NMAK14032U History of Mathematics 2 (Hist2): The Classical Problems

Volume 2014/2015
Education
MSc Programme in Mathematics
Content

The quadrature of the circle, the trisection of an angle and the dublication of the cube; These are the three classical problems whose history we shall investigate in this course. We shall study how they were formulated and soved in classical Greece, and how analytic tecniques were used to solve them in the 17th century. In particular we shall discuss their impossibility with ruler and compass or by other means: How this impossibility was formulated by the ancients, how 17th century mathematicians tried to prove it and how it was finally proved in the 19th century. We shall study the many controvercies concerning the problems and we shall see how the history of the problems was closely linked to the development of diverse mathematical fields such as geometry, algebra and analysis.
As far as possible we will study the original sources as well as the latest historical analyses of the development.
During the course the student will learn to investigate the history of a piece of mathematics, to analyze a mathematical text from the past, and to use the history of mathematics as a background for reflections on philosophical and sociological questions regarding mathematics. Moreover the course will give the students a more mature view on the mathematical subject in question. The course will be particularly relevant for students who aim for a career in the gymnasium (high school) but all mathematics students can benefit from it.

Learning Outcome

Knowledge:
After having completed the course, the student will have a rather deep knowledge of the history of the three classical problems and about the historiographical questions related to this history. Moreover the student will know the mathematics required to show the impossibility of the classical problems.
Skills:
After having completed the course the student will be able to
1. Read a mathematical text on the history of the classical problems or similar mathematical subjects (in translation if necessary).
2. Find primary and secondary literature on the subject of the course.
3. Prove the impossibility of the three classical problems by ruler and compass
4. Solve the classical problems by other means.
Competences:
After having completed the course the student will be able to
1. Communicate orally as well as in written form about the selected topic from the history of mathematics.
2. Analyse a primary historical text (if necessary in translation) within the subject of the course.
3. Analyse, evaluate and discuss a secondary historical text on the subject of the course.
4. Use the historical topic of the course in connection with mathematics teaching and more generally reflect on the development of the selected topic.
5. Place a concrete piece of mathematics from the selected topic in its historical context. 
6. Independently formulate and analyze historical questions within a wide field of the history of mathematics.
7. Use the history of mathematics as a background for reflections about the philosophical and social status of mathematics.
8. Use modern historiographical methods to analyze problems in the history of mathematics.

Primary sources (mostly in English translations) and secondary papers.

Hist1 is usefull but not absolutely necessary. Moreover Analysis 2 and Algebra 2 or similar.
8 hours per weeks divided between lectures by the professor, seminars given by the participating students and discussion sessions for 7 weeks..
  • Category
  • Hours
  • Exam
  • 1
  • Lectures
  • 35
  • Preparation
  • 149
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
The student will start the exam by giving a 10 minutes version of the seminar presentation.
Exam registration requirements
In order to qualify for the exam the student must give a 1½ hour seminar presentation during the course and prepare written materials about the subject of the seminar for the use of the other students.
Aid
Only certain aids allowed

During the 30 minutes preparation time all aids are permitted. During the exam itself the student is allowed to consult a note with at most 20 words. Other aids are not permitted.

Marking scale
7-point grading scale
Censorship form
External censorship
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.