# The Fundamentals of Data Science

The Fundamentals of Data Science Guest blog post by Mic Farris. Mic is a Decision Science & Analytics Leader at CenturyLink.
Two of the biggest buzzwords in our industry are “big data” and “data science”. Big Data seems to have a lot of interest right now, but Data Science is fast becoming a very hot topic.

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I think there’s room to really define the science of data science – what are those fundamentals that are needed to make data science truly a science we can build upon?
What follows are such a set of fundamentals:
Fundamentals of Data Science
Introduction
The easiest thing for people within the big data / analytics / data science disciplines is to say “I do data science”. However, when it comes to data science fundamentals, we need to ask the following critical questions: What really is “data”, what are we trying to do with data, and how do we apply scientific principles to achieve our goals with data?

What is Data?
The Goal of Data Science
The Scientific Method

Probability and Statistics
The world is a probabilistic one, so we work with data that is probabilistic – meaning that, given a certain set of preconditions, data will appear to you in a specific way only part of the time.  To apply data science properly, one must become familiar and comfortable with probability and statistics.

The Two Characteristics of Data
Examples of Statistical Data
Introduction to Probability
Probability Distributions
Connection with Statistical Distributions
Statistical Properties (Mean, Mode, Median, Moments, Standard Deviation, etc.)
Common Probability Distributions (Discrete, Binomial, Normal)
Other Probability Distributions (Chi-Square, Poisson)
Joint and Conditional Probabilities
Bayes’ Rules
Bayesian Inference

Decision Theory
This section is one of the key fundamentals of data science.  Whether applied in scientific, engineering, or business fields, we are trying to make decisions using data.  Data itself isn’t useful unless it’s telling us something, which means we’re making a decision about what it is telling us.  How do we come up with those decisions? What are the factors that go into this decision making process?  What is the best method for making decisions with data?  This section tell us…

Hypothesis Testing
Binary Hypothesis Test
Likelihood Ratio and Log Likelihood Ratio
Bayes Risk
Neyman-Pearson Criterion
Receiver Operating Characteristic (ROC) Curve
M-ary Hypothesis Test
Optimal Decision Making

Estimation Theory
Sometimes we make characterizations of data – averages, parameter estimates, etc.  Estimation from data is essentially an extension of decision making, a natural next section from Decision Theory.

Estimation as Extension of M-ary Hypothesis Test
Unbiased Estimation
Minimum Mean Square Error (MMSE)
Maximum Likelihood Estimation (MLE)
Maximum A Posteriori Estimation (MAP)
Kalman Filter

Coordinate Systems
To bring various data elements together into a common decision making framework, we need to know how to align the data.  Knowledge of coordinate systems and how they are used becomes important to lay a solid foundation for bringing disparate data together.

Introduction to Coordinate Systems
Euclidian Spaces
Orthogonal Coordinate Systems
Properties of Orthogonal Coordinate Systems (angle, dot product, coordinate transformations, etc.)
Cartesian Coordinate System
Polar Coordinate System
Cylindrical Coordinate System
Spherical Coordinate System
Transformations Between Coordinate Systems

Linear Transformations
Once we understand coordinate systems, we can learn why to transform the data to get at the underlying information.  This section describe how we can transform our data into other useful data products through various types of transformations, including the popular Fourier transform.

Introduction to Linear Transformations
Properties of Linear Transformations
Matrix Multiplication
Fourier Transform
Properties of Fourier Transforms (time-frequency relationship, shift invariance, spectral properties, Parseval’s Theorem, Convolution Theorem, etc.)
Discrete and Continuous Fourier Transforms
Uncertainty Principle and Aliasing
Wavelet and Other Transforms

Effects of Computation on Data
An often overlooked aspect of data science is the impact the algorithms we apply have on the information we are seeking to find. Merely applying algorithms and computations to create analytics and other data products has an impact on the effectiveness data-driven decision making ability.  This section take us on a journey of advanced aspects of data science.

Mathematical Representation of Computation
Reversible Computations (Bijective Mapping)
Irreversible Computations
Impulse Response Functions
Transformation of Probability Distributions (due to addition, subtraction, multiplication, division, arbitrary computations, etc.)
mpacts on Decision Making

Prototype Coding / Programming
One of the key elements to data science is the willingness of practitioners to “get their hands dirty” with data.  This means being able to write programs that access, process, and visualize data in important languages in science and industry. This section takes us on a tour of these important elements.

Introduction to Programming
Data Types, Variables, and Functions
Data Structures (Arrays, etc.)
Loops, Comparisons, If-Then-Else
Functions
Scripting Languages vs. Compilable Langugages
SQL
SAS
R
Python
C++

Graph Theory
Graphs are ways to illustrate connections between different data elements, and they are important in today’s interconnected world.

Introduction to Graph Theory
Undirected Graphs
Directed Graphs
Various Graph Data Structures
Route and Network Problems

Algorithms
Key to data science is understanding the use of algorithms to compute important data-derived metrics.  Popular data manipulation algorithms are included in this section.

Introduction to Algorithms
Recursive Algorithms
Serial, Parallel, and Distributed Algorithms
Exhaustive Search
Divide-and-Conquer (Binary Search)
Gradient Search
Sorting Algorithms
Linear Programming
Greedy Algorithms
Heuristic Algorithms
Randomized Algorithms
Shortest Path Algorithms for Graphs

Machine Learning
No data science fundamentals course would be complete without exposure to machine learning.  However, it’s important to know that these techniques build upon the fundamentals described in previous sections.  This section gives practitioners an understanding of useful and popular machine learning techniques and why they are applied.

Introduction to Machine Learning
Linear Classifiers (Logistic Regression, Naive Bayes Classifier, Support Vector Machines)
Decision Trees (Random Forests)
Bayesian Networks
Hidden Markov Models
Expectation-Maximization
Artificial Neural Networks and Deep Learning
Vector Quantization
K-Means ClusteringComment

Originally posted here.
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