- Modeling a process (physical or informational) by probing the underlying dynamics
- Constructing hypotheses
- Rigorously estimating the quality of the data source
- Quantifying the uncertainty around the data and predictions
- Identifying the hidden pattern from the stream of information
- Understanding the limitation of a model
- Understanding mathematical proof and the abstract logic behind it

- Logarithm, exponential, polynomial functions, rational numbers
- Basic geometry and theorems, trigonometric identities
- [[Real numbers]] and complex numbers (basic properties)
- Series, [summation], inequalities
- Graphing and plotting, [[Cartesian coordinates]] / polar coordinates, conic sections

- Data summaries and descriptive statistics, central tendency, variance, covariance, correlation
- Basic probability: basic idea, expectation, probability calculus, Bayes' theorem, conditional probability
- Probability distribution functions: uniform, normal, binomial, chi-square, Student's t-distribution, central limit theorem
- Sampling, measurement, error, random number generation
- Hypothesis testing, A/B testing, confidence intervals, p-values
- ANOVA, t-test
- Linear regression, regularization
- dimensionality reduction, principle component analysis
^{1}

- Basic properties of matrix and vectors: scalar multiplication, linear transformation, transpose, conjugate, rank, determinant
- Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse
- Special matrices: square matrix, identity matrix, triangular matrix, idea about sparse and dense matrix, unit vectors, symmetric matrix, Hermitian, skew-Hermitian and unitary matrices
- Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation
- Vector space, basis, span, orthogonality, orthonormality, linear least square
- Eigenvalues, eigenvectors, diagonalization, singular value decomposition

- Functions of a single variable, limit, continuity, differentiability
- Mean value theorems, indeterminate forms, L’Hospital’s rule
- Maxima and minima
- Product and chain rule
- Taylor’s series, infinite series summation/integration concepts
- Fundamental and mean value-theorems of integral calculus, evaluation of definite and improper integrals
- Beta and gamma functions
- Functions of multiple variables, limit, continuity, partial derivatives
- Basics of ordinary and partial differential equations

- [[Sets Basics]], subsets, power sets
- Counting functions, combinatorics, countability
- Basic proof techniques: induction, proof by contradiction
- Basics of inductive, deductive, and propositional logic
- Basic data structures: stacks, queues, graphs, arrays, hash tables, trees
- Graph properties: connected components, degree, maximum flow/minimum cut concepts, graph coloring
- Recurrence relations and equations
- Growth of functions and O(n) notation concept

- Basics of optimization, how to formulate the problem
- Maxima, minima, convex function, global solution
- Linear programming, simplex algorithm
- Integer programming
- Constraint programming, knapsack problem
- Randomized optimization techniques: hill climbing, simulated annealing, genetic algorithms

- Essential math for data science (Medium)
- The 5 basic statistics concepts data scientists need to know
- Mathematics for data science

[Real numbers]: Real numbers "Real numbers"

[Cartesian coordinates]: Cartesian coordinates "Cartesian coordinates" [Sets Basics]: Sets Basics "Sets Basics"

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