#### 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.
Preface
Basic Packages, Functions, and Concepts
Free Chapter
Mathematical Plotting with Matplotlib
Working with Randomness and Probability
Geometric Problems
Finding Optimal Solutions
Miscellaneous Topics
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# How to do it...

Follow these steps to use Cython to greatly improve the performance of the code for generating an image of the Mandelbrot set:

1. Start a new file called cython_mandel.pyx in the mandelbrot folder. In this file, we will add some simple imports and type definitions:
# mandelbrot/cython_mandel.pyx

import numpy as np
cimport numpy as np
cimport cython
ctypedef Py_ssize_t Int
ctypedef np.float64_t Double
1. Next, we define a new version of the in_mandel routine using the Cython syntax. We add some declarations to the first few lines of this routine:
cdef int in_mandel(Double cx, Double cy, int max_iter):
cdef Double x = cx
cdef Double y = cy
cdef Double x2, y2
cdef Int i
1. The rest of the function is identical to the Python version of the function:
for i in range(max_iter):
x2 = x**2
y2 = y**2
if (x2 + y2) >= 4:
return i
...