SHAW UNIVERSITY
COURSE OUTLINE
MAT 433 HISTORY
OF MATHEMATICS FALL 2007
Instructor: Dr. S. Ugwuoke Office Hours: M,W,F: 12:00 N-1:00 PM, 2:00 PM-3:00 PM
Phone: 546-8543 T,Th: 10:50 AM - 11:50 AM,
Office: Graphics Bldg. Room 4 1:20 PM - 2:20 PM
E-mail: sugwuoke@shawu.edu
Text
Stillwell, J. Mathematics And Its History. New York: Springer-Verlag, Inc., 1989.References:
Hardlock, C.R. Field Theory And Its Classical Problems The Mathematical Association of America, 1978.
Hofmann, J.E. The History of Mathematics. New York: Philosophical Library, Inc.,1957.
Kline, M. Mathematics in the Western Culture. New York: Oxford University Press,1953.
General Description
This course studies the development of mathematical thought and the evolution of mathematical ideas examined in a historical setting. The historical content will be paralleled with, or supplemented and reinforced by a study of the techniques and procedures used in earlier eras in relation to the techniques used in today's mathematics. Some philosophical foundations of mathematics and biographical histories of a few mathematicians will also be examined.
Student Learning Outcomes
After completing this course successfully, students should be able to demonstrate an understanding of the historical development of mathematics in relation to the following topics, and how the techniques and procedures used in the early era relate to the mathematics of today. They should also be able to write a brief biographical history of at least two of the groups or individuals involved in the developmental process, and, in addition, demonstrate an awareness of the philosophical and religious contents associated with some of the topics. They should demonstrate an understanding of the following topics:
·
Philosophical Foundations of Mathematics·
Religious Impact on the Development of Mathematics·
The Three Greek Problems · The Theorem of Pythagoras·
Greek Geometry · Greek Number Theory·
Infinity in Greek Mathematics · Polynomial Equations·
Analytic Geometry · Projective Geometry·
Calculus · Infinite Series·
The Revival of Number Theory · Elliptic Functions·
Mechanics · Complex Numbers in Algebra·
Complex Numbers and Curves · Complex Numbers and Functions·
Differential Geometry · Non-Euclidean Geometry·
Group Theory · Topology·
Set Theory · Logic, and Computation
Topic Outline
A Brief Historical Development from
800 B.C. to 1650 (Hofmann, J.E.) (
NCDPI 12.0)-Contributions to mathematics of historically
underrepresented groups or cultures (
NCDPI 12.3)The Three Greek Problems (Hardlock, pg.2-4 and Ch.1) (
NCDPI 12.1)-constructible lengths (1.1) -doubling the cube (1.2)
-trisecting an angle (1.3) -squaring a circle (1.4)
The Theorem of Pythagoras (Stillwell, J. Chap.1)
Greek Geometry (Chap. 2) (
NCDPI 2.1, 12.2)Greek Number Theory (Chap.3) (
NCDPI 1.3, 12.2)Infinity in Greek Mathematics (Chap.4)
Polynomial Equations (Chap.5)
The Solution of Polynomial Equations by Radicals
-a brief history (Hardlock, pg.4-6)
-polynomials and their roots
(Hardlock, Sec.1.5) (
NCDPI 12.1)Analytic Geometry (Chap. 6)
Projective Geometry (Chap.7)
Calculus (Chap. 8) (
NCDPI 3.0, 12.0)Infinite Series (Chap.9) (
NCDPI 3.1, 12.0The Revival of Number Theory (Chap.10) (
NCDPI 1.3, 12.0Elliptic Functions (Chap.11)
The historical interplay between mathematics
and the physical sciences: (
NCDPI 12.1)Calculus-Chap. 8, Mechanics-chap.12 (
NCDPI 12.2)Complex Numbers in Algebra (Chap.13) (
NCDPI 1.1, 12.2)Complex Numbers and Curves (Chap.14) (
NCDPI 1.1, 12.2)Complex Numbers & Functions (Chap.15) (
NCDPI 1.1, 12.2)Differential Geometry (Chap.16)
Non-Euclidean Geometry (Chap.17) (
NCDPI 2.1, 12.2)Group Theory (Chap.18)
Topology (Chap.19)
Sets, Logic, and Computation (Chap. 20) (
NCDPI 1.4,12.0)
Evaluation
1. Assignments/Quizzes/Class Participation 30% of final grade
2. Hourly Tests 40% of final grade
3. Final Exam 30%
of final grade
Attendance Policy
Regular class attendance and punctuality in this course are stressed.
More than two unexcused absences may lead to a grade of NC (an F grade).
Note that this class meets only two times a week (75 min each).
Two absences are equivalent (class time-wise) to a whole week lost!!
Student Classroom Decorum Expectations
To enhance the learning atmosphere of the classroom, students are expected to dress and behave in a fashion conducive to learning in the classroom. More specifically, students will refrain from disruptive classroom behavior, such as - talking to classmates, disrespectful responses to teacher instructions; swearing; wearing clothes that impede academic learning such as but not limited to, wearing body-revealing clothing and excessively baggy pants; hats/caps, and/or headdress. Students will turn off telephones prior to entering the classroom.
Students who exhibit the behaviors described above, or similar behaviors will be immediately dismissed from class at the third documented offense. The student will be readmitted to class only following a decision by the department chair. The student may appeal the decision of the department chair to the Dean of the College offering the course, and, subsequently, to the Office of the Vice President for Academic Affairs, and then to the President of Shaw University. The decision of the President will be final. Failure to follow the procedures herein outlined will result in termination of the appeal, and revert to the decision of the department chair.
Each behavior construed by the teacher/professor as non-contributive to learning will be recorded, properly documented, and appropriately reported to the student and to the chair of the academic department offering the course. The report will be in written form with a copy provided to both the student and the department chair. The faculty member should retain a copy for his/her own records.
Additional student behavior codes may be found in Student Affairs.