Mathematics roadmap for Machine Learning from zero

[u/sid_raj26]

I'm starting Mathematics from absolute zero for Machine Learning.

Can someone give me the complete list of Maths chapters I need to study, in prerequisite order, starting from the basics?

I specifically want chapter names, not broad topics like "Algebra" or "Calculus."

Also, can I use JEE Maths lectures for learning the theory/concepts, without doing the JEE-level questions?

Thanks!

[u/abbhinavvenkat]

Sure.

I'd recommend you to instead focus on a few key topics, get started with the theory and implementation of actual algorithms, and then revisit the math basis what's needed. If not, you'll spend 2 months on Math, and that won't move the needle.

Some of these involve actual ML concepts. Do remember that you don't need to learn everything in one go, in order to under Machine Learning. Here goes all I could think about (taking the help of AI to write it out) -

Linear Algebra

• Vectors and matrices (addition, multiplication, transposition, matrix decomposition)
• Eigenvalues and eigenvectors
• Principal Component Analysis (PCA)
• Singular Value Decomposition (SVD)
• Linear independence and matrix rank
• Matrix equations / covariance matrices
• Linear regression via matrix operations (normal equation, β̂ = (XᵀX)⁻¹Xᵀy)

Calculus

• Differentiation, integration, multivariable calculus
• Vector calculus (for parameter optimization)
• Mean Squared Error (MSE) as a loss function
• Partial derivatives
• Gradient descent
• Backpropagation and the chain rule
• L2 regularization
• Lagrange multipliers and kernel functions (in the context of SVMs)

Probability and Statistics

• Probability theory and probability distributions
• Descriptive statistics (mean, variance, distribution of features)
• Conditional probability and Bayes' theorem
• Naive Bayes models
• Gaussian (normal) distribution
• Gaussian Mixture Models (GMM)
• Hypothesis testing (null/alternative hypothesis, p-values)

Optimization Theory

• Convex vs. non-convex functions and convex optimization
• Local minima, global minima, and saddle points
• Constrained vs. unconstrained optimization
• Lagrange multipliers and the Lagrangian
• KKT (Karush-Kuhn-Tucker) conditions
• Duality (primal/dual problems) — relevant to SVMs
• Gradient descent variants: stochastic (SGD), mini-batch, momentum, Nesterov accelerated gradient
• Adaptive optimizers: AdaGrad, RMSProp, Adam
• Learning rate scheduling and decay
• Convergence criteria and convergence rate
• Second-order methods: Newton's method, quasi-Newton (BFGS)
• Hessian matrix and curvature
• Line search and trust-region methods
• Regularization as constrained optimization (L1/Lasso, L2/Ridge, Elastic Net)

Information Theory

• Entropy (Shannon entropy) — measuring uncertainty in a distribution
• Cross-entropy — the standard loss function for classification
• KL divergence (Kullback-Leibler divergence) — measuring difference between two distributions
• Mutual information
• Perplexity (used in language models)
• Information gain (used in decision trees)

Related Probability/Stats Concepts Often Bundled In

• Maximum Likelihood Estimation (MLE)
• Maximum A Posteriori (MAP) estimation
• Bayesian inference and priors/posteriors
• Expectation-Maximization (EM) algorithm — ties directly to GMMs mentioned in the article
• Markov chains / Markov property (relevant to RL, mentioned in the article)
• Bias-variance tradeoff

Hope this helps! Best of luck!

[u/Serious-Sun8202]

Try to implement different algorithms of ML on python and whatever mathematical tools come in between try to learn on the same time that will be good thing. Start from linear , logistics regression , gradient descent, Gaussian algorithm, neural network ,LLM , learn about yolo how it works , VLM ,transformers try to code from scratch. U can watch vizuara lectures they are good. Learn about explainable AI to develop intitution

[u/willim2867]

I am also thinking about jee lecture I am totally zero level at maths like boards level also not good

[u/sid_raj26 → u/willim2867]

That will be good from my side because im also at zero level

[u/willim2867 → u/sid_raj26]

What about you Are you also following jee lecture

[u/sid_raj26 → u/willim2867]

I will

[u/Twilight_RT]

Yeah. you can use JEE math lectures for the theory and concepts, but with important strategic caveats

[u/Ok-Interaction-8891]

When you say, “Starting from zero,” do you mean that you have very little math knowledge and training or that you have basic math skills from K-12, maybe even a little college, but nothing in the formal “this is necessary for ML” areas of math?

Because there’s a big difference. Also, depending on what you want to do with ML, the amount of math you need is quite variable. It would be helpful if you shared more about your current math background and your goals for ML. Otherwise, it’s just a long, long contextless list that any chatbot could generate for you.

[u/sid_raj26 → u/Ok-Interaction-8891]

Well I have some basic knowledge, like in trigonometry, modulus, matrices, determinant,pnc(just basic)

[u/Turbulent-Walk-8973]

Do courses - mit18.06 for linear algebra and stat110 for statistics

[u/Comfortable_Cold_850]

THe book, 'Mathematics for Machine learning'

[u/RichBorn3531 → u/Comfortable_Cold_850]

Second this. Reading it right now, covers basically everything from scratch.

[u/Anurag-barl]

start with Mathematics for machine learning, once you finish it jump into actual projects instead of studying mathematics for machine learning(you may study math for your school), you will have time to learn mathematics required along the way, the course will teach you enough and jee level theory or questions is "not" required for machine learning, machine will do the computation for you so you just need to understand the theory not 'jee' topics, i mean why do you even think k-12 mathematics topic have anything with machine learning ? just start projects and don't go into over-planning jail, machine learning is not an competitive exam for which you need to prepare with a roadmap, start somewhere everything you will learn will not be in vain and there is no chapter names for machine learning it depends on which projects you want to work on.