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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

By : Ranja Sarkar
4.1 (7)
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A Handbook of Mathematical Models with Python

A Handbook of Mathematical Models with Python

4.1 (7)
By: Ranja Sarkar

Overview of this book

Mathematical modeling is the art of transforming a business problem into a well-defined mathematical formulation. Its emphasis on interpretability is particularly crucial when deploying a model to support high-stake decisions in sensitive sectors like pharmaceuticals and healthcare. Through this book, you’ll gain a firm grasp of the foundational mathematics underpinning various machine learning algorithms. Equipped with this knowledge, you can modify algorithms to suit your business problem. Starting with the basic theory and concepts of mathematical modeling, you’ll explore an array of mathematical tools that will empower you to extract insights and understand the data better, which in turn will aid in making optimal, data-driven decisions. The book allows you to explore mathematical optimization and its wide range of applications, and concludes by highlighting the synergetic value derived from blending mathematical models with machine learning. Ultimately, you’ll be able to apply everything you’ve learned to choose the most fitting methodologies for the business problems you encounter.
Table of Contents (16 chapters)
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1
Part 1:Mathematical Modeling
4
Part 2:Mathematical Tools
11
Part 3:Mathematical Optimization

Complex optimization algorithms

The nature of the objective function helps select the algorithm to be considered for the optimization of a given business problem. The more information that is available about the function, the easier it is to optimize the function. Of most importance is the fact that the objective function can be differentiated at any point in the search space.

Differentiability of objective functions

A differentiable objective function is one for which the derivative can be calculated at any given point in input space. The derivative (slope) is the rate of change of the function at that point. The Hessian is the rate at which the derivative of the function changes. Calculus helps optimize simple differentiable functions analytically. For differentiable objective functions, gradient-based optimization algorithms are used. However, there are objective functions for which the derivative cannot be computed, typically for very complex (noisy, multimodal, etc.) functions...

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A Handbook of Mathematical Models with Python
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