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Validation of first year

  /    /  Validation of first year
Language teaching

At least one language course is compulsory for all majors each year. It can be validated by a course from the ENS language department (ECLA), or by a long stay in a non-French speaking country.

Bachelor of Mathematics (third year – L3)

Validation of the third year of the Bachelor’s degree (L3) implies the completion of 4 courses plus additional training that varies according to the chosen field of study.

Common to all fields of study

4 undergraduate courses

A L3 course may be replaced by a fundamental M1 course.

(12 ECTS x 4 = 48 ECTS)

Complements according to the option

Option Mathematics: 1st year thesis and presentation
Option Mathematics/Physics: Specific courses of the mixed curriculum

Option Mathematics/Computer science: Specific courses of the mixed curriculum

Option Matjematics/Biology: thesis and presentation at the interface math-biology.

(2 x 6 ECTS = 12 ECTS)

Total : 60 ECTS

ENS Diploma

(First year)

In addition to the L3 in mathematics, obtaining the first year of the ENS Diploma is subject to conditions that differ according to the course of study chosen.

Option mathematics

A fundamental course of M1 in mathematics

Analyse complexe
Analyse fonctionnelle
Géométrie différentielle

This course should not count for L3.

A reading group

Marches et graphes aléatoires
Outils probabilistes pour l’étude de matrices aléatoires
Problèmes variationnels, optimisation et contrôle

Non-mathematical science courses

To be chosen from the list of non-mathematical courses offered by the mathematics department or from the syllabus of another scientific department (physics, computer science, biology…) in agreement with the tutor.

It is necessary to validate a minimum of 12 ECTS in the first year and 24 ECTS in total over the first two years in non-mathematical scientific courses.

Option mathematics / physics

Students enroll in L3 Mathematics and L3 Physics.
Physics courses, an internship and a presentation complete the two L3s.

Physics courses at the Bachelor level (36 ECTS)

These courses are recommended by FIP and are equivalent to two courses per semester.

Physique statistique des systèmes en équilibre (1er semestre) (9 ECTS)
Introduction à la mécanique quantique (1er semestre) (9 ECTS)
Relativité et électromagnétisme (2ème semestre) (9 ECTS)
Hydrodynamique (2ème semestre) (9 ECTS)
Physique du solide (2ème semestre) (9 ECTS)

Internship and presentation of the math/physics curriculum (24 ECTS)

This course is co-supervised by researchers from both disciplines.

Choice of department at the end of the first year

In the second year, students choose either mathematics or physics and join the department of their choice.

Option mathematics / computer science

Students enroll in the L3 of mathematics.

In order to obtain the first year, students must also obtain the L3 in computer science:

Undergraduate computer science courses

They must be equivalent to 36 ECTS and can be chosen from the following courses.

Semester 1

Algorithmique et programmation (9 ECTS)
Systèmes numériques (9 ECTS)
Langages de programmation et de compilation (9 ECTS)
Langages formels, calculabilité et complexité (9 ECTS)
Structures et algorithmes aléatoires (9 ECTS)

Semester 2

Systèmes et réseaux (obligatoire, 9 ECTS)
Sémantique et application à la vérification de programmes (9 ECTS)
Informatique scientifique par la pratique (9 ECTS)
Initiation à la cryptologie (9 ECTS)
Théorie de l’information et codage (9 ECTS)
Bases de données (9 ECTS)
Lambda calcul et logique informatique (6 ECTS, à l’ENS de Paris Saclay)

Subject to the agreement of the course teacher, it is possible to do an additional project (3 ECTS).

The internship and the presentation/memoir

They each count for 12 ECTS.

It consists of a bibliographic work supervised by a researcher and ending with the writing of a thesis and a defense, followed by a research internship in computer science of at least 6 weeks between mid-June and end of August. The internship takes place in a laboratory (university or industrial), primarily in the provinces. The internship also includes the writing of a report and a defense. The subjects of the thesis and the internship are linked to each other.

Choice of department at the end of the first year

In the second year, students choose either mathematics or computer science and join the department of their choice.

Option mathematics / biology

Students enroll only in L3 Mathematics.

Completion of the first year requires, in addition to the L3 in mathematics, the following courses.