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  • Data Science: Mathematical Techniques for Big Data Analytics

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    Major courses like Calculus, theory of optimization, differential equations, linear algebra, and probability complete a wide range of mathematical tools used in data science. Since data science is used in almost every place in our society, the book includes data science-specific examples and problems as well as a clear explanation of complex mathematical ideas, particularly data-driven differential equations, making it suitable for researchers and graduate students in both data science and mathematics.

     

    Data science is the practice of cleaning, preparing, and aligning data. It combines statistics, mathematics, programming, and problem-solving skills. It also involves creative data collection methods. It refers to different methods used to draw conclusions and information from data. Unshaped, shaped, and semi-shaped data are all subjects of data science. There are a few methods like data preparation, analysis, and cleaning.

     

    Moreover, in this article, six techniques of big data analysis and three major pillars of math need to know to become an effective data analyst will be discussed.

     

    A brief idea about big data analytics

     

    Data analytics is a complicated process that involves separating valuable information from raw data to use that knowledge to improve planning and operation optimization decisions in a variety of industries. Many data analytics approaches have been integrated into numerous automated systems as a result of recent efforts in data analysis, particularly in the financial sector, social networks, and the travel, retail, communications, and hospitality industries. 

     

    Due to the short-term periodicity of business operations and a relatively high level of uncertainty in customer behavior in the service industries, data analytics on customer data can provide timely information on consumer behaviors, emerging needs, and dissatisfaction with service, all of which are crucial for business success.

    Understanding of These Major Topics for Data Science

     

    In this section one by one three subjects will be discussed also with the help of examples subjects will be explained.

     

    Linear Algebra

     

    It is the gist of mathematics its prior focus is to deal with vectors and those functions which are linear and it is a principal idea for all kinds of mathematics using its geometry is presented and its a fundamental idea. Moreover, it is used to solve linear equations with unknown values which helps to understand machine learning.

     

    It also helps in logic-making through a step of a series and while conducting an analysis that focuses on giving an answer to a specific problem or simplifying the problem.

     

    Example:

     

    Question: Consider the following system of linear equations:

    2x + 3y = 8

    4x - y = 2

     

    Answer:

    Now having two equations for variables x and y. Now the main objective is to calculate the value of x and y.

     

    There are different methods to solve this problem substitution method, inverse method, Cramer rule, or elimination method. We can start by eliminating one variable by adding or subtracting the equations. In this case, we can eliminate the y variable by multiplying the second equation by 3 and adding it to the first equation:

     

    2x + 3y = 8

    (3) (4x - y) = (3)(2)

    2x + 3y = 8        (i)

    12x - 3y = 6       (ii)

     

    Now, we can add the two equations together:

        (2x + 3y) = 8

    + (12x - 3y) = 6

    14x = 14

    Canceling 14 on both sides

    x = 1

     

    Now, we can substitute the value of x back into one of the original equations (let's use the first equation) to find the value of y:

     

    2(1) + 3y = 8

    2 + 3y = 8

    Subtracting 2 from both sides, we have:

     

    3y = 6

     

    Now divide 3 into both sides

    y = 2

     

    Thus, the solution is (1,2)

     

    You can also take assistance from a system of equations calculator that will allow you to solve the system of linear eqiations either with the help of elimination method or substitution method. 

     

    Probability

     

    It deals with the chances to happen something like easily you can say the possibility of a scenario which happens and making the prior decision about the prediction of the future. The two courses statistics and probability are much similar and the combined study of these two is used to get results differently. 

     

     

    Two different probabilities can be utilized to examine data sets. 

     

    The kind of probability with rules associated with it is known as classical probability. For instance, you might establish a rule that, for a website to be valid, the likelihood that a customer will purchase it must be higher than 0.33.

     

    Relative frequency:

     Relative frequency is a type of probability that examines the ratio of the occurrence of one event to all other potential outcomes. This might be used, for instance, to compare the outcome of a subset of data to the overall amount of data gathered.

     

    Example:

    Question: What is the probability of drawing a spade from the deck if you have a standard deck of 52 playing cards?

     

    Answer:

     

    Step 1:

    The number of possibilities in a standard deck of 52 cards, there are 13 spades (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King). 

    The total number of outcomes in a standard deck of 52 cards, there are 52 cards in total.

     

    Step 2:

    Calculating the probability by using the formula

    Probability = no. of possible outcomes / Total number of outcomes

    Probability of drawing a spade = 13 / 52

    Simplifying, we get:

    Probability of drawing a spade = 1 / 4

    The probability of drawing a spade from a standard deck of 52 cards is 1/4 which can also be expressed as 25%.

     

    Statistics

     

    Almost all scientific fields, including the physical and social sciences, as well as business, the humanities, government, and manufacturing, use statistics. Fundamentally, statistics is a subfield of applied mathematics that emerged from the use of mathematical techniques like calculus and linear algebra in probability theory.

     

    In actuality, statistics is the concept that by examining the traits of a smaller group of related objects or events (a sample), we can learn about the features of huge populations of objects or occurrences (a population).

     

     

    Measures of central tendency and measures of variability, which gauge various facets of a population. Descriptive statistics might be used to conclude a range of test scores gathered or the average age of persons who subscribe to a website newsletter. Based on sample data, while inferential statistics create inferences about the population. 

     

    For instance, a hypothesis about a population may be approved or denied based on a research sample using hypothesis testing is a type of inferential statistics.

     

    Example: 

    Question: Consider the following dataset of exam scores: (85, 92, 78, 92, 90, 85, 78, 85)

    Ans:

    To find the mode, we need to identify the value(s) that appear most frequently in the dataset.

    Step 1: 

    Sort the dataset in ascending order:

    (78, 78, 85, 85, 85, 90, 92, 92)

    Step 2: 

    Count the frequency of each value:

    78 appears 2 times

    85 appears 3 times

    90 appears 1 time

    92 appears 2 times

    Step 3: 

    Identify the value(s) with the highest frequency:

    In this case, the value 85 appears the most frequently with a count of 3.

    Therefore, the mode of this dataset is 85.

     

    Conclusion:

     

    In this article, the basic idea about data science and big data analytics and the name of six different techniques used in big data analytics are mentioned. Furthermore, three major subjects which have much more importance in data science are discussed with the help of examples. Hopefully, after reading this article you will have much more info about data science. 

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