# Maths for Data Science

## Key skills required

• 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

## Study Areas

### Functions

• 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

### Statistics

• 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

### Linear Algebra

• 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

### Calculus

• 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

### Discrete maths

• [[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

### Optimization and Operations Research

• 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

## Footnotes

[Real numbers]: Real numbers "Real numbers"

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