**Mathematics**

**a. ****Probability
**

Basic
rules and axioms, events, sample space, frequentist approach, dependent and
independent events, conditional probability, Random variables, continuous and
discrete, expectation, variance, distributions- joint and conditional, Bayes’
Theorem, MAP, MLE, Popular distributions- binomial, bernoulli, poisson,
exponential, Gaussian, Conjugate priors

**b. ****Linear
Algebra**

·Vectors, definition, scalars, addition, scalar
multiplication, inner product (dot product), vector projection, cosine
similarity, orthogonal vectors, normal and orthonormal vectors, vector norm,
vector space, linear combination, linear span, linear independence, basis
vectors

·Matrices definition, addition, transpose, scalar
multiplication, matrix multiplication, matrix multiplication properties,
hadamard product, functions, linear transformation, determinant, identity
matrix, invertible matrix and inverse, rank, trace, popular type of matrices-
symmetric, diagonal, orthogonal, orthonormal, positive definite matrix

·Eigenvalues & eigenvectors, concept, intuition,
significance, how to find Principle component analysis, concept, properties,
applications

·
Singular value decomposition, concept, properties,
applications

**c. ****Calculus**

·Functions, Scalar derivative, definition, intuition, common
rules of differentiation, chain rule, partial derivatives, Gradient, concept,
intuition, properties, directional derivative

·
Vector and matrix calculus, how to find derivative of scalar-valued,
vector-valued function with respect to scalar, vector} four combinations- Jacobian

·
Gradient algorithms, local/global maxima and minima, saddle
point, convex functions, gradient descent algorithms- batch, mini-batch,
stochastic, their performance comparison

**d. ****Miscellaneous
Topics**

Information theory, entropy, cross entropy, KL divergence,
mutual information

Markov Chain, definition, transition
matrix, stationarity.

**Statistics**:

Descriptive
Statistics, Summary Statistics Basic probability theory, Statistical Concepts
(uni-variate and bi-variate sampling, distributions, re-sampling, statistical
Inference, prediction error), Probability Distribution(Continuous and discrete-
Normal, Bernoulli, Binomial, Negative Binomial, Geometric and Poisson distribution),Bayes’ Theorem, Central Limit
theorem, Data Exploration & preparation, Concepts of Correlation,
Regression, Covariance, Outliers etc.