MA350 History of Mathematics

for FA 2012

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Vision Statement: Park University, a pioneering institution of higher learning since 1875, will provide leadership in quality, innovative education for a diversity of learners who will excel in their professional and personal service to the global community.


MA 350 History of Mathematics


FA 2012 HOZ


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

SC 214

Office Hours

MWF 9-10 AM; TR 10-11 AM; W 2-3 PM

Daytime Phone



Semester Dates

August 20, 2012 - December 14, 2012

Class Days


Class Time

8:45 - 10:00 AM


It is strongly recommended that the student has passed MA 135 or its equivalent.

Credit Hours


The History of Mathematics, An Introduction; David Burton; McGraw-Hill; ISBN: 978073383156.

Textbooks can be purchased through the Parkville Bookstore

Additional Resources:
Linda Hall Library of Science, Engineering, and Technology; 5109 Cherry, Kansas City, MO 64110, (816) 363-4600; - Thousands of books and journals, several user services.

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: 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:
Mathematics is my lifelong passion and obsession. In the classroom, I try to convey my enthusiasm and excitement for mathematics; I emphasize its pristine beauty and logical structure. Students are required to work a substantial number of homework problems in order to learn the material. Typically two major tests are given each semester. Material is presented in lecture format; students are encouraged to interrupt to ask questions.

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:
Core Learning Outcomes 1, 2, and 3. Core Learning Outcome number 4 will not be required at this time.  All Core Assessment items except class attendance, class participation and oral presentation will be assessed this semester.


Problem Assignments (35%)
   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 135 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.
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 pages 7 - 9 of the syllabus.
  2. An investigation of a significant mathematical concept from a historical perspective, chosen from the List of Topics on pages 9 and 10 of the syllabus.
  3. An investigation of a topic of current relevance in mathematics.  The topic MUST be approved by the instructor.
  4. Be original and creative.  Design your own topic.  The topic MUST be approved by 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 30% 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 contianing plagiarized material will automatically receive a score of ZERO, and futhermore the Chairman of the Mathematics Department and 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 the choice for a topic can write a paper on that topic.
Important Deadlines:
   You MUST have your topic selected and approved no later than Tuesday, August 28, 2012.  The paper must be submitted to me no later than Tuesday, October 23, 2012.
   Make sure that your first version has been proofread before turning it in.  If there are too many mistakes in grammar, spelling, punctuation, word choice, organization, and the like, I will return your paper and ask you to have it proofread by somebody and corrected before I will grade it.
   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 is announced at the Honor's Convocation in Spring Semester 2013.
Guidelines for Writing the Major Term Paper
   If you choose the biographical option (1), then attempt as best you can to address the following concern 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?
  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.
Final Examination (25%)
   Date: Thursday, December 13, 2012; 1:00 - 3:00 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 the regular classes, Thursday, December 6, 2013.
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.
90-100%   A
80-89%     B
70-79%     C
60-69%     D
Problem Assignments 35%
Major Term Paper 40%
Final Examination 25%

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 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.

   Show respect for the instructor. Show respect for your classmates. Disruptive behavior in any form will not be tolerated.

Responsibility:  The student is entirely responsible for obtaining and learning any new material missed because of absence.  Get handounts and assignments from the 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 than $15 or so.  You can probably find one on sale somewhere.  Most students use Texas Instruments, Casio, or some other 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 or 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 mathematics majors, 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:  Fall 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:  Renaissance Mathematics
Week 16:  Review for the 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 students and faculty members are encouraged to take advantage of the University resources available for learning about academic honesty ( or Park University 2011-2012 Undergraduate Catalog Page 95-96

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. from Park University 2011-2012 Undergraduate Catalog Page 95

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 2011-2012 Undergraduate Catalog Page 98

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'Albert, Dedekind, Descartes, De Moivre, De Morgan, Diophantus, Dirichlet


Einstein, Eratosthenes, Erdös, Euclid, Eudoxus, Euler


Fermat, Fibonacci, Fisher, Fourier, Frege


Galileo, Galois, Gauss, Germain, Gödel


Halley, Hamilton, Hardy, Hausdorff, Hermite, Heron, Hilbert, Hooke, Hippias, Hippocrates of Chios, Huygens, Hypatia


Jacobi, Jordan


Kepler, Khayyam, Klein, Kovalevsky, Kronecker, Kummer


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


Maclaurin, Mersenne


Napier, Newton, Noether


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


Ramanujan, Recorde, Regiomontanus, Riemann, Russell


Saccheri, Sylvester


Tartaglia, Thales


Vièta, Von Neuman


Wallis, Weierstrass, Weyl, Whitehead, Wiles


Zeno, Zermelo 


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 

 5.  The History of the Number

 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 Univeristy 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:8/22/2012 11:22:22 AM