fanne wrote:
Negi ji and Arjun Pandit Ji,
Maths and I were born for each other, I do some exotic math just as hobby (very niche concerned with my hobby). So ya probability, permutation combo, algebra, calculus, STAT etc. has been my best friend. They do not intimidate me. In fact most of my friend (here at BR and otherwise) have been pushing for me to get into this field.
But I do not really know how to start. A well laid out course and lucid material going to appropriate depth goes a long way. Perhaps that is 80% of the fight, 20% is the drive and effort to know it. I am seeking help on the 80% of it.
From my IIT preparation day, it was good to know what book to read for each chapter/area for Physics/Math/chemistry. Once you knew it, it was easy. Many were lost trying to study things from the wrong place (and could have been very successful) had they known the right place. I would not do it just for consulting, but to know and maybe be a successful entrepreneur (hint: What is hot or going to be hot). From Business application I don't have any passion, I can swing any way.
Here is a list that might help:
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
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 wrt a {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
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
Miscellaneous
Information theory- entropy, cross-entropy, KL divergence, mutual information
Markov Chain- definition, transition matrix, stationarity