Python for Scientific Computing and Artificial Intelligence

Python for Scientific Computing and Artificial Intelligence is split into 3 parts: in Section 1, the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2, the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally, in Section 3, the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI).This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modeling. Features: • No prior experience of programming is required.• Online GitHub repository available with codes for readers to practice.• Covers applications and examples from biology, chemistry, computer science, data science, electrical and mechanical engineering, economics, mathematics, physics, statistics and binary oscillator computing. • Full solutions to exercises are available as Jupyter notebooks on the Web.In 2022, Stephen Lynch was named a National Teaching Fellow, which celebrates and recognises individuals who have made an outstanding impact on student outcomes and teaching in higher education. He won the award for his work in programming in the STEM subjects, research feeding into teaching, and widening participation (using experiential and object-based learning). Although educated as a pure mathematician, Stephen's many interests now include applied mathematics, cell biology, electrical engineering, computing, neural networks, nonlinear optics and binary oscillator computing, which he co-invented with a colleague. He has authored 2 international patents for inventions, 8 books, 4 book chapters, over 40 journal articles, and a few conference proceedings. Stephen is a Fellow of the Institute of Mathematics and Its Applications (FIMA) and a Senior Fellow of the Higher Education Academy (SFHEA). This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling. Cover 1 Half Title 2 Series Page 3 Title Page 4 Copyright Page 5 Dedication 6 Contents 8 Foreword 14 Preface 16 SECTION I: An Introduction to Python 22 CHAPTER 1: The IDLE Integrated Development Learning Environment 24 1.1. INTRODUCTION 25 1.1.1. Tutorial One: Using Python as a Powerful Calculator (30 Minutes) 26 1.1.2. Tutorial Two: Lists (20 Minutes) 28 1.2. SIMPLE PROGRAMMING IN PYTHON 29 1.2.1. Tutorial Three: Defining Functions (30 Minutes) 30 1.2.2. Tutorial Four: For and While Loops (20 Minutes) 32 1.2.3. Tutorial Five: If, elif, else constructs (10 Minutes) 32 1.3. THE TURTLE MODULE AND FRACTALS 32 CHAPTER 2: Anaconda, Spyder and the Libraries NumPy, Matplotlib and SymPy 42 2.1. A TUTORIAL INTRODUCTION TO NUMPY 44 2.1.1. Tutorial One: An Introduction to NumPy and Arrays (30 Minutes) 44 2.2. A TUTORIAL INTRODUCTION TO MATPLOTLIB 46 2.2.1. Tutorial Two: Simple Plots using the Spyder Editor Window (30 minutes) 46 2.3. A TUTORIAL INTRODUCTION TO SYMPY 49 2.3.1. Tutorial Three: An Introduction to SymPy (30 Minutes) 49 CHAPTER 3: Jupyter Notebooks and Google Colab 54 3.1. JUPYTER NOTEBOOKS, CELLS, CODE AND MARKDOWN 54 3.2. ANIMATIONS AND INTERACTIVE PLOTS 58 3.3. GOOGLE COLAB AND GITHUB 62 CHAPTER 4: Python for AS-Level (High School) Mathematics 66 4.1. AS-LEVEL MATHEMATICS (PART 1) 67 4.2. AS-LEVEL MATHEMATICS (PART 2) 71 CHAPTER 5: Python for A-Level (High School) Mathematics 82 5.1. A-LEVEL MATHEMATICS (PART 1) 83 5.2. A-LEVEL MATHEMATICS (PART 2) 89 SECTION II: Python for Scientific Computing 100 CHAPTER 6: Biology 102 6.1. A SIMPLE POPULATION MODEL 102 6.2. A PREDATOR-PREY MODEL 105 6.3. A SIMPLE EPIDEMIC MODEL 108 6.4. HYSTERESIS IN SINGLE FIBER MUSCLE 110 CHAPTER 7: Chemistry 116 7.1. BALANCING CHEMICAL-REACTION EQUATIONS 116 7.2. CHEMICAL KINETICS 118 7.3. THE BELOUSOV-ZHABOTINSKI REACTION 120 7.4. COMMON-ION EFFECT IN SOLUBILITY 122 CHAPTER 8: Data Science 128 8.1. INTRODUCTION TO PANDAS 128 8.2. LINEAR PROGRAMMING 131 8.3. K-MEANS CLUSTERING 136 8.4. DECISION TREES 140 CHAPTER 9: Economics 146 9.1. THE COBB-DOUGLAS QUANTITY OF PRODUCTION MODEL 147 9.2. THE SOLOW-SWAN MODEL OF ECONOMIC GROWTH 149 9.3. MODERN PORTFOLIO THEORY (MPT) 151 9.4. THE BLACK-SCHOLES MODEL 154 CHAPTER 10: Engineering 160 10.1. LINEAR ELECTRICAL CIRCUITS AND THE MEMRISTOR 160 10.2. CHUA'S NONLINEAR ELECTRICAL CIRCUIT 163 10.3. COUPLED OSCILLATORS: MASS-SPRING MECHANICAL SYSTEMS 165 10.4. PERIODICALLY FORCED MECHANICAL SYSTEMS 167 CHAPTER 11: Fractals and Multifractals 174 11.1. PLOTTING FRACTALS WITH MATPLOTLIB 174 11.2. BOX-COUNTING BINARY IMAGES 179 11.3. THE MULTIFRACTAL CANTOR SET 181 11.4. THE MANDELBROT SET 183 CHAPTER 12: Image Processing 188 12.1. IMAGE PROCESSING, ARRAYS AND MATRICES 189 12.2. COLOR IMAGES 190 12.3. STATISTICAL ANALYSIS ON AN IMAGE 191 12.4. IMAGE PROCESSING ON MEDICAL IMAGES 193 CHAPTER 13: Numerical Methods for Ordinary and Partial Differential Equations 198 13.1. EULER'S METHOD TO SOLVE IVPS 199 13.2. RUNGE KUTTA METHOD (RK4) 200 13.3. FINITE DIFFERENCE METHOD: THE HEAT EQUATION 202 13.4. FINITE DIFFERENCE METHOD: THE WAVE EQUATION 205 CHAPTER 14: Physics 212 14.1. THE FAST FOURIER TRANSFORM 213 14.2. THE SIMPLE FIBER RING (SFR) RESONATOR 215 14.3. THE JOSEPHSON JUNCTION 217 14.4. MOTION OF PLANETARY BODIES 219 CHAPTER 15: Statistics 224 15.1. LINEAR REGRESSION 224 15.2. MARKOV CHAINS 228 15.3. THE STUDENT T-TEST 231 15.4. MONTE-CARLO SIMULATION 235 SECTION III: Artificial Intelligence 242 CHAPTER 16: Brain Inspired Computing 244 16.1. THE HODGKIN-HUXLEY MODEL 245 16.2. THE BINARY OSCILLATOR HALF-ADDER 248 16.3. THE BINARY OSCILLATOR SET RESET FLIP-FLOP 252 16.4. REAL-WORLD APPLICATIONS AND FUTURE WORK 255 CHAPTER 17: Neural Networks and Neurodynamics 262 17.1. HISTORY AND THEORY OF NEURAL NETWORKS 262 17.2. THE BACKPROPAGATION ALGORITHM 266 17.3. MACHINE LEARNING ON BOSTON HOUSING DATA 268 17.4. NEURODYNAMICS 271 CHAPTER 18: TensorFlow and Keras 276 18.1. ARTIFICIAL INTELLIGENCE 277 18.2. LINEAR REGRESSION IN TENSORFLOW 278 18.3. XOR LOGIC GATE IN TENSORFLOW 280 18.4. BOSTON HOUSING DATA IN TENSORFLOW AND KERAS 282 CHAPTER 19: Recurrent Neural Networks 288 19.1. THE DISCRETE HOPFIELD RNN 288 19.2. THE CONTINUOUS HOPFIELD RNN 291 19.3. LSTM RNN TO PREDICT CHAOTIC TIME SERIES 294 19.4. LSTM RNN TO PREDICT FINANCIAL TIME SERIES 299 CHAPTER 20: Convolutional Neural Networks, TensorBoard and Further Reading 306 20.1. CONVOLVING AND POOLING 306 20.2. CNN ON THE MNIST DATASET 309 20.3. TENSORBOARD 311 20.4. FURTHER READING 313 CHAPTER 21: Answers and Hints to Exercises 320 21.1. SECTION 1 SOLUTIONS 320 21.2. SECTION 2 SOLUTIONS 324 21.3. SECTION 3 SOLUTIONS 327 Index 330 Python;,Scientific,Computation;,High,School,Mathematics;,chemistry;,economics;,mathematics;,physics;,statistics;,electrical,and,mechanical,engineering;,biology;,data,science;,computer,science;,binary,oscillator,computing Python,Scientific Computation,High School Mathematics,chemistry,economics,mathematics,physics,statistics,electrical and mechanical engineering,biology,data science,computer science,binary oscillator computing Python for Scientific Computing and Artificial Intelligence is split into 3 parts: in Section 1, the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2, the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally, in Section 3, the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI). This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling. Features : No prior experience of programming is required. Online GitHub repository available with codes for readers to practice. Covers applications and examples from biology, chemistry, computer science, data science, electrical and mechanical engineering, economics, mathematics, physics, statistics and binary oscillator computing. Full solutions to exercises are available as Jupyter notebooks on the Web. Support Material GitHub Repository of Python Files and Notebooks:https://github.com/proflynch/CRC-Press/ Solutions to All Exercises: Section 1: An Introduction to Python:https://drstephenlynch.github.io/webpages/Solutions_Section_1.html Section 2: Python for Scientific Computing:https://drstephenlynch.github.io/webpages/Solutions_Section_2.html Section 3: Artificial Intelligence:https://drstephenlynch.github.io/webpages/Solutions_Section_3.html Python for Scientific Computing and Artificial Intelligence is split into 3 parts: in Section 1, the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2, the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally, in Section 3, the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI).This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling.Features: No prior experience of programming is required Online GitHub repository available with codes for readers to practice Covers applications and examples from biology, chemistry, computer science, data science, electrical and mechanical engineering, economics, mathematics, physics, statistics and binary oscillator computing Full solutions to exercises are available as Jupyter notebooks on the Web Support MaterialGitHub Repository of Python Files and Notebooks: https://github.com/proflynch/CRC-Press/Solutions to All Exercises:Section 1: An Introduction to Python: https://drstephenlynch.github.io/webpages/Solutions_Section_1.htmlSection 2: Python for Scientific Computing: https://drstephenlynch.github.io/webpages/Solutions_Section_2.htmlSection 3: Artificial Intelligence: https://drstephenlynch.github.io/webpages/Solutions_Section_3.html "Python for Scientific Computation and Artificial Intelligence is split into 3 parts: in Section 1, the reader is introduced to the Python programming language and shown how Python can aid in the understanding of advanced High School Mathematics. In Section 2, the reader is shown how Python can be used to solve real-world problems from a broad range of scientific disciplines. Finally, in Section 3, the reader is introduced to neural networks and shown how TensorFlow (written in Python) can be used to solve a large array of problems in Artificial Intelligence (AI). This book was developed from a series of national and international workshops that the author has been delivering for over twenty years. The book is beginner friendly and has a strong practical emphasis on programming and computational modelling. Features: No prior experience of programming is required. Online GitHub repository available with codes for readers to practice. Covers applications and examples from biology, chemistry, computer science, data science, electrical and mechanical engineering, economics, mathematics, physics, statistics and binary oscillator computing. Full solutions to exercises are available as Jupyter notebooks on the Web"-- Provided by publisher