MATHEMATICS IN DATA SCIENCE

BY MANASVI LOGANI

BSc(Hons)Mathematics

Indraprastha College for Women

What is Data Science?

Data Science is about extraction, preparation, analysis, visualization, and maintenance of information. It is a cross-disciplinary field which uses scientific methods and processes to draw insights from data.

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It is a multidisciplinary field that combines mathematics, statistics, and computer science.

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Purpose of Data Science

• Analyze and draw insights from the data.
• Making predictions from the data. 
• Derive conclusions from the data and using these to assist companies in making smarter business decisions.

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TOP COMPANIES REQUIRE DATA SCIENCE FOR FUNCTIONING

APPLE

AMAZON

NETFLIX

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650%

11.5 million

Growth of roles of data scientist since 2012.

Jobs will be created by 2026 according to the US Bureau of Labour Statistics.

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Mathematics for Data Science

Linear Algebra

• Linear Algebra is widely used in image recognition, text analysis and also dimensionality reduction.
• Uses the concept of matrices to store images and design algorithm for classification.

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WHAT DO YOU SEE HERE?

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XGBOOST

• It stores the numeric data in the form of Matrix to give predictions. It enables XGBOOST to process data faster and provide more accurate results.

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NEURAL NETWORKS

• A neural network is a series of algorithms that endeavors to recognize underlying relationships in a set of data through a process that mimics the way the human brain operates.
• Weights learned by a Neural Network are also stored in Matrices.

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CALCULUS

Calculus is used essentially in optimization techniques. One cannot have a deep knowledge of machine learning without calculus.

The two components of calculus:

• Differential Calculus
• Integral Calculus

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Differential Calculus

Differential Calculus studies the rate at which the quantities change.

• Derivates are used in optimization techniques where we have to find the minima in order to minimize the error function.
•  the partial derivates that are used for designing backpropagation in neural networks.
• Chain Rule is another important concept used to compute backpropagation.

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Integral Calculus

• Integral Calculus is the mathematical study of the accumulation of quantities and for finding the area under the curve. 
• Integration is most widely used in computing probability density functions and variance of the random variable.

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In the next 10 years, Data Science and Software will do more for Medicines than all of the Biological Sciences together.

-Vinod Khosla, an American Billionaire Businessman and Co-founder of Sun Microsystems 

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REFERENCES

• https://data-flair.training/blogs/data-science-projects-code/
• https://pathmind.com/wiki/neural-network
• https://www.analyticsvidhya.com/blog/2017/05/comprehensive-guide-to-linear-algebra/

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THANK YOU!

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