The History of Mathematics (David M. Burton)
UNIVERSITY OF SARGODHA
DEPARTMENT OF MATHEMATICS
COURSE OUTLINE Spring 2021
Course Title: History of Mathematics
Course Code: MATH-429
Credit Hours: 03
Instructor: FARYAL ANJUM
Email: [email protected]
DESCRIPTION & OBJECTIVES
There are many excellent reasons to study the history of mathematics. It helps students develop a deeper understanding of the mathematics they have already studied by seeing how it was developed over time and in various places. It encourages creative and flexible thinking by allowing students to see historical evidence that there are different and perfectly valid ways to view concepts and to carry out computations. Ideally, a History of Mathematics course should be a part of every mathematics major program. The objectives (and outcomes) for math history courses also include clear, critical, creative, and flexible thinking, and an appreciation for the beauty and joy of mathematics.
READINGS
Recommended book
1. Boyer C.B. and Mersbach U.V. The History of Mathematics. 2nd ed. John Wiley, 1989.
2. David M. Burton, The History of Mathematics: An Introduction, 7th Ed. McGraw-Hill, 2010
3. Boyer, Carl B. and (revised by) Uta Merzbach, A History of Mathematics, New York: John Wiley, 2nd ed., 1989.
CONTENTS
History of numerations; Egyptian, Babylonian, Hindu and Arabic contributions. Algebra: Including the contributions of Al-Khwarzmi and Ibn Kura. Geometry: areas, the work of Al-Toussi on Euclid’s axioms. Analysis: The CalculusNewton, Lebnitz, Gauss. The concept of limit: Cauchy, Laplace. An introduction to some famous old open problems.
COURSE SCHEDULE
Week |
Topics and Readings |
Dates |
1. |
History of numerations; Egyptian |
Feb 22-26, 2021 |
2. |
History of numerations; Babylonian |
Mar 08-12, 2021 |
3. |
The concept of limit: Cauchy |
Mar15-19, 2021 |
4. |
The concept of limit: Laplace |
Mar 22-26, 2021 |
5. |
Contribution of Hindu Scholars |
Mar 29-Apr 02, 2021 |
6. |
Contribution of Arabic Scholars |
Apr 05-09, 2021 |
7. |
Hindu and Arabic System of Numeration |
Apr 12-16, 2021 |
8. |
Mid Term Exam |
Apr 19-23, 2021 |
9. |
Algebra: Including the contributions of Al-Khwarzmi |
Apr 26-30, 2021 |
10. |
Algebra: Including the contributions of Ibn Kura |
May 03-07, 2021 |
11. |
Geometry: areas, the work of Al-Toussi on Euclid’s axioms |
May 10-14, 2021 |
12. |
Newton work in Calculus |
May 17-21, 2021 |
13. |
Lebnitz work in Calculus |
May 24-28, 2021 |
14. |
Gauss work in Calculus |
May 31- June 04, 2021 |
15. |
Difference between Newton and Leibnitz ; Calculus |
June 07-11, 2021 |
16. |
An introduction to some famous old open problems.
|
June 14-18, 2021 |
17. |
Final Term Exam |
June 21-25, 2021 |
RESEARCH PROJECT
N/A
ASSESSMENT CRITERIA
Mid exam: 30
Sessional: 20
Project: --
Assignments: 10
Presentation: 10
Final exam: 50
Total: 100
RULES AND REGULATIONS
75% attendance is compulsory to appear in Final Term exam.