NMAK15016U History of Mathematics 2 (Hist2)

Volume 2017/2018

MSc Programme in Mathematics


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 Taylor-series 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 Fourier-series and Riemann's theory of integration. At the end ogf 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 non-standard 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.

Learning Outcome

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
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.
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.

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

Hist1 is usefull but not absolutely necessary. Moreover Analysis 2 or similar.
8 hours per weeks divided between lectures by the professor, seminars given by the participating students and discussion sessions.
  • Category
  • Hours
  • Exam
  • 1
  • Lectures
  • 28
  • Preparation
  • 149
  • Theory exercises
  • 28
  • Total
  • 206
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minutes oral exam with 30 minutes preparation time. 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.

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

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 re-exam week.

Criteria for exam assesment

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