Course syllabus - The history of mathematical ideas

Objectives

The course will give a general survey of the development of mathematics. Special emphasis is put on mathematical concepts and methods. The student will study old concepts, notations and algorithms and do some calculations using these methods, thus gaining a wider perspective and a more profound knowledge of modern mathematics.
The student will realize how the needs of the surrounding society have affected mathematics, and also, how mathematics has affected the development of society. The mutual dependency between mathematics on one hand and philosphy, economics, astronomy, physics, other sciences and technology on the other hand, will be investigated. On one hand throughout history mathematics has had a development "of its own", and therefore a position as an independent subject in the humanistic tradition. On the other hand mathematics has often been considered as an auxiliary science, whose sole right to exist has been to satisfy the needs of more practically directed subjects. Still today - for example at universities - there is an ongoing debate about the double role of mathematics. The course is primarily intended for teacher education but is also of great interest for other students with an interest in the described issues.

Learning outcomes

At the end of the course the student is expected to be able to
- describe the life and work of about 20 of great mathematicians of world history.
- give an outline of old Babylonian , Egyptian , Greek , Arabic, Indian ,and Chinese mathematics
- describe contents and structure in Euklides´ Elementa.
- prove about 10 important theorems formulated by the old Greek.
- use historical methods of multiplication, division extraction roots.
- compare different number systems.
- calculate areas and volumes using old Greek and Chinese methods .
- solve equations and systems of equations with methods used before the sixteenth century .
- carry out infinitesimal calculus with methods from the seventeenth century.
- describe the development of analysis from Greek to modern time.

Course content

The course begins with classical problems, associated with the development of concepts and methods in different parts of the world from prehistoric timme to modern time. Connected with a chronological survey of the history of mathematical ideas, the course will pay special attention to certain topics, e. g.:
Solution of equations
Calculation of areas and volumes
Optimization
Analysis and mechanics
Classical and analytical geometry
Trigonometry and astronomy
Combinatorics, probability and statistics
The strange numbers "square root of 2", "pi", "e" and "i"
Discrete mathematics and datology
Number theory
Modern algebra

Tuition

Lectures and exercises.

Specific requirements

30 credits in mathematics, including algebra, geometry and analysis.

Examination

Examination. Continous assesment (EXA1), 3 credits, marks Pass (G) or Pass with distinction (VG)
Examination. Written or oral examination (TEN1), 4.5 credits, marks Pass (G) or Pass with distinction (VG)

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Pass with distinction, Pass, Fail