Mastering the Mathematical Foundations of ML

While mathematics is a valuable part of ML, it's not always necessary to grasp it fully from the outset. Start by learning to code, building projects, and gaining practical experience. High school-level math is often sufficient for many ML tasks. Later, as you grow more comfortable with the field, you can gradually delve into the deeper mathematical concepts.

This approach accommodates learners from various backgrounds and allows you to get your hands dirty with real-world applications before diving into the math. However, if you have a strong interest in understanding the mathematics behind machine learning, you can explore additional resources.

Courses

• Mathematics for Machine Learning Specialization (opens in a new tab): By Imperial College London, bridges the gap between basic mathematics and its application in computer science, machine learning, and data science. Tailored for those refreshing their math knowledge for advanced machine learning and data science courses, it offers an intuitive understanding of relevant mathematics, providing a solid foundation for effective application of machine learning algorithms. The program is comprised of three courses: Linear Algebra, Multivariate Calculus and Probability & Statistics.

• Coding the Matrix: Linear Algebra through Computer Science Applications (opens in a new tab) by Philip Klein, provides a unique perspective on linear algebra by integrating it with CS applications. Dive into the world of matrix mathematics, gain a deep understanding of its essential concepts, and discover how these principles play a crucial role in CS. (book) (full course)

• MIT 18.06SC Linear Algebra (opens in a new tab): Professor Gilbert Strang's concise Linear Algebra lectures covering key topics such as linear equation geometry and the four fundamental subspaces. Delve into vectors, matrices, and linear transformations to build a strong foundation in this essential mathematical discipline. It parallels the combination of theory and applications in Professor Strang’s textbook "Introduction to Linear Algebra". (full course)

• Khan Academy’s courses on Linear Algebra (opens in a new tab), Probability & Statistics (opens in a new tab), Multivariable Calculus (opens in a new tab) and Optimization (opens in a new tab) - A highly inclusive resource caters to all eager learners seeking to enhance their understanding of intricate topics such as linear algebra, analytic geometry, and matrices.

• Stanford CS109: Probability for Computer Scientists (opens in a new tab): This class covers combinatorics and probability theory, delving into probability distributions, properties, and tools. It also explores the application of probability in data analysis and ML, making it pertinent to computer science.

• Mathematics for Machine Learning & Data Science Specialization (opens in a new tab) by DeepLearning.AI is the essential foundation for mastering the mathematics behind ML. Equips you with the mathematical tools and intuition needed to excel in the field. If you find the mathematical aspects of machine learning challenging, this course is your key to understanding and applying the math with confidence. This specialization comprises three courses: Linear Algebra, Calculus and Probability & Statistics for Machine Learning and Data Science.

Explainers

• Essence of Calculus (opens in a new tab) by 3Blue1Brown, delve into the foundational principles of calculus and witness the elegance of mathematical insights unfolding through mesmerizing animations.

• Essence of Linear Algebra (opens in a new tab) by 3Blue1Brown, where learning comes to life through captivating animations. Immerse yourself in the fundamental principles of linear algebra and gain a profound understanding of this crucial mathematical concept in a visually engaging and enlightening way.

• Highlights of Calculus (opens in a new tab) by MIT OpenCourseWare, offers short videos explaining calculus fundamentals and their significance. The resources include summary slides, practice problems, and audio narration by Professor Strang. (full course) (opens in a new tab)

• Probability (opens in a new tab) by Serrano.Academy, delve into the realm of probability through engaging animations. Explore key concepts, including Bayes' theorem, Shannon entropy, Naive Bayes, binomial & Poisson distributions and more.

• Softmax Function Explained In Depth with 3D Visuals (opens in a new tab) by Elliot Waite, offers a thorough explanation of the softmax function, provides in-depth insights into its applications, and utilizes 3D visuals to facilitate understanding. Softmax function is commonly used in ML to convert the outputs of the final neural network layer (logits) into probabilities.

Articles

• Sigmoid Function (opens in a new tab) by Deniz Tuzsuz, offer a mathematical definition for the sigmoid function, its derivative, binary classification, and a Python code example to elucidate these concepts.

• Loss Functions Explained (opens in a new tab) by Harsha Bommana, explores loss functions in ML, which measure the error between algorithm output and the target value. Common loss functions include the 0-1 and quadratic functions, crucial in optimization for minimizing error.

Books

• Mathematics for Machine Learning (opens in a new tab) by Marc Peter Deisenroth might assist you in beginning your mathematical adventure. The math underlying the algorithms and their practical applications has been made obvious. All mathematical ideas have been fully explained.

• Practical Statistics for Data Science (opens in a new tab) by Peter Bruce & Andrew Bruce offers practical insights into statistical concepts and their real-world applications.

• Calculus (opens in a new tab) by Michael Spivak is a renowned work that provides an in-depth exploration of this fundamental branch of mathematics. Delve into the intricacies of calculus, from its foundational principles to advanced concepts.

• Introduction to Linear Algebra (opens in a new tab) by Gilbert Strang is a seminal text that introduces readers to the fundamental concepts of linear algebra. Immerse yourself in the world of vectors, matrices, and linear transformations, gaining a solid grasp of this essential mathematical discipline.

• Linear Algebra Done Right (opens in a new tab) by Sheldon Axler, covers vector spaces, linear maps, determinants, eigenvalues, Euclidean spaces, inner product spaces, and quadratic forms. It aims to teach linear algebra rigorously, focusing on proofs and theory rather than computation.

• Probabilistic Machine Learning (opens in a new tab): The book series by Kevin Murphy, provide a comprehensive treatment of the field of machine learning, built on a foundation of probability theory. The series covers a wide range of topics in probabilistic machine learning and is considered a landmark achievement in the field.

• Mathematical Notation: A Guide for Engineers and Scientists (opens in a new tab) is a concise reference book designed to help engineers & scientists understand common mathematical symbols. Organized by topic, it provides explanations for each symbol, along with guidance on producing them in LaTeX. The book serves as a valuable resource for quickly grasping mathematical notation used in research papers, offering clarity without delving into the underlying mathematics.