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Mathematics for Data Science

Mathematics for Data Science

Matrices and vectors
Addition and scalar Multiplication
Mean, Standard Deviation, Median
Matrix vector multiplication
Matrix Multiplication and Properties
Inverse and Transpose
Coordinate systems
Mathematical Representation of a line (2D), plane(3D) and hyperplane (n*D)
Hyper planes and Hyper spaces
Geometric Representation of a circle (2D), sphere (3D) and hypersphere (n*D)
Equation of an ellipse (2D), ellipsoid (3D) and hyper ellipsoid (n*D)
Vector Spaces
Determinants
Eigen Vectors
Correlation, Coefficient intuition
Length and Dot Products
Linear Equations


Introduction to probability
Frequentist Interpretation
Bayesian Interpretation & Bayes Rules and Bayes Theorem
Analyze Dataset for Distributions
Refining the Qualitative and Quantitative Data.
Variation in Datasets (Univariate, Bivariate and Multivariate Data)
Population & Sample.
Gaussian/Normal Distribution and its PDF (Probability Density Function).
CDF (Cumulative Density Function) of Gaussian/Normal Distribution
Symmetric distribution, Skewness, and Kurtosis
Standard normal variate (z) and standardization.
Kernel density estimation.
Hypothesis Testing
Law of large Number?
Joint and Disjoint Outcomes
Probability Distribution
Sample Space and Complements
Probability Casting
Permutation and combination
Markov Decision Process
Discrete Sample Space (Finite and Infinite)
Events, Independence
Joint Probability and Conditional Probability
General Multiplication Rule
Inverting Probabilities
Z Score
Laws of Total Probability
Correlation and causation
Chebyshev’s inequality
Discrete and Continuous Uniform distributions.
Bernoulli and Binomial distribution