# Mathematical programming - build up for advancing in data science

We show how, by simulating the random throw of a dart, you can compute the value of pi approximately. This is a small step towards building the habit of mathematical programming, which should be a key skill in the repertoire of a budding data scientist.

#### Introduction

The essence of mathematical programming is that you build a habit of coding up mathematical concepts, especially the ones involving a series of computational tasks in a systematic manner.

This kind of programming habit is extremely useful for a career in analytics and data science, where one is expected to encounter and make sense of a wide variety of numerical patterns every day. The ability of mathematical programming helps in rapid prototyping of quick numerical analyses, which are often the first steps in building a data model.

#### A few examples

So, what do I mean by mathematical programming? Isn’t a bunch of mathematical functions already built-in and optimized in various Python libraries like NumPy and SciPy?

Yes, but that should not stop you from coding up various numerical computation tasks from scratch and getting into the habit of mathematical programming.

Here are a few random examples,

As you can see, the examples can be made extremely interesting and close to real-life scenarios. This technique, therefore, also leads to the ability of writing code for discrete or stochastic simulations.

When you are browsing through some mathematical properties or ideas on the internet, do you feel the urge to quickly test the concept using a simple piece of code in your favorite programming language?

If yes, then congratulations! You have the ingrained habit of mathematical programming and it will take you far in your pursuit of a satisfactory data science career.

#### Why is mathematical programming a key skill for data science?

The practice of data science needs an extremely friendly relationship with numbers and numerical analyses. However, this does not mean memorization of complicated formula and equations.

A faculty of discovering patterns in numbers and an ability to quickly testing ideas by writing simple code go far for a budding data scientist.

This is akin to an electronics engineer being fairly hands-on with laboratory-equipments and automation scripting to run those pieces of equipment to capture hidden patterns in the electrical signals.

Or, think of a young biologist who is proficient in creating cross-section samples of cells on a slide and quickly run automated tests under a microscope to gather data for testing her ideas.

The point is that while the whole enterprise of data science may comprise of many disparate components — data wrangling, text processing, file handling, database processing, machine learning and statistical modeling, visualization, presentation, etc. — a quick experimentation with ideas often do not require much more than solid mathematical programming ability.

It is difficult to exactly pin-point all the necessary elements that are required to develop the skill of mathematical programming, but some of the common ones are,

• A habit of modularized programming,
• A clear idea about various randomization techniques
• Ability to read and understand the fundamental topics of linear algebra, calculus, and discrete mathematics,
• Familiarity with basic descriptive and inferential statistics,
• Rudimentary ideas about discrete and continuous optimization methods (such as linear programming)
• Basic proficiency with the core numerical libraries and functions in the language of choice, in which the data scientists wants to test her ideas

You can refer to this article which discusses what to learn in essential hands-on mathematics for data science.

In this article, we will illustrate the mathematical programming by discussing a very simple example, computing the approximate value of pi using a Monte Carlo method of throwing random darts at a board.

#### Computing pi by throwing (a lot of) darts

This is a fun method to compute the value of pi by simulating the random process of throwing darts at a board. It does not use any sophisticated mathematical analysis or formula but tries to compute the approximate value of pi from the emulation of a purely physical (but stochastic) process.

This technique falls under the banner of Monte Carlo method, whose basic concept is to emulate a random process, which, when repeated a large number of times, gives rise to the approximation of some mathematical quantity of interest.

Imagine a square dartboard.

Then, the dartboard with a circle drawn inside it touching all its sides.

And then, you throw darts at it. Randomly. That means some fall inside the circle, some outside. But assume that no dart falls outside the board.

At the end of your dart throwing session, you count the fraction of darts that fell inside the circle of the total number of darts thrown. Multiply that number by 4.

The resulting number should be pi. Or, a close approximation if you had thrown a lot of darts.

#### What’s the idea?

The idea is extremely simple. If you throw a large number of darts, then the probability of a dart falling inside the circle is just the ratio of the area of the circle to that of the area of the square board. With the help of basic mathematics, you can show that this ratio turns out to be pi/4. So, to get pi, you just multiply that number by 4.

The key here is to simulate the throwing of a lot of darts so as to make the fraction (of the darts that fall inside the circle) equal to the probability, an assertion valid only in the limit of a large number of trials of this random event. This comes from the law of large number or the frequentist definition of probability.

#### Python code

A Jupyter notebook illustrating the Python code is given here in my Github repo. Please feel free to copy or fork. The steps are simple.

First, create a function to simulate the random throw of a dart.

``````def throw_dart():
"""
Simulates the randon throw of a dart. It can land anywhere in the square (uniformly randomly)
"""
# Center point
x,y = 0,0
# Side of the square
a = 2

# Random final landing position of the dart between -a/2 and +a/2 around the center point
position_x = x+a/2*(-1+2*random.random())
position_y = y+a/2*(-1+2*random.random())

return (position_x,position_y)
``````

compute_pi_dart_1.py

Then, write a function to determine if a dart, given its landing coordinates, falls inside the circle,

``````def is_within_circle(x,y):
"""
Given the landing coordinate of a dart, determines if it fell inside the circle
"""
# Side of the square
a = 2

distance_from_center = sqrt(x**2+y**2)

if distance_from_center < a/2:
return True
else:
return False
``````

compute_pi_dart_2.py

Finally, write a function to simulate a large number of dart throwing and calculate the value of pi from the cumulative result.

``````def compute_pi_throwing_dart(n_throws):
"""
Computes pi by throwing a bunch of darts at the square
"""
n_throws = n_throws
count_inside_circle=0
for i in range(n_throws):
r1,r2=throw_dart()
if is_within_circle(r1,r2):
count_inside_circle+=1

result = 4*(count_inside_circle/n_throws)

return result
``````

compute_pi_dart_3.py

But the programming must not stop there. We must test how good the approximation is and how it changes with the number of random throws. As with any Monte Carlo experiment, we expect the approximation to get better with a higher number of experiments.

This is the core of data science and analytics. It is not enough to write a function which prints the expected output and stop there. The essential programming may be done but the scientific experiment does not stop there without further exploration and testing of the hypothesis.

We can see that a large number of random throws can be repeated a few times to calculate an average and get a better approximation.

``````n = 5000000
sum=0
for i in range(20):
p=compute_pi_throwing_dart(n)
sum+=p
print("Experiment number {} done. Computed value: {}".format(i+1,p))
print("-"*75)
pi_computed = round(sum/20,4)
print("Average value from 20 experiments:",pi_computed)
``````

compute_pi_dart_4.py

#### Simple code, rich ideas

The theory and code behind this technique seem extremely simple. However, behind the facade of this simple exercise, some pretty interesting ideas are hidden.

Functional programming approach: The description of the technique can be coded using a monolith code block. However, we show how the tasks should be partitioned into simple functions mimicking real human actions —

• throwing a dart,
• examining the landing coordinate of the dart and determining whether it landed inside the circle,
• repeating this process an arbitrary number of times

To write high-quality code for large programs, it is instructive to use this kind of modularized programming style.

Emergent behavior: Nowhere in this code, any formula involving pi or properties of a circle was used. Somehow, the value of pi emerges from the collective action of throwing a bunch of darts randomly at a board and calculating a fraction. This is an example of emergent behavior in which a mathematical pattern emerges from a set of a large number of repeated experiments of a similar kind through their mutual interaction.

Frequentist definition of probability: There are two broad categories of the definition of probability and two fiercely rival camps — frequentists and Bayesians. It is easy to think as a frequentist and define probability as a frequency (as a fraction of the total number of random trials) of an event. In this coding exercise, we could see how this particular notion of probability emerges from repeating random trials a large number of times.

Stochastic simulation: The core function of throwing dart uses a random generator at its heart. Now, a computer-generated random number is not truly random, but for all practical purpose, it can be assumed to be one. In this programming exercise, we used a uniform random generator function from the `random` module of Python. Use of this kind of randomization method is at the heart of stochastic simulation, which is a powerful method used in the practice of data science.

Testing the assertion by repeated simulations and visualization: Often, in data science, we deal with stochastic processes and probabilistic models, which must be tested based on a large number of simulations/experiments. Therefore, it is imperative to think in those asymptotic terms and test the validity of the data model or the scientific assertion in a statistically sound manner.

#### Summary (and a challenge for the reader)

We demonstrate what it means to develop a habit of mathematical programming. Essentially, it is thinking in terms of programming to test out the mathematical properties or data patterns that you are developing in your mind. This simple habit can aid in the development of good practices for an upcoming data scientist.

An example was demonstrated using simple geometric identities, concepts of stochastic simulation, and frequentist definition of probability.

If you are looking for more challenge,

can you compute pi by simulating a random walk event?

If you want to fork the code for this fun exercise, please fork this repo.

## Learn Data Science | How to Learn Data Science for Free

Learn Data Science | How to Learn Data Science for Free. In this post, I have described a learning path and free online courses and tutorials that will enable you to learn data science for free.

The average cost of obtaining a masters degree at traditional bricks and mortar institutions will set you back anywhere between \$30,000 and \$120,000. Even online data science degree programs don’t come cheap costing a minimum of \$9,000. So what do you do if you want to learn data science but can’t afford to pay this?

I trained into a career as a data scientist without taking any formal education in the subject. In this article, I am going to share with you my own personal curriculum for learning data science if you can’t or don’t want to pay thousands of dollars for more formal study.

The curriculum will consist of 3 main parts, technical skills, theory and practical experience. I will include links to free resources for every element of the learning path and will also be including some links to additional ‘low cost’ options. So if you want to spend a little money to accelerate your learning you can add these resources to the curriculum. I will include the estimated costs for each of these.

### Technical skills

The first part of the curriculum will focus on technical skills. I recommend learning these first so that you can take a practical first approach rather than say learning the mathematical theory first. Python is by far the most widely used programming language used for data science. In the Kaggle Machine Learning and Data Science survey carried out in 2018 83% of respondents said that they used Python on a daily basis. I would, therefore, recommend focusing on this language but also spending a little time on other languages such as R.

### Python Fundamentals

Before you can start to use Python for data science you need a basic grasp of the fundamentals behind the language. So you will want to take a Python introductory course. There are lots of free ones out there but I like the Codeacademy ones best as they include hands-on in-browser coding throughout.

I would suggest taking the introductory course to learn Python. This covers basic syntax, functions, control flow, loops, modules and classes.

### Data analysis with python

Next, you will want to get a good understanding of using Python for data analysis. There are a number of good resources for this.

To start with I suggest taking at least the free parts of the data analyst learning path on dataquest.io. Dataquest offers complete learning paths for data analyst, data scientist and data engineer. Quite a lot of the content, particularly on the data analyst path is available for free. If you do have some money to put towards learning then I strongly suggest putting it towards paying for a few months of the premium subscription. I took this course and it provided a fantastic grounding in the fundamentals of data science. It took me 6 months to complete the data scientist path. The price varies from \$24.50 to \$49 per month depending on whether you pay annually or not. It is better value to purchase the annual subscription if you can afford it.

The Dataquest platform

### Python for machine learning

If you have chosen to pay for the full data science course on Dataquest then you will have a good grasp of the fundamentals of machine learning with Python. If not then there are plenty of other free resources. I would focus to start with on scikit-learn which is by far the most commonly used Python library for machine learning.

When I was learning I was lucky enough to attend a two-day workshop run by Andreas Mueller one of the core developers of scikit-learn. He has however published all the material from this course, and others, on this Github repo. These consist of slides, course notes and notebooks that you can work through. I would definitely recommend working through this material.

Then I would suggest taking some of the tutorials in the scikit-learn documentation. After that, I would suggest building some practical machine learning applications and learning the theory behind how the models work — which I will cover a bit later on.

SQL

SQL is a vital skill to learn if you want to become a data scientist as one of the fundamental processes in data modelling is extracting data in the first place. This will more often than not involve running SQL queries against a database. Again if you haven’t opted to take the full Dataquest course then here are a few free resources to learn this skill.

Codeacamdemy has a free introduction to SQL course. Again this is very practical with in-browser coding all the way through. If you also want to learn about cloud-based database querying then Google Cloud BigQuery is very accessible. There is a free tier so you can try queries for free, an extensive range of public datasets to try and very good documentation.

#### R

To be a well-rounded data scientist it is a good idea to diversify a little from just Python. I would, therefore, suggest also taking an introductory course in R. Codeacademy have an introductory course on their free plan. It is probably worth noting here that similar to Dataquest Codeacademy also offers a complete data science learning plan as part of their pro account (this costs from \$31.99 to \$15.99 per month depending on how many months you pay for up front). I personally found the Dataquest course to be much more comprehensive but this may work out a little cheaper if you are looking to follow a learning path on a single platform.

#### Software engineering

It is a good idea to get a grasp of software engineering skills and best practices. This will help your code to be more readable and extensible both for yourself and others. Additionally, when you start to put models into production you will need to be able to write good quality well-tested code and work with tools like version control.

There are two great free resources for this. Python like you mean it covers things like the PEP8 style guide, documentation and also covers object-oriented programming really well.

The scikit-learn contribution guidelines, although written to facilitate contributions to the library, actually cover the best practices really well. This covers topics such as Github, unit testing and debugging and is all written in the context of a data science application.

#### Deep learning

For a comprehensive introduction to deep learning, I don’t think that you can get any better than the totally free and totally ad-free fast.ai. This course includes an introduction to machine learning, practical deep learning, computational linear algebra and a code-first introduction to natural language processing. All their courses have a practical first approach and I highly recommend them.

Fast.ai platform

#### Theory

Whilst you are learning the technical elements of the curriculum you will encounter some of the theory behind the code you are implementing. I recommend that you learn the theoretical elements alongside the practical. The way that I do this is that I learn the code to be able to implement a technique, let’s take KMeans as an example, once I have something working I will then look deeper into concepts such as inertia. Again the scikit-learn documentation contains all the mathematical concepts behind the algorithms.

In this section, I will introduce the key foundational elements of theory that you should learn alongside the more practical elements.

The khan academy covers almost all the concepts I have listed below for free. You can tailor the subjects you would like to study when you sign up and you then have a nice tailored curriculum for this part of the learning path. Checking all of the boxes below will give you an overview of most elements I have listed below.

#### Maths

Calculus

Calculus is defined by Wikipedia as “the mathematical study of continuous change.” In other words calculus can find patterns between functions, for example, in the case of derivatives, it can help you to understand how a function changes over time.

Many machine learning algorithms utilise calculus to optimise the performance of models. If you have studied even a little machine learning you will probably have heard of Gradient descent. This functions by iteratively adjusting the parameter values of a model to find the optimum values to minimise the cost function. Gradient descent is a good example of how calculus is used in machine learning.

What you need to know:

Derivatives

• Geometric definition
• Calculating the derivative of a function
• Nonlinear functions

Chain rule

• Composite functions
• Composite function derivatives
• Multiple functions

• Partial derivatives
• Directional derivatives
• Integrals

Linear Algebra

Many popular machine learning methods, including XGBOOST, use matrices to store inputs and process data. Matrices alongside vector spaces and linear equations form the mathematical branch known as Linear Algebra. In order to understand how many machine learning methods work it is essential to get a good understanding of this field.

What you need to learn:

Vectors and spaces

• Vectors
• Linear combinations
• Linear dependence and independence
• Vector dot and cross products

Matrix transformations

• Functions and linear transformations
• Matrix multiplication
• Inverse functions
• Transpose of a matrix

### Statistics

Here is a list of the key concepts you need to know:

Descriptive/Summary statistics

• How to summarise a sample of data
• Different types of distributions
• Skewness, kurtosis, central tendency (e.g. mean, median, mode)
• Measures of dependence, and relationships between variables such as correlation and covariance

Experiment design

• Hypothesis testing
• Sampling
• Significance tests
• Randomness
• Probability
• Confidence intervals and two-sample inference

Machine learning

• Linear and non-linear regression
• Classification

### Practical experience

The third section of the curriculum is all about practice. In order to truly master the concepts above you will need to use the skills in some projects that ideally closely resemble a real-world application. By doing this you will encounter problems to work through such as missing and erroneous data and develop a deep level of expertise in the subject. In this last section, I will list some good places you can get this practical experience from for free.

“With deliberate practice, however, the goal is not just to reach your potential but to build it, to make things possible that were not possible before. This requires challenging homeostasis — getting out of your comfort zone — and forcing your brain or your body to adapt.”, Anders Ericsson, Peak: Secrets from the New Science of Expertise

### Kaggle, et al

Machine learning competitions are a good place to get practice with building machine learning models. They give access to a wide range of data sets, each with a specific problem to solve and have a leaderboard. The leaderboard is a good way to benchmark how good your knowledge at developing a good model actually is and where you may need to improve further.

In addition to Kaggle, there are other platforms for machine learning competitions including Analytics Vidhya and DrivenData.

Driven data competitions page

### UCI Machine Learning Repository

The UCI machine learning repository is a large source of publically available data sets. You can use these data sets to put together your own data projects this could include data analysis and machine learning models, you could even try building a deployed model with a web front end. It is a good idea to store your projects somewhere publically such as Github as this can create a portfolio showcasing your skills to use for future job applications.

#### Contributions to open source

One other option to consider is contributing to open source projects. There are many Python libraries that rely on the community to maintain them and there are often hackathons held at meetups and conferences where even beginners can join in. Attending one of these events would certainly give you some practical experience and an environment where you can learn from others whilst giving something back at the same time. Numfocus is a good example of a project like this.

In this post, I have described a learning path and free online courses and tutorials that will enable you to learn data science for free. Showcasing what you are able to do in the form of a portfolio is a great tool for future job applications in lieu of formal qualifications and certificates. I really believe that education should be accessible to everyone and, certainly, for data science at least, the internet provides that opportunity. In addition to the resources listed here, I have previously published a recommended reading list for learning data science available here. These are also all freely available online and are a great way to complement the more practical resources covered above.

## Data Science vs Data Analytics vs Big Data

When we talk about data processing, Data Science vs Big Data vs Data Analytics are the terms that one might think of and there has always been a confusion between them. In this article on Data science vs Big Data vs Data Analytics, I will understand the similarities and differences between them

When we talk about data processing, Data Science vs Big Data vs Data Analytics are the terms that one might think of and there has always been a confusion between them. In this article on Data science vs Big Data vs Data Analytics, I will understand the similarities and differences between them

We live in a data-driven world. In fact, the amount of digital data that exists is growing at a rapid rate, doubling every two years, and changing the way we live. Now that Hadoop and other frameworks have resolved the problem of storage, the main focus on data has shifted to processing this huge amount of data. When we talk about data processing, Data Science vs Big Data vs Data Analytics are the terms that one might think of and there has always been a confusion between them.

In this article on Data Science vs Data Analytics vs Big Data, I will be covering the following topics in order to make you understand the similarities and differences between them.
Introduction to Data Science, Big Data & Data AnalyticsWhat does Data Scientist, Big Data Professional & Data Analyst do?Skill-set required to become Data Scientist, Big Data Professional & Data AnalystWhat is a Salary Prospect?Real time Use-case## Introduction to Data Science, Big Data, & Data Analytics

Let’s begin by understanding the terms Data Science vs Big Data vs Data Analytics.

### What Is Data Science?

Data Science is a blend of various tools, algorithms, and machine learning principles with the goal to discover hidden patterns from the raw data.

[Source: gfycat.com]

It also involves solving a problem in various ways to arrive at the solution and on the other hand, it involves to design and construct new processes for data modeling and production using various prototypes, algorithms, predictive models, and custom analysis.

### What is Big Data?

Big Data refers to the large amounts of data which is pouring in from various data sources and has different formats. It is something that can be used to analyze the insights which can lead to better decisions and strategic business moves.

[Source: gfycat.com]

### What is Data Analytics?

Data Analytics is the science of examining raw data with the purpose of drawing conclusions about that information. It is all about discovering useful information from the data to support decision-making. This process involves inspecting, cleansing, transforming & modeling data.

[Source: ibm.com]

What Does Data Scientist, Big Data Professional & Data Analyst Do?

### What does a Data Scientist do?

Data Scientists perform an exploratory analysis to discover insights from the data. They also use various advanced machine learning algorithms to identify the occurrence of a particular event in the future. This involves identifying hidden patterns, unknown correlations, market trends and other useful business information.

Roles of Data Scientist

### What do Big Data Professionals do?

The responsibilities of big data professional lies around dealing with huge amount of heterogeneous data, which is gathered from various sources coming in at a high velocity.

Roles of Big Data Professiona

Big data professionals describe the structure and behavior of a big data solution and how it can be delivered using big data technologies such as Hadoop, Spark, Kafka etc. based on requirements.

### What does a Data Analyst do?

Data analysts translate numbers into plain English. Every business collects data, like sales figures, market research, logistics, or transportation costs. A data analyst’s job is to take that data and use it to help companies to make better business decisions.

Roles of Data Analyst

Skill-Set Required To Become Data Scientist, Big Data Professional, & Data Analyst

What Is The Salary Prospect?

The below figure shows the average salary structure of **Data Scientist, Big Data Specialist, **and Data Analyst.

A Scenario Illustrating The Use Of Data Science vs Big Data vs Data Analytics.

Now, let’s try to understand how can we garner benefits by combining all three of them together.

Let’s take an example of Netflix and see how they join forces in achieving the goal.

First, let’s understand the role of* Big Data Professional* in Netflix example.

Netflix generates a huge amount of unstructured data in forms of text, audio, video files and many more. If we try to process this dark (unstructured) data using the traditional approach, it becomes a complicated task.

Approach in Netflix

Hence a Big Data Professional designs and creates an environment using Big Data tools to ease the processing of Netflix Data.

Big Data approach to process Netflix data

Now, let’s see how Data Scientist Optimizes the Netflix Streaming experience.

Role of Data Scientist in Optimizing the Netflix streaming experience

### 1. Understanding the impact of QoE on user behavior

User behavior refers to the way how a user interacts with the Netflix service, and data scientists use the data to both understand and predict behavior. For example, how would a change to the Netflix product affect the number of hours that members watch? To improve the streaming experience, Data Scientists look at QoE metrics that are likely to have an impact on user behavior. One metric of interest is the rebuffer rate, which is a measure of how often playback is temporarily interrupted. Another metric is bitrate, that refers to the quality of the picture that is served/seen — a very low bitrate corresponds to a fuzzy picture.

### 2. Improving the streaming experience

How do Data Scientists use data to provide the best user experience once a member hits “play” on Netflix?

One approach is to look at the algorithms that run in real-time or near real-time once playback has started, which determine what bitrate should be served, what server to download that content from, etc.

For example, a member with a high-bandwidth connection on a home network could have very different expectations and experience compared to a member with low bandwidth on a mobile device on a cellular network.

By determining all these factors one can improve the streaming experience.

### 3. Optimize content caching

A set of big data problems also exists on the content delivery side.

The key idea here is to locate the content closer (in terms of network hops) to Netflix members to provide a great experience. By viewing the behavior of the members being served and the experience, one can optimize the decisions around content caching.

### 4. Improving content quality

Another approach to improving user experience involves looking at the quality of content, i.e. the video, audio, subtitles, closed captions, etc. that are part of the movie or show. Netflix receives content from the studios in the form of digital assets that are then encoded and quality checked before they go live on the content servers.

In addition to the internal quality checks, Data scientists also receive feedback from our members when they discover issues while viewing.

By combining member feedback with intrinsic factors related to viewing behavior, they build the models to predict whether a particular piece of content has a quality issue. Machine learning models along with natural language processing (NLP) and text mining techniques can be used to build powerful models to both improve the quality of content that goes live and also use the information provided by the Netflix users to close the loop on quality and replace content that does not meet the expectations of the users.

So this is how Data Scientist optimizes the Netflix streaming experience.

Now let’s understand how Data Analytics is used to drive the Netflix success.

Role of Data Analyst in Netflix

The above figure shows the different types of users who watch the video/play on Netflix. Each of them has their own choices and preferences.

So what does a Data Analyst do?

Data Analyst creates a user stream based on the preferences of users. For example, if user 1 and user 2 have the same preference or a choice of video, then data analyst creates a user stream for those choices. And also –
Orders the Netflix collection for each member profile in a personalized way.We know that the same genre row for each member has an entirely different selection of videos.Picks out the top personalized recommendations from the entire catalog, focusing on the titles that are top on ranking.By capturing all events and user activities on Netflix, data analyst pops out the trending video.Sorts the recently watched titles and estimates whether the member will continue to watch or rewatch or stop watching etc.
I hope you have *understood *the *differences *& *similarities *between Data Science vs Big Data vs Data Analytics.

## Data Science Training | Data Science for Beginners | Intellipaat - YouTube

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Why should you opt for a Data Science career?

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