To fully grasp future lectures, it's crucial to establish a strong foundation in mathematics. This post offers resources to help you build that mathematical foundation, specifically tailored to be both time-efficient and deeply informative.
These resources are where I've learned my concepts so far, and I can vouch for their quality. Remember, this isn’t a promotional post—just a collection of materials that have personally helped me on my learning journey.
Learning is an ongoing process. It's not just about understanding concepts but also appreciating different perspectives on the same topic. This approach might shift your frame of reference and spark a deeper curiosity to learn even more.
If you come across any videos or references that you believe are superior to the ones I've provided, please share them in the comments. I’ll be sure to review them.
Here are the resources
Calculus
Calculus comes in two phases: Differential Calculus and Integral Calculus. If you like to study the concept which explains more briefly about the concepts but its too lengthy and takes more time to read. refer book from MIT CALCULUS by Gilbert Strang. If you're interested in learning through videos, I recommend checking out Khan Academy for their Calculus 1 course. They have a fantastic collection of educational videos that can really help you grasp the concepts.
Besides Khan Academy, you can also check out the "Essence of Calculus" series by 3Blue1Brown. They offer excellent visually driven videos that make complex calculus concepts easier to understand
Probability and Statistics
Probability and statistics are closely related fields. Probability provides the mathematical foundation for analyzing random events and quantifying uncertainty. Statistics, on the other hand, uses probability to make inferences about a population based on a sample. In essence, statistics relies on probability calculations to draw conclusions and make predictions from data.
a. Statistics and Probability by Khan Academy, is a comprehensive course that explains everything from the basics.
b. The "Essence of Probability" series by 3Blue1Brown covers key concepts in probability, making it easier to grasp the fundamental nature of this mathematical field.
Linear Algebra
Matrices - Matrix definition and types (square, diagonal, identity), Matrix addition, subtraction, multiplication, Transpose of a matrix
Here, focus only on learning the basic definitions. There is no need to delve deeper. Future references will explain how to use them and what they mean
Essence of Linear Algebra from 3Blue1Brown - It is a wonderful series explaining the concepts using visuals making it simpler. It explain the concepts of Vectors, Linear Combinations , Span, Basis, Determinants, Inverse of a matrix, row space, null space and null space, Dot product and cross product, change of basis and Eigen Values and Eigen vectors.
Systems of Linear Equations - Solving systems using matrix methods (Gaussian elimination), Application in optimization.
Norms and Distance Metrics - Euclidean norm, Manhattan norm, and other vector norms, Distance between vectors (Euclidean, cosine similarity).
Orthogonality and Orthonormality - Orthogonal vectors and matrices, Gram-Schmidt process for orthonormalization.
For Orthogonal and Orthonormal vectors - Click here and here
Orthogonal Diagonalization
For Gram-Schmidt process - Click here and here and here too
Singular Value Decomposition (SVD) - Understanding SVD and its applications , Dimensionality reduction and noise reduction using SVD
To learn SVD - first Learn matrices Visualization then Spectral Decomposition finally Singular value Decomposition.
Visual-driven explanations are beneficial, but they have their limitations. To fully comprehend complex mathematical definitions and proofs, you need to delve into the mathematics of Linear Algebra. MIT OpenCourseWare playlist is lengthy but explain from scratch to expert level.
Foundational concepts take a significant amount of time to master, but they establish a strong understanding necessary for machine learning. You can learn machine learning by grasping the basic concepts of each foundation. In this blog, we explain important foundational concepts as they arise within the topics. While knowing the basics is sufficient for understanding the material, diving deeply into the foundations will help you comprehend advanced concepts and current research more easily.
In Upcoming Lectures ,we will dive into the Technical Foundations essential to enter to Machine Learning.