### 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.

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.