What this book covers
This book is split into two parts:
Part 1 (chapters 1 to 6) covers relatively advanced methods in interactive numerical computing, high-performance computing, and data visualization.
Part 2 (chapters 7 to 15) introduces standard methods in data science and mathematical modeling. Many of these methods are applied to real-world data.
Part 1 – Interactive Computing with Jupyter
Chapter 1, A Tour of Interactive Computing with Jupyter and IPython, contains a brief introduction to data analysis and numerical computing with IPython and Jupyter. It not only covers common packages such as Python, NumPy, pandas, and Matplotlib, but also advanced IPython/Jupyter topics such as interactive widgets in the Notebook, custom magic commands, configurable IPython extensions, and custom Jupyter kernels.
Chapter 2, Best Practices in Interactive Computing, details best practices to write reproducible, high-quality code: task automation, version control with Git, workflows with IPython and Jupyter, unit testing, continuous integration, debugging, and other related topics. The importance of these subjects in computational research and data analysis cannot be overstated.
Chapter 3, Mastering the Jupyter Notebook, covers topics related to the Jupyter Notebook, notably the Notebook format, notebook conversions, and interactive widgets.
Chapter 4, Profiling and Optimization, covers methods to make your code faster and more efficient: CPU and memory profiling in Python, advanced optimization techniques with NumPy (including large array manipulations), and memory mapping of huge arrays. These techniques are essential for big data analysis.
Chapter 5, High-Performance Computing, covers techniques to make your code much faster: code acceleration with Numba and Cython, wrapping C libraries in Python with ctypes, parallel computing with IPython and Dask, OpenMP, and General-Purpose Computing on Graphics Processing Units (GPGPU) with CUDA. The chapter ends with an introduction to the Julia language, a high-performance numerical computing programming language that can be used in the Jupyter Notebook.
Chapter 6, Data Visualization, introduces several visualization or interactive visualization libraries, such as matplotlib, seaborn, bokeh, D3, Altair, and others.
Part 2 – Standard Methods in Data Science and Applied Mathematics
Chapter 7, Statistical Data Analysis, covers methods for getting insights into data. It introduces classic frequentist and Bayesian methods for hypothesis testing, parametric and nonparametric estimation, and model inference. The chapter leverages Python libraries such as pandas, SciPy, statsmodels, and PyMC. The last recipe introduces the statistical language R, which can be easily used in the Jupyter Notebook.
Chapter 8, Machine Learning, covers methods to learn and make predictions from data. Using the scikit-learn Python package, this chapter illustrates fundamental data mining and machine learning concepts such as supervised and unsupervised learning, classification, regression, feature selection, feature extraction, overfitting, regularization, cross-validation, and grid search. Algorithms addressed in this chapter include logistic regression, Naive Bayes, K-nearest neighbors, support vector machines, random forests, and others. These methods are applied to various types of datasets: numerical data, images, and text.
Chapter 9, Numerical Optimization, covers minimizing and maximizing mathematical functions. This topic is pervasive in data science, notably in statistics, machine learning, and signal processing. This chapter illustrates a few root-finding, minimization, and curve-fitting routines with SciPy.
Chapter 10, Signal Processing, covers extracting relevant information from complex and noisy data. These steps are sometimes required prior to running statistical and data mining algorithms. This chapter introduces basic signal processing methods such as Fourier transforms and digital filters.
Chapter 11, Image and Audio Processing, covers signal processing methods for images and sounds. It introduces image filtering, segmentation, computer vision, and face detection with scikit-image and OpenCV. It also presents methods for audio processing and synthesis.
Chapter 12, Deterministic Dynamical Systems, describes the dynamical processes underlying particular types of data. It illustrates simulation techniques for discrete-time dynamical systems, as well as for ordinary differential equations and partial differential equations.
Chapter 13, Stochastic Dynamical Systems, describes the dynamical random processes underlying particular types of data. It illustrates simulation techniques for discrete-time Markov chains, point processes, and stochastic differential equations.
Chapter 14, Graphs, Geometry, and Geographic Information Systems, covers analysis and visualization methods for graphs, flight networks, road networks, maps, and geographic data.
Chapter 15, Symbolic and Numerical Mathematics, introduces SymPy, a computer algebra system that brings symbolic computing to Python. The chapter ends with an introduction to Sage, another Python-based system for computational mathematics.
