Description

This repository contains fundamental concepts of different branches of mathematics and stochastics, which are cornerstones for a successful career in machine learning and data science. More specifically, this repository contains concepts from different areas of functional analysis, linear algebra, stochastics etc.

Note: The chapters are divided based on my understanding and in a sequence which I found easier to comprehend one-by-one. The repository as a whole is still work in progress and many of the files are, as of now, placeholders, only to be updated later. This gives an idea which area I will be updating the next. I am taking some time out from my daily schedule and contributing to this repository. Since, I cannot afford to spend a lot of time on a regular basis, the completion may take some time. Meanwhile, I ask whoever is visiting this repository to have a little patience. And I do appreciate anyone willing to collaborate.

Content

Currently I am working on the functional analysis part of this repository.
.doc files are stored in the docs folder and .pdf files are stored in the pdfs folder. Currently the repository contains concepts from following areas:

1. 01_Vector Space: Concepts of a vector space, basis, span and linear independence.

Further topics:

• Inner Products and Norms
• Metrics
• Linear Mappings
• Affine Spaces
• Sequences, Limits, Open and Closed Sets
• Cauchy Sequences and Complete Spaces
• Cauchy-Schwartz Inequality
• Banach Spaces
• Hilbert Spaces
• Orthogonality
• Continuity
• Operator Norm

References

1. Lecture notes from the Calculus section of the course Ramp Up Mathematics taken by Dr. Konstantin Merz (Summer Semester 2024, Technische Universität Braunschweig), lecture notes prepared by Prof. Dr. Dirk Lorenz
2. Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong. Published by Cambridge University Press (2020).

Books

1. Mathematics for Machine Learning by Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong (Note: This version is free to view and download for personal use only. Not for re-distribution, re-sale, or use in derivative works. ©by M. P. Deisenroth, A. A. Faisal, and C. S. Ong, 2024. https://mml-book.com.)