Institut Polytechnique de Paris
Ecole Polytechnique ENSTA ENSAE Télécom Paris Télécom SudParis

Master Year 2 Mathematics of Randomness

Master Year 2 Mathematics of Randomness
Year

Master Year 2

Program

Mathematics of Randomness

ECTS Credits

60

Language

English, French

Orientation

Research (mainly), Industry

Location

Palaiseau Campus, Université Paris-Sud (Orsay)

Course duration

12 months, full time

Course start

September

Degree awarded

Master’s degree

WHY ENROLL IN THIS PROGRAM?

Asset n° 1 

Open up exciting career opportunities in a variety of sectors through the wide range of courses

Asset n°2

Become familiar with research, choosing between writing a Master’s thesis and completing an internship

Asset n°3

Specialize in probability and statistics or statistics and machine learning

The Mathematics of Randomness Master’s degree is a top-level training program covering diverse fields relating to probability, statistics and machine learning. Largely devoted to fundamental knowledge and skills, the program also considers constraints due to applied considerations. On graduating, most students embark on an academic or industrial PhD, while others directly begin a career in industry.

Courses are split into two specializations:

  • Probability and statistics with a focus on mathematical research
  • Statistics and machine learning oriented toward research and job opportunities in private companies

During the second semester, students will deliver a Master’s thesis based on the analysis of several research papers, under the supervision of a professor from the Master’s program. This thesis can be replaced by an internship in a firm or a research laboratory.

Objectives

This program enables students to:

  • Understand, master and use different modern mathematical tools for modelling randomness and analyzing and treating data
  • Perform predictions and take decisions

This program equips students to complete a PhD or build a research or industry career in:

  • Various fields of application where randomness is analyzed, processed and summarized to make predictions and decisions
  • Sectors such as insurance, banking, pharmaceutical laboratories, energy, climate, transport, aeronautics, communication and signaling

The first semester includes a set of fundamental courses providing the basics of theoretical probabilities and statistics.

Mandatory seminar

Weekly seminar presenting the current research fields in probability and statistics

20h

2.5 ECTS

English

Elective courses (27.5 ECTS)

Students choose their courses (27.5 ECTS total) from the following list. The study program is to be validated afterwards with the Master's coordinator during a personal interview.

Théorie ergodique 

37h

7.5 ECTS

Français

High dimensional Probability and Statistics

40h

10 ECTS

English

Statistical Learning Theory 

20h

2.5 ECTS

English

Projet Machine Learning pour la prévision 

36h

10 ECTS

Français

Optimization for Data Science

30h

5 ECTS

English

Mouvement brownien et calcul stochastique 

48h

7.5 ECTS

Français

Modèles graphiques pour l'accès à l'information à grande échelle 

20h

2.5 ECTS

Français

Hidden Markov chains and sequential Monte-Carlo methods

20h

2.5 ECTS

English

Méthodes bayésiennes pour l'apprentissage 

20h

2.5 ECTS

Français

Graphes aléatoires 

37h

7.5 ECTS

Français

Generalisation properties of algorithms in ML 

20h

2.5 ECTS

English

Non paramétric estimation 

20h

2.5 ECTS

English

Convex analysis and optimisation theory

20h

5 ECTS

English

Théorèmes limites et applications 

30h

5 ECTS

English

Model Selection

20h

5 ECTS

English

Concentration of measure

20h

5 ECTS

English

Chaîne de Markov : approfondissements 

20h

5 ECTS

Français

Apprentissage statistique et rééchantillonnage 

20h

5 ECTS

Français

Reinforcement learning 

20h

5 ECTS

English

The second semester includes more specialized courses opening on current research topics.
Students choose their courses (16 ECTS total) from the following list.

Sequential learning and optimization

20h

4 ECTS

English

Temps locaux et théorie des excursions 

20h

4 ECTS 

Français

Systèmes de particules en intéraction 

20h

4 ECTS 

Français

Statistiques spatiales pour l'environnement 

20h

4 ECTS 

Français

Processus de branchement et populations structurées 

20h

4 ECTS 

Français

Statistics and optimization

20h

4 ECTS 

Anglais

Modèles solubles en probabilités 

20h 

4 ECTS 

English

Matrices aléatoires 

20h

4 ECTS 

Français

Mathematical Introduction to compressed sensing 

20h

4 ECTS 

English

Inférence sur de grandes graphes 

20h

4 ECTS 

Français

Extremes 

20h

4 ECTS 

English

Fiabilité des systèmes 

20h

4 ECTS 

Français

Calcul de Malliavin 

20h

4 ECTS 

Français

Bayésien non paramétrique 

20h

4 ECTS 

Français

Permutations aléatoires et théorie des représentations des groupes symétriques 

20h

4 ECTS 

Français

Analyse topologique des données 

20h

4 ECTS 

Français

The internship or master thesis must last between 4 and 6 months and is carried out between April 1st and September 1st. It is compulsory and counts for 14 ECTS

Admission requirements

Academic prerequisites

Completion of a first year of Master in mathematics at Institut Polytechnique de Paris or equivalent in France or abroad.

Language prerequisites

  • English
  • French

How to apply

Applications can be submitted exclusively online. You will need to provide the following documents:

  • Transcript
  • Two academic references (added online directly by your referees)
  • CV/resume
  • Statement of purpose

You will receive an answer in your candidate space within 2 months of the closing date for the application session.

Fees and scholarships

  • EU/EEA/Switzerland students: 243€
  • Non-EU/EEA/Switzerland students: 3770€
  • Engineer students enrolled in one of the five member schools of Institut Polytechnique de Paris (Ecole polytechnique, ENSTA Paris, ENSAE Paris, Télécom Paris and Télécom SudParis): 159€
  • Special cases: please refer to the "Cost of studies" section of the FAQs

Find out more about scholarships

Applications and admission dates

Coordinators

Program office

Nicolas Apoteker

General enquiries

master-admission@ip-paris.fr

Description

The Mathematics of Randomness Master’s degree is a top-level training program covering diverse fields relating to probability, statistics and machine learning. Largely devoted to fundamental knowledge and skills, the program also considers constraints due to applied considerations. On graduating, most students embark on an academic or industrial PhD, while others directly begin a career in industry.

Courses are split into two specializations:

  • Probability and statistics with a focus on mathematical research
  • Statistics and machine learning oriented toward research and job opportunities in private companies

During the second semester, students will deliver a Master’s thesis based on the analysis of several research papers, under the supervision of a professor from the Master’s program. This thesis can be replaced by an internship in a firm or a research laboratory.

Objectives

This program enables students to:

  • Understand, master and use different modern mathematical tools for modelling randomness and analyzing and treating data
  • Perform predictions and take decisions

This program equips students to complete a PhD or build a research or industry career in:

  • Various fields of application where randomness is analyzed, processed and summarized to make predictions and decisions
  • Sectors such as insurance, banking, pharmaceutical laboratories, energy, climate, transport, aeronautics, communication and signaling

The first semester includes a set of fundamental courses providing the basics of theoretical probabilities and statistics.

Mandatory seminar

Weekly seminar presenting the current research fields in probability and statistics

20h

2.5 ECTS

English

Elective courses (27.5 ECTS)

Students choose their courses (27.5 ECTS total) from the following list. The study program is to be validated afterwards with the Master's coordinator during a personal interview.

Théorie ergodique 

37h

7.5 ECTS

Français

High dimensional Probability and Statistics

40h

10 ECTS

English

Statistical Learning Theory 

20h

2.5 ECTS

English

Projet Machine Learning pour la prévision 

36h

10 ECTS

Français

Optimization for Data Science

30h

5 ECTS

English

Mouvement brownien et calcul stochastique 

48h

7.5 ECTS

Français

Modèles graphiques pour l'accès à l'information à grande échelle 

20h

2.5 ECTS

Français

Hidden Markov chains and sequential Monte-Carlo methods

20h

2.5 ECTS

English

Méthodes bayésiennes pour l'apprentissage 

20h

2.5 ECTS

Français

Graphes aléatoires 

37h

7.5 ECTS

Français

Generalisation properties of algorithms in ML 

20h

2.5 ECTS

English

Non paramétric estimation 

20h

2.5 ECTS

English

Convex analysis and optimisation theory

20h

5 ECTS

English

Théorèmes limites et applications 

30h

5 ECTS

English

Model Selection

20h

5 ECTS

English

Concentration of measure

20h

5 ECTS

English

Chaîne de Markov : approfondissements 

20h

5 ECTS

Français

Apprentissage statistique et rééchantillonnage 

20h

5 ECTS

Français

Reinforcement learning 

20h

5 ECTS

English

The second semester includes more specialized courses opening on current research topics.
Students choose their courses (16 ECTS total) from the following list.

Sequential learning and optimization

20h

4 ECTS

English

Temps locaux et théorie des excursions 

20h

4 ECTS 

Français

Systèmes de particules en intéraction 

20h

4 ECTS 

Français

Statistiques spatiales pour l'environnement 

20h

4 ECTS 

Français

Processus de branchement et populations structurées 

20h

4 ECTS 

Français

Statistics and optimization

20h

4 ECTS 

Anglais

Modèles solubles en probabilités 

20h 

4 ECTS 

English

Matrices aléatoires 

20h

4 ECTS 

Français

Mathematical Introduction to compressed sensing 

20h

4 ECTS 

English

Inférence sur de grandes graphes 

20h

4 ECTS 

Français

Extremes 

20h

4 ECTS 

English

Fiabilité des systèmes 

20h

4 ECTS 

Français

Calcul de Malliavin 

20h

4 ECTS 

Français

Bayésien non paramétrique 

20h

4 ECTS 

Français

Permutations aléatoires et théorie des représentations des groupes symétriques 

20h

4 ECTS 

Français

Analyse topologique des données 

20h

4 ECTS 

Français

The internship or master thesis must last between 4 and 6 months and is carried out between April 1st and September 1st. It is compulsory and counts for 14 ECTS

Admission requirements

Academic prerequisites

Completion of a first year of Master in mathematics at Institut Polytechnique de Paris or equivalent in France or abroad.

Language prerequisites

  • English
  • French

How to apply

Applications can be submitted exclusively online. You will need to provide the following documents:

  • Transcript
  • Two academic references (added online directly by your referees)
  • CV/resume
  • Statement of purpose

You will receive an answer in your candidate space within 2 months of the closing date for the application session.

Fees and scholarships

  • EU/EEA/Switzerland students: 243€
  • Non-EU/EEA/Switzerland students: 3770€
  • Engineer students enrolled in one of the five member schools of Institut Polytechnique de Paris (Ecole polytechnique, ENSTA Paris, ENSAE Paris, Télécom Paris and Télécom SudParis): 159€
  • Special cases: please refer to the "Cost of studies" section of the FAQs

Find out more about scholarships

Applications and admission dates

Coordinators

Program office

Nicolas Apoteker

General enquiries

master-admission@ip-paris.fr