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Browse the figure galleryA visual introduction
An Introduction to Data Sciences
How do we compress a message, restore an image, compare distributions, or learn from examples? A short, illustrated journey through the mathematics behind these questions.
English: 39 pages · 13.3 MB French: 39 pages · 13.4 MBRevised September 9, 2026
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01Claude Shannon and data compression
Binary codes, entropy, Huffman coding, and the limits of lossless compression.
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02Image processing
Pixels, quantization, filtering, edges, colors, and elementary image transformations.
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03Sparsity, inverse problems and compressed sensing
Sparse representations, regularization, and recovery from incomplete measurements.
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04Optimal transport
Assignments, transport plans, Wasserstein distances, and applications to distributions.
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05Neural networks
Classification, backpropagation, generative models, and connections with transport.
Figures and further reading
Mathematical Foundations of Data Sciences
A more extensive treatment of Fourier analysis, wavelets, approximation, inverse problems, and optimization, developing the ideas introduced here.
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