, Gödel


Halley, Hamilton, Hardy, Hausdorff, Hermite, Hero(n), Hilbert, Hippias, Hippocrates of Chios, Hooke, Huygens, Hypatia


Jacobi, Jordan


Kepler, Khayyam, Klein, Kovalevsky, Kronecker, Kummer


Lagrange, Lambert, Laplace, Lebesgue, Legendre, Leibniz, L’Hôspital, Lindemann, Liouville, Littlewood, Lobachevsky


Maclaurin, Mersenne


Napier, Newton, Noether


Pacioli, Pappus, Pascal, Peano, Pearson, Poincare, Poisson, Ptolemy, Pythagoras


Ramanujan, Recorde, Regiomontanus, Riemann, Russell


Saccheri, Sylvester


Tartaglia, Thales


Vièta, Van der Waerden, Von Neuman


Wallis, Weierstrass, Weyl, Whitehead, Wiles


Zeno, Zermelo


List of Topics for Major Term Paper:

   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 e

   5.  The History of the Number π

   6.  The History of the 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.  The Search for Prime Numbers

12.  Mathematics and Physics

13.  Mathematics and Computer Science

14.  Mathematics and Engineering

15.  Mathematics and Chemistry

16.  Mathematics and Biology

17.  Mathematics and Elementary Education

18.  Mathematics and Middle School Education

19.  Mathematics and High School Education

20.  Mathematics and College Level Education

21.  Mathematics and Art

22.  Mathematics and Music

23.  Mathematics and Architecture

24.  Mathematics and YOUR MAJOR
25.  Ancient Babylonian Mathematics

26.  Ancient Egyptian Mathematics

27.  The Seven Sages of Ancient Greece

28.  Alexandria: The University and the Library

29.  The Commentators

30.  Chinese Mathematics

31.  Arabic Mathematics

32.  Hindu Mathematics

33.  The Translators

34.  Mathematics in the Dark Ages

35.  Medieval Mathematics

36.  Renaissance Mathematics

37.  Women in Mathematics


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Last Updated:1/18/2008 2:46:41 PM