Skip to content

Maths for Machine Learning — Map of Content#

Source: Maths for Machine Learning — CampusX (23 videos)

ML ki har algorithm asal mein maths hai. Ye playlist wo saara maths cover karti hai jo ML aur Deep Learning ke liye chahiye — Linear Algebra, Calculus, aur Probability & Statistics.

Notes Index#

🟦 Linear Algebra#

Note Topics
[[01 Vectors]] Vector kya hai, row/column, magnitude, unit vector, addition, scalar multiplication, dot product, angle, projection, cross product, norms (L1/L2/L∞)
[[02 Lines Planes and Hyperplanes]] 2D line, 3D plane, n-D hyperplane, general equation, distance from point, ML mein decision boundary
[[03 Matrices]] Matrix types, operations, multiplication, transpose, trace, special matrices, NumPy implementation
[[04 Determinant Inverse Rank]] Determinant ka matlab, inverse, rank, singular matrix, system of linear equations solve karna
[[05 Linear Transformations]] Matrix as transformation, rotation/scaling/shear, composition, basis change, geometric intuition
[[06 Eigenvalues Eigenvectors PCA SVD]] Eigen equation, eigendecomposition, PCA step-by-step, SVD, dimensionality reduction

🟩 Calculus#

Note Topics
[[07 Functions and Derivatives]] Function, limit, continuity, derivative ka matlab, rules, common derivatives, higher order
[[08 Multivariable Calculus and Gradient]] Partial derivative, gradient vector, chain rule, Jacobian, Hessian, directional derivative
[[09 Optimization and Gradient Descent]] Maxima/minima, convexity, gradient descent, learning rate, variants, backpropagation ka maths

🟨 Probability & Statistics#

Note Topics
[[10 Descriptive Statistics]] Mean/median/mode, variance, std, quartiles, skewness, kurtosis, covariance, correlation
[[11 Probability Basics]] Sample space, conditional probability, independence, Bayes theorem, Naive Bayes
[[12 Random Variables and Distributions]] Discrete/continuous RV, PMF/PDF/CDF, Bernoulli, Binomial, Poisson, Normal, expectation, variance
[[13 Inferential Statistics]] Sampling, CLT, confidence interval, hypothesis testing, p-value, t-test, chi-square, ANOVA

ML mein Maths kahan use hota hai?#

Maths Topic Kahan use hota hai
Vectors, Dot Product Feature vectors, similarity (cosine), embeddings
Hyperplanes SVM, Logistic Regression ki decision boundary
Matrix Multiplication Neural network ka har layer
Determinant, Inverse Linear Regression ka closed-form solution
Eigenvalues/Eigenvectors PCA, spectral clustering, PageRank
SVD Recommendation systems, LSA, image compression
Derivatives Loss function ko minimize karna
Partial derivatives, Gradient Backpropagation
Chain rule Deep learning ki poori training
Convexity Kya optimization guaranteed converge karega
Probability Naive Bayes, generative models
Bayes theorem Bayesian ML, spam filters
Distributions Assumptions, noise modelling, GMM
Expectation/Variance Bias-Variance tradeoff
Covariance matrix PCA, Mahalanobis distance, LDA
Hypothesis testing Feature selection, A/B testing

Study order (recommendation)#

Vectors → Hyperplanes → Matrices → Determinant/Inverse
    ↓
Linear Transformations → Eigenvalues → PCA/SVD
    ↓
Derivatives → Partial Derivatives/Gradient → Gradient Descent
    ↓
Descriptive Stats → Probability → Distributions → Inference

Time estimate: har note ko theek se padhne aur code chalane mein 1–2 ghante. Poori series ~25–30 ghante.

Setup (har note ka code chalane ke liye)#

import numpy as np
import matplotlib.pyplot as plt
import scipy.stats as stats
import sympy as sp
from scipy import linalg

np.set_printoptions(precision=3, suppress=True)
plt.rcParams['figure.figsize'] = (8, 6)

Extra resources#

  • 3Blue1Brown — Essence of Linear Algebra (visual intuition ke liye best)
  • 3Blue1Brown — Essence of Calculus
  • Mathematics for Machine Learning book — mml-book.github.io (free PDF)
  • StatQuest (statistics ke liye)
  • Khan Academy — Linear Algebra, Multivariable Calculus, Statistics