NAMEHaideh GhaderiPRACTICAL/TUTORIAL GROUP
Unit Course book
History of Mathematics
Course code: MthP318HM
Unit Coordinator
Haideh Lotfolla Ghaderi
2012/2013
Soran University
Faculty of Science
Department of Mathematics
Stage 3
Course Description:
This course is an attempted introduction to the history of mathematics that can serve as a textbook for a one-semester undergraduate course which meets three hours a week. Consequently, the treatment is restricted principally to “elementary” mathematics, that is, mathematics through the beginnings of calculus. It is the author’s conviction that the history of a subject cannot be appreciated properly whit out at least a fair acquaintance with the subject itself.
The historical material in this book is presented roughly in chronological order, and the reader will find that a knowledge of simple arithmetic and of high school algebra, geometry, and trigonometry is in general sufficient for a proper understanding of the first nine chapters. A knowledge of the rudiments of plane analytic geometry is needed for chapter 10, and a knowledge of the basic concepts of the calculus is required for chapter 11 and 12. Any concepts or developments of a more advanced nature appearing in the book are, it is hoped, sufficiently explained at the points where they are introduced. A certain amount of mathematical maturity is desirable, and whether nine, ten, or all twelve chapters are to covered will depend upon class time and the students previous preparation.
An important innovation in the treatment is the inclusion of problems. At the end of each chapter, a set of problem studies, with each problem study containing a number of associated problems and questions, is found. It is felt that by discussing a number of these problem studies in class, and working others as home assignments, the course will become more concrete and meaningful for the student, and the student’s grasp of a number of historically important concepts will become crystallized. For example, no better appreciation and understanding of numeral systems can be gained than by actually working with these systems. And rather than just tell a student that the ancient Greeks solved equations geometrically, let him solve some by the Greek method; in so doing he will not only thoroughly understand the Greek method, but he will achieve a deeper appreciation of Greek mathematical accomplishment. Thus it is hoped that the student will learn much of his history, as well as some interesting in mathematics, from these problem studies. Some of the problem studies concern themselves with historically important problems and procedures, others furnish valuable material for the future teacher of either high school or college mathematics, and still others are purely recreational. Of course, there are many more problem studies than can be covered in any one semester, and they are of varying degrees of difficulty. This permits an instructor to select problems according to his students’ abilities and to vary his assignments from year to year. At the end of the book is a collection of suggestions for the solution of many of the problem studies.
There is often some difficulty experienced in pronouncing the Hindu and Arabian names.
The history of mathematics, even that of elementary mathematics, is so vast that only an introduction to the subject is possible in a one-semester course. The interested student will want to consult further literature. accordingly, to each chapter has been appended a bibliography dealing with the material of that chapter. An additional general bibliography, given immediately after the final chapter, applies to every, or almost every, chapter.
It must be realized that the bibliography makes no pretense to completeness and is intended merely to serve as a start in any search material.
Few periodical references have been furnished; important references of this sort are very numerous and will soon be encountered by an inquiring student. The references given are generally accessible and in English.
Homework:
Solution of problem in for each History of Mathematics subject in this course. Presentation of Problems: When you come into class, you should be prepared to it. One person will present each problem and then we will all discuss it.
Quiz: Each quiz will be an equivalent percentage to one homework set.
Email:
E.mail:haideh.ghaderi@gmail.com
M: 07508954775
Staff associated with the unit:
Staff
Room Number
Email
D.Farhad Janati
Teaching room
fdjanaty@yahoo.com
Soran University
Department of mathematics
Unit: History of Mathematics
Credit 3
Method of Assessment:
1 x 3 h lectures per week.
Examination and Grading:
Month’s exam: 10%
Classroom participation and assignments and homework 30%
Final exam: 60%
Marking System:
The grades for each piece of assessed work are as follows:
* 90-100 % is excellent
* 80-89% is very good
* 70-79% is good
* 60-69% is a moderate pass
* 50-59% is a pass
* <49% is a fail
Unit Timetable/Content
University Academic Week
Lecture Title & Content
Assessments1st weekNumeral system, Primitive Counting, Number Bases, Written Number Systems, Simple Grouping Systems, Multiplicative Grouping Systems.2nd weekCiphered Numeral Systems, Positional Numeral Systems, Early Computing, The Hindu-Arabic Numeral System, Arbitrary Bases.3rd weekProblem solving sessions4th weekBabylonian and Egyptian Mathematics, The Ancient Orient, BABYLONIA: Sources, Commercial and Agrarian Mathematics, Geometry, Algebra, Plimpton.5th weekEGYPT: Sources and Dates, Arithmetic and Algebra, Geometry, A Curious Problem in the Rhind Papyrus.6th week Problem solving sessions7th weekProblem solving sessions and exam.8th weekPythagorean Mathematics, Birth of Demonstrative Mathematics, Pythagoras and the Pythagoreans, Pythagorean Arithmetic, Pythagorean Theorem and Pythagorean Triples.9th weekDiscovery of Irrational Magnitudes, Algebraic Identities, Geometric Solution of Quadratic Equations, Transformation of Areas, The Regular Solids, Postulational Thinking.10th weekProblem Studies11th weekDuplication, Trisection, and Quadrature, The Period from Thales to Euclid, Lines of Mathematical Development, The Three Famous Problems.12th week The Euclidean Tools, Duplication of the Cube, Trisection of an Angle, Quadrature of the Circle, Chronology of ( .13th weekImpossibility of Solving the Three Famous Problems with Euclidean Tools, Compasses or Straightedge Alone.14th weekProblem solving sessions15th weekProblem solving session
Second examination
16th weekEuclid’s Elements, Alexandria, Euclid, Euclid’s “Elements”, Content of the ”Elements”.17th weekLogical Shortcoming of the “Elements”, Non-Euclidean Geometries, Axiomatics, Sequel to Euclid, Euclid’s Other Works.18th weekProblem solving session
Third examination
19th weekGreek Mathematics after Euclid, Historical Setting, Archimedes, Eratosthenes, The Prime Numbers, Apollonius, Greek Trigonometry, Heron, Diophantus, Pappus, The Commentators.20th weekProblem solving session21st weekHindu and Arabian Mathematics, General Survey, Number Computing, Arithmetic and Algebra, Geometry and Trigonometry, Contast between Greek and Hindu Mathematics.22nd weekARABIA: The Risa of Moslem Culture, Arithmetic and Algebra, Geometry and Trigonometry, Some Etymology, The Arabian Contribution. 23rd weekProblem solving sessions.
Fourth examination.
24th weekEuropean Mathematics,The Dark Ages, The period of Transmission, Fibonacci and the Thirteenth Century, The Fourteenth Century, The Fifteenth Century.25th weekThe Early Arithmetics, Beginning of Algebraic Symbolism, Cubic and Quartic Equations, Francois Viete, Other Mathematicians of the Sixteenth Century.26th weekProblem solving27th weekProblem solving
Fifth examination
* Note that, Tutorials will be arranged by your lecturer during the class.
Tutorials & Assessments :
Attendance at tutorials & Assessments is necessary in order to gain marks for the given exercise.
Recommendation :
Keeping a wall diary is recommended to enter all deadline dates so you can see what assignments are due in. It is also essential to leave yourself sufficient time to complete the work.
Recommended Reading &References:
1.Howard Eves;” An Introduction of the History of Mathematics. University of Maine.
2.Cajori, Florian;” A History of Mathematical Notations. 2 Vols. Chicago: Open Court Publishing, 1925-29.
3.Van Der Wrerden, B.L., Science Awakening Translated by Arnold Dresden. New York: Oxford University Press, 1961.