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Master the Math for Data Science
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Linear algebra
Prob and stats
Machine learning
1. Vectors
Introduction
Position vectors
Planes
Dot product
2. Matrices
Introduction
Transpose of matrices
Trace of matrices
Invertible matrices
Elementary matrices
3. Linear equations
System of linear equations
Gaussian Elimination
Pivot positions and columns
Linear dependence and independence
Linear transformation
4. Matrix determinant
Introduction
Determinant of elementary matrices
Invertibility, multiplicative and transpose properties of determinants
Laplace expansion theorem
Cramer's rule and finding inverse matrix using determinants
Geometric interpretation
5. Vector space
Subspace
Relationship between pivots and linear dependence
Spanning Set of a vector space
Basis vectors
Constructing a basis for a vector space
Null space
Column space
Rank and nullity
6. Special matrices
Symmetric matrices
Triangular matrices
Diagonal matrices
Block matrices
LU factorization
7. Eigenvalues and Eigenvectors
Introduction
Basic properties
Eigenspace and eigenbasis
Similar matrices
Diagonalization
Algebraic and geometric multiplicity
8. Orthogonality
Orthogonal projections
Orthonormal sets and bases
Orthogonal complement
Orthogonal matrices
Least squares
Gram-Schmidt process
9. Matrix decomposition
QR decomposition
Orthogonal diagonalization
Positive definite matrices
Schur's triangulation theorem
Cholesky decomposition
Singular value decomposition
Data compression using singular value decomposition
1. Basics of statistics
Population, samples and sampling techniques
Measures of central tendency
Measures of spread
Quantiles, quartiles and percentiles
Histogram
Box-plot diagrams
2. Basics of probability theory
Basics of set theory and Venn diagrams
Counting with permutations
Counting with combinations
Sample space, events and probability axioms
Conditional probability
Multiplication and addition rule
Law of total probability
Bayes' theorem
3. Random variables
Random variables
Expected value
Properties of expected value
Variance
Properties of variance
Covariance
Correlation
4. Point estimation
Sample estimators
Sample mean
Sample variance
Sample covariance
Sample correlation
Unbiased estimator
Mean squared error
Sampling distribution of the sample mean
5. Discrete probability distributions
Probability mass function
Binomial distribution
Geometric distribution
Negative binomial distribution
Hypergeometric distribution
Poisson distribution
1. ML models
Simple linear regression
Logistic regression
k-means clustering
Hierarchical clustering
DBSCAN
Naive bayes
Decision trees
k-nearest neighbors
Perceptrons
2. Feature engineering
Feature scaling
Log transformation
Text vectorization
Grid search
Random search
Principal component analysis
3. Optimization
Gradient descent
4. Model evaluation
Confusion matrix
ROC curve
Cross validation
Mean squared error
Mean absolute error
Root mean squared error
r-squared
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We achieve the best of worlds by deep-diving into the technical details while developing your intuition with:
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Theorem.
Product of block matrices (3)
Suppose we have two block matrices where each matrix is composed of four sub-matrices. The product of the two block matrices is:
Note that the shape of the matrices must match for the matrix product to be valid. For instance, the number of columns of
We're not just another math course
Most DS courses either gloss over the details or throw around complex math equations without explanation. We achieve the best of both worlds by deep-diving into the technical details while developing your intuition with:
format_list_numbered
Step-by-step proofs
local_library
Insightful diagrams
layers
Simple examples
Elevate your learning experience
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Meet the team
Obtained a bachelors at UTokyo, a masters of DS at HKU, and now working as a MLE. I'm mainly in charge of the tech-side of SkyTowner, and I love writing articles about data science!
Graduated from UTokyo, and now working in the finance industry. I consider myself a citizen developer and write about topics as they come!
Eva
Graduated from HKUST, and now brushing up my programming skills. I enjoy documenting my learning process on SkyTowner!
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