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Essential Mathematics for Artificial Intelligence & Data Science

The mathematical foundations that every data scientist should master

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Enrollment is Closed



High school degree, basics of Python programming.


This course is taught in English.


In most job interviews for a data scientist position, candidates are tested on their mathematical knowledge . This is no coincidence: data science software like scikitlearn, tensorflow or pytorch are very powerful and quite easy to use, but if you don't master the mathematical principles that guide them, you may create unstable artificial intelligence, or biased solutions with terrible social impacts.
In this course, you will learn the essentials of mathematics that you need to be able to become a good data scientist: linear algebra, statistics, calculus and convex optimization. In contrary to a pure mathematics course, all concepts will be explained to you within the framework of machine learning. You will acknowledge throughout this course why and how mathematical concepts are used in data science projects.
Along the way, you will discover various machine learning algorithms, and the course will culminate with a complete mathematical analysis of neural networks.


Upon completion of this SPOC, learners will have acquired:

  • The minimal mathematical level required to become a good data scientist, machine learning or deep learning practitioner.
  • The ability to avoid the pitfalls of statistics, understand the limits of machine learning models and their biases.
  • An overview of many classical machine learning algorithms (linear models, support vector machine, principal component analysis, recommender systems, ...)
  • A full understanding of neural networks and their training processes


1. Descriptive Statistics

Learn how to analyze a dataset and get key information about its structure. Descriptive statistics will make you better at performing the pre-processing tasks of any machine learning project: data quality evaluation, feature engineering and algorithm selection.

2. Inferential Statistics

Learn how to detect correlations between data and how to test them rigorously. Inferential statistics helps you against cognitive biases and makes sure your algorithm will work well in a real-life situation. Your knowledge of statistics will be tested in data science job interviews, so you need to be prepared!

3. Linear Algebra

Learn how to describe and manipulate data with multi-dimensional arrays, also called matrices or tensors. Linear algebra is a fundamental requirement to truly master data science libraries like numpy, pandas, scikitlearn, or tensorflow.

4. Differential Calculus

Learn how to approximate numerically learning equations that are too complex to be solved in a reasonable time. With differential calculus you will be able to write down and understand the equations of many machine learning models.

5. Convex Optimization

Learn the main technique used in machine learning / deep Learning to fit a model on training data. You will develop a deep understanding of how machine learning algorithms work and acquire an intuition about how to tweak the parameters of your model to better fit your data.

6. Neural Networks

With all the mathematics you’ve learned in this course, you are now able to tackle one of the most sophisticated models: neural networks. You will learn why they are so effective in almost every situation, and you will understand everything about their delicate training process.


The main teaching materials include teaching video capsules, numerous video supports and a range of textual resources diversified in their degree of analysis and complexity (research but also popularization) as well as in their approach (philosophical, psychological, business, legal, computational) so that all participants can develop a multidimensional point of view, enabling them to grasp the subject in all its complexity as well as to stimulate debate.
The program is also built around group discussions and interactive presentations that provide learners with thought-provoking circuits that can be tailored as closely as possible to their answers in order to boost their attention and stimulate their reflection.


Learners support

Learners are guided along their learning journey and homework by the teaching team.


This program is made of 6 modules, published at a pace of 1 per week. 7 to 10 hours of work is expected per week. For learners who wish to go further, additional content can be made available.


Course Staff Image #1

Dr. Frédéric Oru

Expert Professor in AI Mathematics at aivancity School for Technology, Business & Society Paris-Cachan
Founder & CEO of AI4Better

Frédéric is an entrepreneur, professor and specialist of artificial intelligence. He is an alumn from École Polytechnique and holds a PhD in mathematics from École Normale Supérieure de Paris-Saclay.
With more than 20 years of experience in a diversity of positions in scientific research, big companies and start-ups, he supervised international data innovation programs such as "Data City", "Digital Industry", and "AI Hub".


Pursue a Verified Certificate to highlight the knowledge and skills you gain

The SPOC catalog is the premium of aivancity's online offer. Investing in a SPOC program ensures receiving the knowledge, learning by doing, and having a direct interaction with your professor. All aivancityX SPOC certificates aim at improving performances and transitioning to a 4.0 AI-oriented industry.


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