Book Image

Applying Math with Python

By : Sam Morley
Book Image

Applying Math with Python

By: Sam Morley

Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (12 chapters)

Using least squares to fit a curve to data

Least squares is a powerful technique for finding a function from a relatively small family of potential functions that best describe a particular set of data. This technique is especially common in statistics. For example, least squares is used in linear regression problems – here, the family of potential functions is the collection of all linear functions. Usually, this family of functions that we try to fit has relatively few parameters that can be adjusted to solve the problem.

The idea of least squares is relatively simple. For each data point, we compute the square of the residual – the difference between the value of the point and the expected value given a function – and try to make the sum of these squared residuals as small as possible (hence least squares).

In this recipe, we'll learn how to use least squares to fit a curve to a sample set of data.

Getting ready