Data science is fast becoming one of the hottest professions. It acts as a backbone for businesses and organizations, so the need to hire a data scientist becomes inevitable.
There are many fundamentals to learn if you want to pursue a career in data science. Getting a job can be easy, as most people tag it as a nogo area of study. But this is not true if you are determined, and committed to developing your understanding.
As a data scientist, you have the option to choose how you want to utilize your skills. If you want to work as a freelancer, there are many businesses that will need your services. You may also decide to become an employee in an organization, and help them move forward through relevant data analysis. There are lots of benefits to enjoy as a data scientist, but you need a solid background in probability and statistics to do well in this field.
Having talked about the prospect of data science, lets move a step further by considering the fundamentals of this area of specialization.
Data Science: The fundamentals
The two biggest buzzwords in this industry are “data science” and “big data.” While the latter is gaining interest all over the world, the former is turning out to be a very hot subject.
You should make sure you fully understand the background of data science  what are the basics required to truly make data science a science? Our quest can begin from here.
There are some critical questions we need to ask when it comes to the basics of data science: what does the word “data” really mean, what are our intentions with it, and what scientific approaches do we need to apply to achieve our set goals with data?

What is data?

What is the purpose of data science

The scientific approach
Probability & Statistics
The world we live in is probabilistic, so the data we work with is probabilistic  this implies that when given a set of preconditions, it is normal that data will show information in a particular way, for a specific period of time. For this reason, you need to be acquainted and comfortable with probability and statistics to be able to apply data science properly.

The two characteristics of data

Introduction to probability

Examples of statistical data

Statistical properties (Median, Mean, Mode, Standard Deviation, Moments, etc.)

Probability distribution

Joint & conditional probabilities

Common probability distributions (Binomial, Discrete, Normal)

Other probability distributions (Poisson, Chisquare)

Connections with statistical distribution

Bayesian interface

Bayes rule
Decision Theory
This is certainly one of the major fundamentals. Whether applied in engineering, business, or science, our sole aim is to use data to make decisions. Data on its own is insignificant unless it is revealing something with which we can make a decision. How do these decisions come about? What factors do we consider during this decision making process? Which approach is best to use for deciding with data? Decision Theory tells us;

Bayes risk

Hypothesis testing

Likelihood ratio & log likelihood ratio

Binary hypothesis test

Optimal decision making

NeymanPearson criterion

Mary hypothesis test

Receiver operating characteristic curve
Estimation Theory
There are times we make characterization of data  parameter estimates, averages, etc. Estimating data is absolutely an extension of decision theory. It is the thing that follows immediately after decision making.

Unbiased estimation

Estimation as extension of Mary hypothesis test

Kalman filter

Minimum mean square error (MMSE)

Maximum A posteriori estimation (MAP)

Maximum likelihood estimation (MLE)
Coordinate Systems
This is another crucial section that plays a significant role in the outcome of data interpretation. To group different data elements into a single decisionmaking structure, we need to understand how to align the data correctly. At this point, it becomes imperative to have adequate knowledge of coordinate systems, and how to utilize them in bringing together disparate data.

Introduction to coordinate systems

Orthogonal coordinate system

Properties of orthogonal coordinate system (dot product, angle, coordinate transformation, etc.)

Transformation between coordinate systems

Polar coordinate system

Euclidian spaces

Cylindrical coordinate system

Cartesian coordinate system

Spherical coordinate system
Linear Transformation
After gaining mastery over coordinate systems, the next step is to learn how to transform the data to produce the underlying information. Linear transformation talks about turning our data into useful information through various transformation types, including the wellknown Fourier transform.

Introduction to linear transformation

Matrix multiplication

Properties of linear transformation

Fourier transform

Uncertainty principle & aliasing

Properties of Fourier transform (shift variance, timefrequency relationship, convolution theorem, Parseval’s theorem, spectral properties, etc.)

Discrete & continuous Fourier transform

Wavelet & other transforms
Computation, and its Effect on Data
One aspect of data science that doesn’t get much attention is the impact algorithms play on the information we are trying to achieve. Merely applying computations and algorithms to create data products has a huge impact on effective, datadriven decision making. This section leads us on a road of advanced areas of data science.

Irreversible computation

Mathematical representation of computation

Impulse response function

Impacts on decision making

Reversible computation (Bijective mapping)

Transformation of probability distribution (due to subtraction, addition, division, multiplication, arbitrary computation, etc.)
Prototype coding/programming
One of the main features of data scientists is the willingness to get their hands dirty with data. They should be able to write programs that process, access, and visualize data in essential in languages in science & industry. This segment takes us to these crucial elements.

Introduction to programming

Functions

Data structures

Data types, functions, and variables

Loops, ifthenelse, comparisons

Compilable languages vs. scripting languages

SAS

SQL

Python

C++

R
Graph Theory
Graphs are used to illustrate connections between various data elements. They are also crucial in the current interconnected world.

Introduction to graph theory

Directed graphs

Undirected graphs

Route & network problems

Various graph data framework
Algorithms
Having an understanding of how to use algorithms to compute essential dataderived metrics is the key to data science.

Introduction to algorithms

Gradient search

Recursive algorithms

Parallel, serial, & distributed algorithms

Randomized algorithms

Exhaustive search

DivideandConquer binary search

Linear programming

Sorting algorithms

Shortest path algorithm for graphs

Heuristic algorithms

Greedy algorithms
Machine Learning
When looking at the fundamentals of data science, it would be incomplete if machine learning gets ignored. However, these techniques can be acquired by gaining mastery over the fundamentals described in sections above. Machine learning offers practitioners an understanding of essential and wellknown machine learning techniques, and their importance.

Introduction to machine learning

Decision trees

Linear classifiers (NaÃ¯ve Bayes Classifier, Logistic Regression, Support Vector Machines)

Expectation Maximization

Bayesian networks

Vector quantization

Hidden Markov Models

Kmeans Clustering comment

Artificial neural networks & deep learning
Conclusion
The importance of data science in all fields of life cannot be refuted. There is a lot of work available for a data scientist, and the rate at which businesses need this profession suggests more more people should venture into it. The fundamentals given above will guide you in starting a career in data science. There are more advanced topics to go through in this field, so you need to be extremely good in statistics and probability for you to succeed as a data scientist.
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