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### Importance of Different Maths in Data Science

- Modelling 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,
- Training oneâ??s sense for identification of the hidden pattern from the stream of information,
- Understanding clearly the limitation of a model
- (Occasionally) trying to understand a mathematical proof and all the abstract logic behind it

- Data summaries and descriptive statistics, central tendency, variance, covariance, correlation,
- Basic probability: basic idea, expectation, probability calculus, Bayes theorem, conditional probability,
- Probability distribution functionsâ??-â??uniform, normal, binomial, chi-square, studentâ??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

- Basic properties of matrix and vectorsâ??-â??scalar multiplication, linear transformation, transpose, conjugate, rank, determinant,
- Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse,
- Special matricesâ??-â??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, and diagonalization, singular value decomposition (SVD)

- Functions of single variable, limit, continuity and differentiability,
- Mean value theorems, indeterminate forms and Lâ??Hospital rule,
- Maxima and minima,
- Product and chain rule,
- Taylorâ??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 (not too advanced)

- Sets, subsets, power sets
- Counting functions, combinatorics, countability
- Basic Proof Techniquesâ??-â??induction, proof by contradiction
- Basics of inductive, deductive, and propositional logic
- Basic data structures- stacks, queues, graphs, arrays, hash tables, trees
- Graph propertiesâ??-â??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 techniquesâ??-â??hill climbing, simulated annealing, Genetic algorithms