ALGANT Courses Information

You can choose Bordeaux only for the second year of the ALGANT programme. The programme at Bordeaux is called M2 ALGANT. The current programme can be found here. Next year’s programme here.

Both first and second year students have to choose six courses chosen among the 600-level courses offered at Concordia, or equivalent courses offered at other ISM universities, such as, but not limited to:

• Algebraic Number Theory
• Algebraic Geometry
• Elliptic Curves
• Modular Forms
• Analytic Number Theory
• Topics in Algebra
• Reading course in Algebra

Second year students have to write a research thesis of 27 credits.

More information on the courses offered can be found here.

To graduate from the master’s programme in Mathematics at the University of Duisburg-Essen one should obtain 120 credit subject to the following rules:

• Erweiterungsbereich: at most 45 ECTS
• Vertiefungsbereich: at least 18 ECTS
• Seminarbereich: from 18 to 45 ECTS
• at least 18 ECTS in an area different from Algebra.
• Master Thesis: 30 ECTS

Example of lecture courses:

Erweiterungsbereich:

• Algebraic Geometry 1
• Algebraic Topology
• Analytic Number Theory 1
• Algebraic Number Theory 2
• Complex Geometry 1
• Modular Forms 1
• Riemann Surfaces 1
• Differential Geometry 1

Vertiefungsbereich:

• Algebraic Geometry 2
• Complex Geometry 2
• Riemann Surfaces 2
• Advanced Topics in Algebraic Geometry
• Advanced Topics in Algebraic Number Theory
• Advanced Topics in Complex Geometry

Seminarbereich:

• Seminar in Algebraic Geometry
• Seminar in Algebraic Number Theory

Lectures and Seminars typically carry 9 Credits each. The current offer can be found here.

For each student a programme will be tailored individually.

First year students need to take 60 ECTS advanced courses from the course lists below. At most 2 courses can be from the complementary ALGANT course list. In case of any missing prerequisites, the board of examiners may approve other courses as well.

Second year students need to have at least 120 ECTS:

• a research project in Mathematics of 34 EC (incl. a thesis and an oral presentation) in the Algebra, Geometry, Number Theory research group of the Leiden Mathematical Institute;
• A choice of 26 ECTS of the course lists below. At most 2 courses can be from the complementary ALGANT course list.

ALGANT Core courses:

• Advanced Algebraic Geometry (8)
• Algebraic Curves (6)
• Algebraic Geometry 1 (8)
• Algebraic Geometry 2 (8)
• Algebraic Number Theory (8)
• Algebraic Topology 1 (8)
• Algebraic Topolgy 2 (8)
• Analytic Number Theory (8)
• Commutative Algebra (8)
• Differentiable Manifolds (6)
• Differential Geometry (8)
• Elliptic Curves (8)
• Lie Algebras (8)
• Modern Cryptography (8)
• Representation Theory (6)
• Riemann Surfaces (8)
• Selected Areas in Cryptology (8)
• Symplectic Geometry (8)
• Topics in Algebraic Number Theory (6)
• Topics in Algebraic Topology (6)

Complementary ALGANT courses:

• Automatic sequences (8)
• Category Theory (8)
• Lie Groups (8)
• Homotopy Type Theory (8)
• Noncommutative Geometry (8)
• Operator algebras (8)
• Quantum Information Theory (8)
• Topos Theory (8)

A language course of 3 ECTS may be taken each year, after approval by the Board of Examiners.

More information can be found here and here.

First year students need to take 60 ECTS in courses. Second year students need to take 30 ECTS in courses and a Master’s thesis for 30 ECTS. One of the courses should be in applied mathematics, Numerical Linear Algebra is recommended. Among the courses should be a seminar activity of 3 ECTS

A complete list of offered courses can be found here.

Students are free to take any course from the ALGANT curriculum, subject to the following constraints:

Students spending either the first or second year in Padova should pass exams in Mathematical Analysis for at least 12 ECTS and in Mathematical Physics and/or Probability and/or Statistics for at least 6 ECTS. Students have to take a language course or partecipate in a seminar. These requirements may be fulfilled at the partner university, upon approval of the local coordinator in Padova

First year students should take the courses Algebraic Geometry 1 and Number Theory 1, unless they have followed similar courses during the bachelor. Moreover, they should take at least one of Introduction to Group Theory or Rings and Categories of Modules. Second year students should write a Master thesis for 36 ECTS.

One you can find a list of ALGANT courses here.

You can choose Paris Saclay only for the second year.

For the first semester, at least two fundamental courses (30 ECTS) chosen among the courses offered at the University Paris-Saclay for the master programme M2 Analysis, Arithmetic and Geometry. For the second semester, a research thesis of 21 ECTS with one complementary course (3 ECTS) chosen among the courses offered at the University Paris-Saclay for the master programme M2 Analysis, Arithmetic and Geometry. In addition one specialised course (6 ECTS) chosen among the courses offered at the University Paris-Saclay for the master programme Analysis, Arithmetic and Geometry and which changes every couple of years.

For a list of courses for the current courses see here.

These are the requirements that must be fulfilled in order to graduate from the master’s programme in Mathematics at the University of Regensburg (in total, at the end of the study program).

• Two of the three following elective modules (18 ECTS each) are required (only lectures, no seminars):
  • MArGeo: Arithmetic Geometry (Algebraic Number Theory, Algebraic Geometry….)
  • MGAGeo: Global Analysis and Geometry (Differential Geometry, Algebraic Topology,…)
  • MAngAn: Applied Analysis (Functional Analysis, Partial Differential Equations, Numerics,…)
• MV: Master Specialisation (18 ECTS), lectures and/or seminars
• MSem: Seminar Module (9 ECTS) two seminars
• Master thesis (30 ECTS)
• Minor subject (>=12 ECTS), for ALGANT students usually mathematics (lectures and/or seminars)
• General interest module (>=8 ECTS)
• In the minor subject and the general interest module together at least 27 ECTS are required. The `general interest’ module covers the whole course programme of the university (for example language courses, presentation and rhetoric events, computer courses). Lectures (4h) usually have 9 ECTS, seminars 4,5 ECTS

Information on the current offer of courses can be found at https://hellus.app.uni-regensburg.de/KVV/