NMAK14032U History of Mathematics 2 (Hist2): The Classical Problems
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.
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.
- Category
- Hours
- Exam
- 1
- Lectures
- 35
- Preparation
- 149
- Theory exercises
- 21
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutesThe 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.
Course information
- Language
- English
- Course code
- NMAK14032U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- C (Mon 13-17 + Wednes 8-17)
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Jesper Lützen (6-737c7b816c754774687b6f35727c356b72)