History of Mathematics 2 (Hist2)
Practical information  

Study year  2016/2017 
Time 
Block 2 
Programme level  Full Degree Master 
ECTS  7,5 ECTS 
Course responsible  
Phone +45 35 32 07 41, office 04.2.01  

Course content
History of geometry 17701920.
During the indicated period geometry underwent a development that had wide ranging influence on our understanding of
1. what mathematics is and
2. the nature of space.
It is often mentioned as one of the few examples of a revolution
in mathematics.' Arround 1830 the discussion of the parallel
postulate led to the creation of nonEuclidean geometry. Whether
this geometry was consistent remained an open question until
Gauss' and Riemann's works on differential geometry made it
possible to create a model of the nonEuclidean plane as a surface
of constant negative Gauss curvature. This model was also
interpreted in projective geometry that was also devellopped in the
19th century. The century ended with different new attempts to give
axiomatic descriptions of geometry, among which Hilbert's is
the most famous. The considerations concerning nonEuclidean
geometry was not only an exercise in axiomatics. For all the actors
it was also a question of understanding the nature of (physical)
space. The discovery of nonEuclidean geometry led to a rejection
of Kant's opinion that geometry (for Kant this meant Euclidean
geometry) was an a priori but synthetic intuition. Instead various
empirical, conventional or formalistic epistemologies were put
forward. The mathematical and philosophical considerations of the
19th century created a background for the revolutionary ideas that
Einstein put forward in his special and in particular general
theory of relativity. In the course all these interacting subjects
will be discussed.
Students are required to take an active part and give seminars.
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 geometry in the period 1770 to
1920 and about the historiographical questions related to this
history
Skills:
After having completed the course the student will be able to
1. Read a mathematical text on foundational issues concerning
geometry from the period 1770 to 1920 (in translation if
necessary).
2. Find primary and secondary literature on the subject of the
course.
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 (history of geometry).
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.
Recommended prerequisites
Hist1 is usefull but not absolutely necessary. Moreover Geometry 1 or similar.Sign up
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Education
MSc Programme in Mathematics
Studyboard
Study Board of Mathematics and Computer ScienceCourse type
Single subject courses (day)Duration
1 blockSchedulegroup
Teaching and learning methods
8 hours per weeks divided between lectures by the professor, seminars given by the participating students and discussion sessions.Capacity
No limitLanguage
EnglishLiterature
Primary sources (mostly in English translations) and secondary papers.
Workload
Category  Hours 
Lectures  35 
Theory exercises  21 
Preparation  149 
Exam  1 
English  206 
Exam
Type of assessment
Aid
Only certain aids allowedDuring 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
7point grading scaleCriteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Censorship form
External censorshipReexam
Same as ordinary exam. If the student has not presented the required seminar, he or she must hand in a 20 page written presentation of one of the seminar questions no later than two weeks before the beginning of the reexam week.
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