Book Image

Applying Math with Python - Second Edition

By : Sam Morley
Book Image

Applying Math with Python - Second Edition

By: Sam Morley

Overview of this book

The updated edition of Applying Math with Python will help you solve complex problems in a wide variety of mathematical fields in simple and efficient ways. Old recipes have been revised for new libraries and several recipes have been added to demonstrate new tools such as JAX. You'll start by refreshing your knowledge of several core mathematical fields and learn about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you progress, you'll gradually get to grips with more advanced topics of calculus, probability, and networks (graph theory). Once you’ve developed a solid base in these topics, you’ll have the confidence to set out on math adventures with Python as you explore 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 (13 chapters)

Working with matrices and linear algebra

NumPy arrays also serve as matrices, which are fundamental in mathematics and computational programming. A matrix is simply a two-dimensional array. Matrices are central in many applications, such as geometric transformations and simultaneous equations, but also appear as useful tools in other areas such as statistics. Matrices themselves are only distinctive (compared to any other array) once we equip them with matrix arithmetic. Matrices have element-wise addition and subtraction operations, just as for NumPy arrays, a third operation called scalar multiplication, where we multiply every element of the matrix by a constant number, and a different notion of matrix multiplication. Matrix multiplication is fundamentally different from other notions of multiplication, as we will see later.

One of the most important attributes of a matrix is its shape, defined exactly as for NumPy arrays. A matrix with rows and columns is usually described...