Information about the German "Vordiplom in Mathematik" at the University of Hamburg

The certificate "Vordiplom" (Pre-Diploma) is awarded after successful completion of 5 semesters (2 1/2 years) of fundamental study in Mathematics.

(A "Diplom in Mathematik" is awarded after successful completion of a further 5 semesters of advanced studies, comparable to a Masters degree).

The Vordiplom certificate features five grades, three in Mathematics, one in a nonmathematical option ("Anwendungsfach") and one grade "Gesamtnote" (average grade) with the following meaning:

"sehr gut" (1)	= very good, excellent		"befriedigend" (3)	= satisfactory
"gut" (2)	= good		"ausreichend" (4)	= passed, acceptable

The grades are obtained from oral examinations (of half an hour each) in

1. Analysis, Linear Algebra and Analytical Geometry I,
2. Analysis, Linear Algebra and Analytical Geometry II-III,
3. Numerical Mathematics or Mathematical Stochastics,
4. "Anwendungsfach" - non-mathematical option, e.g. Physics or Computer Science, others see below .

In detail, the Vordiplom is based on the following courses¹:

ECTS Points	Title per week	Hours	Semester
11 11 8	Analysis I Linear Algebra and Analytical Geometry I Numerical Mathematics, Part 1	6 6 4	1 1 1
11 11 8	Analysis II Linear Algebra and Analytical Geometry II Numerical Mathematics, Part 2	6 6 4	2 2 2
15 12 xx	Analysis III Mathematical Stochastics "Zusatzbereich"	8 6 2	3 3 3
6 10 xx xx	"Proseminar" Selected standard lecture "Anwendungsfach" "Zusatzbereich"	2 6 6 5	4 4 4 4
10 10 xx	Selected standard lecture Selected standard lecture "Anwendungsfach"	6 6 6	5 5 5

¹ECTS points marked xx are not yet decided.

All lectures include homework assignments where a certain number of problems have to be solved each week. If successfully completed, the students obtain a certificate called

"Übungsschein" related to the corresponding course. The Vordiplom requires 6 of these certificates.

In a "Proseminar", an oral presentation has to be given together with a short written report. The subject is taken from one of the preceding courses.

If this is performed successfully, the students obtain a corresponding certificate called "Proseminar-Schein" which is needed for the Vordiplom.

The "Anwendungsfach" is a non-mathematical option which has a total volume of about 12 hours per week. The aim of these courses is to gain an appreciation of how mathematics may be applied to other areas of science, engineering and commerce. Possible areas (see the German name in the Vordiplom certificate) are:

Physics, Computer Science (German: Informatik), Technical Mechanics, Economics (Wirtschaftswissenschaften), Electrical Engineering (Elektrotechnik), Biology, Chemistry, Philosophy, Meteorology, Astronomy.

Within the "Zusatzbereich" (additional area) students may choose subjects from the history of mathematics, philosophy, as well as from topics on the correlation of society and mathematics.

The "Standard lectures" are to be chosen in semesters 4 and 5, and consists of advanced courses in pure mathematics, applied mathematics or mathematical stochastics. popular choices are algebra, number theory, geometry, complex analysis, ordinary differential equations, optimization, mathematical statistics, stochastic processes.

After having changed to Bachelor/Master (probably in 2006), the credits marked above, will be changed too.

January 28, 2005
Prof. Dr. Bodo Werner
Head of the Examination Committee