If you want to became a data scientist then it is necessary to have the knowledge of mathematics or you have a very strong mathematical background.

Now we organized the order of learning topics which makes it easier to learn from basic to advanced level.

### Start with probability ( Conditional Basic Marginal etc …)

Formula => P(Event) = Favourable Outcomes / Total Possible Outcomes . Lets look at some examples:

Problem: Throwing a Dice (1 time ) — Means [1,2,3,4,5,6] ie. total possible outcomes = 6. What is the probability of getting 5 on throwing a dice ? Ans : 1 / 6 .

And more topics which is belongs to machine learning probabilty:

Statistical and Probability Theory needed for ML are Combinatorics, Probability Rules & Axioms, Bayes’ Theorem, Random Variables, Variance and Expectation, Conditional and Joint Distributions, Standard Distributions (Bernoulli, Binomial, Multinomial, Uniform and Gaussian), Moment Generating Functions, Maximum Likelihood Estimation (MLE), Prior and Posterior, Maximum a Posteriori Estimation (MAP) and Sampling Methods.

### Mathematical Series and Convergence , Numerical methods for Analysis

The concept of convergence is a well defined mathematical term. It essentially means that "eventually" a sequence of elements get closer and closer to a single value. We call this single value the "limit".

examples:

Given (infinite) sequence of real numbersX0, X1, X2, ... Xn ...we say Xn converges to a given number L if for every positive error that you think, there is a Xm such that every element Xn that comes after Xm differs from L by less than that error.

Imagine a sequence as such:

X0 = 1

X1 = 0.1

X2 = 0.01

X3 = 0.001

X4 =0.0001

...

Xn = 1/(10^n)

This means that Xn = 1/(10^5) converges to 0. As in "it can get closer and closer to zero" as much as we want.

### Matrix and Linear Algebra

These fields of mathematics are useful to you because you can describe (and even execute with the right libraries) complex operations used in machine learning using the notation and formalisms from linear algebra.

### Bayesian Statistics

Bayesian statistics encompasses a specific class of models that could be used for machine learning. Typically, one draws on Bayesian models for one or more of a variety of reasons, such as:

Having relatively few data points

Having strong prior intuitions (from pre-existing observations/models) about how things work

Having high levels of uncertainty, or a strong need to quantify the level of uncertainty about a particular model or comparison of models

Wanting to claim something abut the likelihood of the alternative hypothesis, rather than simply accepting/rejecting the null hypothesis

### Vectors ( Most Important)

Vectors are a foundational element of linear algebra.

Vectors are used throughout the field of machine learning in the description of algorithms and processes such as the target variable (y) when training an algorithm.

### Calculus

Calculus is an important field in mathematics and it plays an integral role in many machine learning algorithms.

### Markov Process and Chains

Markov chains are a fairly common, and relatively simple, way to statistically model random processes. They have been used in many different domains, ranging from text generation to financial modeling. Markov chains are used to model probabilities using information that can be encoded in the current state

### Basics of Optimization ( Linear/ Quadratic)

This section covers all the mathematical equation like linear and quadratic

### example:

### 2x^1 − 3x^2 = 5

### 3x^1 + 4x^2 = 6

## After this you can go through some machine learning algorithms:

K-NN is great starting point learn it , and code it from scratch.

Logistic Regression with Gradient Descent.

## After this you will go through these topics:

Stochastic Models and Time Series Analysis

Differential Equations

Dynamic Programming and Optimization Techniques

Fourier's and Wavelengths

Random Fields

Basic Knowledge of PDEs

Techniques to solve PDEs using Monte-Carlo , Polynomial Expansions.

## Now next level go to the higher level:

PDEs numerical solution with numerical input/ random input. ( fascinating subject to work on )

Stochastic Differential Equations and Solutions

PCA etc

Dirichlet Processes, Markov Decision Process.

Uncertainty Quantification - Polynomial Chaos, Projections on vector space

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