History of Mathematics 2 (Hist2)
Course content
History of Analysis
The course will deal with the foundations of analysis starting with Newton's fluxions and Leibniz' differentials over Euler's formal calculations with zeroes and his bold manipulations with infinite series and Lagrange's definition of the derivative using Taylorseries to Cauchy's and Weierstrass' epsilon delta analysis. In order to understand this development we will also discuss more technical subjects such as Fourier's theory of Fourierseries and Riemann's theory of integration. At the end of the course we may have time to discuss a special theme such as complex function theory or differential equations. As far as possible we will study the original sources as well as the latest historical analyses of the development. In particular we will take up hotly debated questions such as: What did infinitesimals mean to e.g. Leibniz and Cauchy and can nonstandard analysis help us discuss this question? Did Cauchy plagiarize Bolzano? Can Lakatos' philosophy of mathematics be used to understand the development of concepts such as uniform convergence?
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.
MSc Programme in Mathematics
Knowledge:
After having completed the course, the student will have a rather
deep knowledge of the history of mathematical analysis from 1660 to
1900 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 elementary analysis from the period
1660 to 1900 (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 analysis).
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.
8 hours per weeks divided between lectures by the professor, seminars given by the participating students and discussion sessions.
Primary sources (mostly in English translations) and secondary papers.
Hist1 is usefull but not absolutely necessary. Moreover Analysis 2 or similar.
 ECTS
 7,5 ECTS
 Type of assessment

Oral examination, 30 minutes30 minutes oral exam with 30 minutes preparation time. The student will start the exam by giving a 10 minutes version of the seminar presentation.
 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
 7point grading scale
 Censorship form
 External censorship
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
 Category
 Hours
 Lectures
 28
 Theory exercises
 28
 Preparation
 149
 Exam
 1
 English
 206
Kursusinformation
 Language
 English
 Course number
 NMAK15016U
 ECTS
 7,5 ECTS
 Programme level
 Full Degree Master
 Duration

1 block
 Schedulegroup

C
 Capacity
 No limit
 Studyboard
 Study Board of Mathematics and Computer Science
 Department of Mathematical Sciences
Course Coordinator
 Jesper Lützen (6717a797f6a73457266796d33707a336970)
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