MAT 406 An Introduction to the History of Mathematics Credit, 3 sem. hrs.

Prerequisites: MAT 221 or instructor=s consent

 

This class is a development of areas of mathematics such as algebra, geometry, and analysis and a study of the lives and works of outstanding mathematicians.

 

Rationale

 

This course will help mathematics students gain an understanding of the nature of mathematics and the relationships within it by viewing it historically. The courses emphasize the historical development of mathematics from the perspective of many mathematicians/philosophers from many cultures.

 

Professor

 

Dr. Teresa Floyd - 925-3468 Office: 316 MCC e-mail: floyd@mc.edu

Office hours: vary by semester

 

Learning Objectives

At the conclusion of the course, successful students should be able to:

-demonstrate methods of counting and number systems used by ancient civilizations

-state methods of recording information that provided modern knowledge of ancient mathematics

-find triangular, square and pentagonal numbers

-calculate amicable, perfect, prime, abundant and deficient numbers

-name the Platonic solids

-state the three classic problems of antiquity with a proposed solution

-state Euclid=s accomplishments

-name several Greek mathematicians, their major accomplishments, and solve problems similar to their work

-name the accomplishments of and work problems relating to early Chinese, Hindu and Arabic mathematicians

-list reasons why there was minimal mathematical progress during the Dark Ages

-name prominent mathematicians of the 17th century, identify their work and work similar problems

-name the major mathematicians whose work prepared the world for calculus and work similar problems

-name the creators of calculus and identify how their work was different

-name prominent mathematicians of the 18th century; identify their work and work similar problems

-name prominent mathematicians of the 19th century; identify their work and work similar problems

-name prominent mathematicians of the 20th century; identify their work and work similar problems

 

Outline of Topics

 

The topics will come from the material in Chapters 1-13 of the text. Students are expected to

read all assigned sections and attempt solutions to problems assigned relating to these topics.

 

I. Early Number Systems and Symbols VII. The Renaissance of Mathematics

A. Sources A. Europe in 14th & 15th Century

B. Properties B. Cardano=s Ars Magna

C. Ferrari

II. Mathematics in Early Civilizations

A. Egyptian Mathematics VIII. The Mechanical World

1. Arithmetic A. Galileo

2. Geometry B. Copernicus

B. Babylonian Mathematics C. Kepler

D. Descartes

III. The Beginnings of Greek Mathematics E. Newton=s Principia

A. Thales F. Leibniz

B. Pythagorean Mathematics

C. Three Problems of Antiquity IX. The Development of Probability Theory

D. Quadratrix A. The Origins of Probability

B. Pascal

IV. The Alexandrian School: Euclid C. Bernoullis & Laplace

A. Euclid=s Elements

B. Euclidean Geometry X. The Revival of Number Theory

C. Euclid=s Number Theory A. Mersenne=s Search for Perfect Numbers

D. Erathosthenes B. From Fermat to Euler

E. Archimedes C. Gauss

 

V. The Twilight of Greek Mathematics XI. Nineteenth-Century

A. Diophantus= Arithmetica A. Attempts to Prove the Parallel Postulate

B. Diophantine Equations B. Non-Euclidean Geometry

C. Commentators C. The Age of Rigor

D. Mathematics in Near & Far East

XII. Transition to the Twentieth Century

VI.. The First Awakening A. American Mathematics

A. Fibonacci B. Counting the Infinite

B. Liber Abaci C. Paradoxes of Set Theory

C. Fibonacci Sequence

XIII.       Extensions and Generalizations

Academic Integrity

 

Honesty and integrity are basic virtues expected of all students at Mississippi College. The Mississippi College Undergraduate Catalog lists the policies and penalties for plagiarism and cheating. See the Mississippi College Student Handbook for specific information regarding penalties. On tests, quizzes, and individual out-of-class projects, the work is assumed to be the student=s own and no cheating will be tolerated.

 

Methods of Instruction

 

The methods of instruction will include lecture, discussion, student reports, group problem solving, individual problem solving, demonstrations, hands-on construction, exploration using graphing calculators/software, and quizzes. Each student is expected to be prepared for class, have a copy of the text, paper, pencils, calculator, and compass.

 

Required Practices

 

Required practices for successful completion of this course include reading assigned materials on time, timely written completion of problems, oral and written reports using internet sources as well as traditional ones, proficient use of calculators, classroom explanation of solved problems, and completion of written examinations. Homework is due at the beginning of the class for which it was assigned.

 

Instructional Materials

 

Text: Burton, D. B. (2007). The History of Mathematics (6th Ed.). Boston, MA: WCB McGraw Hill.

 

Assessment

 

Assessment will include tests, oral and written reports, in-class explanations/demonstrations of problems, and unannounced homework evaluations. Active class participation is expected and included in final grade evaluation. The final grade will be determined based on total points and a ten-point scale.

 

Other Policies

 

v  Makeup work is the responsibility of the student and should be cleared with the instructor in advance whenever possible.

v  Students are responsible for all material covered and all assignments given when they are absent.

v  The college stipulates that the grade for the course is automatically an F in the event of 8 absences. The student can expect a reduction of a letter grade for each week of unexcused absences. An unexcused tardy or absence will result in a zero for homework taken/daily work/quizzes. [See Mississippi College Undergraduate Catalog for excused absences]

v  If you need special accommodations due to learning, physical, psychological, or other disabilities, please contact Dr. Buddy Wagner in the Counseling and career Development Center. He may be reached at 601-925-3354.

 

Dr. Floyd=s Responsibilities

 

v  Start/stop on time.

v  Be prepared to conduct class, answer questions and ask questions.

v  Evaluate student progress.

 

Student Responsibilities

 

  Attend all class meetings ON TIME.

  READ all assigned material promptly.

  Complete homework timely.

  THINK!

 

MISSISSIPPI COLLEGE ACADEMIC POLICIES:

Students should consult the Mississippi College policy manual located at http://www.mc.edu/resources/publications/policies/ for official information regarding:

  • Class attendance - Policy 2.10
  • Grading - Policy 2.15
  • Cheating - Policy 2.19
  • Counseling and Career Services - Policy 2.25
  • Research - Policy 2.27
  • Counseling and Testing Center - Policy 2.34

 

Students who may require accomodation due to a documented handicap should follow the procedures located at http://www.mc.edu/about/offices/counseling/disabilities/

 

The Generic Grading Scale for this course is A = 90-100, B = 80-89, C = 70-79, D = 60-69. Individual instructors are free to choose a different grading scheme so students should consult their section's particular syllabus for the official grading scale to be utilized.

 

Tutoring Hours:

Hours and location for the departmental tutoring center are posted at http://www.mc.edu/academics/academic-tutoring/ .