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
Fees for 2023-2024 are :
- EU/EEA/Switzerland students: 243€
- Non-EU/EEA/Switzerland students: 4130€
- 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
General enquiries
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
Fees for 2023-2024 are :
- EU/EEA/Switzerland students: 243€
- Non-EU/EEA/Switzerland students: 4130€
- 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