book

Doing Math with Python

by Amit Saha

August 2015

Beginner

264 pages

5h 57m

English

No Starch Press

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Who Should Read This BookWhat’s in This Book?Scripts, Solutions, and Hints
Basic Mathematical OperationsLabels: Attaching Names to NumbersDifferent Kinds of NumbersWorking with FractionsComplex NumbersGetting User InputHandling Exceptions and Invalid InputFractions and Complex Numbers as InputWriting Programs That Do the Math for YouCalculating the Factors of an IntegerGenerating Multiplication TablesConverting Units of MeasurementFinding the Roots of a Quadratic EquationWhat You LearnedProgramming Challenges#1: Even-Odd Vending Machine#2: Enhanced Multiplication Table Generator#3: Enhanced Unit Converter#4: Fraction Calculator#5: Give Exit Power to the User
Understanding the Cartesian Coordinate PlaneWorking with Lists and TuplesIterating over a List or TupleCreating Graphs with MatplotlibMarking Points on Your GraphGraphing the Average Annual Temperature in New York CityComparing the Monthly Temperature Trends of New York CityCustomizing GraphsAdding a Title and LabelsCustomizing the AxesPlotting Using pyplotSaving the PlotsPlotting with FormulasNewton’s Law of Universal GravitationProjectile MotionGenerating Equally Spaced Floating Point NumbersDrawing the TrajectoryComparing the Trajectory at Different Initial VelocitiesWhat You LearnedProgramming Challenges#1: How Does the Temperature Vary During the Day?#2: Exploring a Quadratic Function Visually#3: Enhanced Projectile Trajectory Comparison Program#4: Visualizing Your Expenses#5: Exploring the Relationship Between the Fibonacci Sequence and the Golden Ratio

Finding the MeanFinding the MedianFinding the Mode and Creating a Frequency TableFinding the Most Common ElementsFinding the ModeCreating a Frequency TableMeasuring the DispersionFinding the Range of a Set of NumbersFinding the Variance and Standard DeviationCalculating the Correlation Between Two Data SetsCalculating the Correlation CoefficientHigh School Grades and Performance on College Admission TestsScatter PlotsReading Data from FilesReading Data from a Text FileReading Data from a CSV FileWhat You LearnedProgramming Challenges#1: Better Correlation Coefficient–Finding Program#2: Statistics Calculator#3: Experiment with Other CSV Data#4: Finding the Percentile#5: Creating a Grouped Frequency Table
Defining Symbols and Symbolic OperationsWorking with ExpressionsFactorizing and Expanding ExpressionsPretty PrintingPrinting a SeriesSubstituting in ValuesCalculating the Value of a SeriesConverting Strings to Mathematical ExpressionsExpression MultiplierSolving EquationsSolving Quadratic EquationsSolving for One Variable in Terms of OthersSolving a System of Linear EquationsPlotting Using SymPyPlotting Expressions Input by the UserPlotting Multiple FunctionsWhat You LearnedProgramming Challenges#1: Factor Finder#2: Graphical Equation Solver#3: Summing a Series#4: Solving Single-Variable InequalitiesHints: Handy Functions
What’s a Set?Set ConstructionChecking Whether a Number Is in a SetCreating an Empty SetCreating Sets from Lists or TuplesSet Repetition and OrderSubsets, Supersets, and Power SetsSet OperationsUnion and IntersectionCartesian ProductApplying a Formula to Multiple Sets of VariablesDifferent Gravity, Different ResultsProbabilityProbability of Event A or Event BProbability of Event A and Event BGenerating Random NumbersSimulating a Die RollCan You Roll That Score?Is the Target Score Possible?Nonuniform Random NumbersWhat You LearnedProgramming Challenges#1: Using Venn Diagrams to Visualize Relationships Between Sets#2: Law of Large Numbers#3: How Many Tosses Before You Run Out of Money?#4: Shuffling a Deck of Cards#5: Estimating the Area of a CircleEstimating the Value of Pi
Drawing Geometric Shapes with Matplotlib’s PatchesDrawing a CircleCreating Animated FiguresAnimating a Projectile’s TrajectoryDrawing FractalsTransformations of Points in a PlaneDrawing the Barnsley FernWhat You LearnedProgramming Challenges#1: Packing Circles into a Square#2: Drawing the Sierpiński Triangle#3: Exploring Hénon’s Function#4: Drawing the Mandelbrot SetThe imshow() FunctionCreating a List of ListsDrawing the Mandelbrot Set
What Is a Function?Domain and Range of a FunctionAn Overview of Common Mathematical FunctionsAssumptions in SymPyFinding the Limit of FunctionsContinuous Compound InterestInstantaneous Rate of ChangeFinding the Derivative of FunctionsA Derivative CalculatorCalculating Partial DerivativesHigher-Order Derivatives and Finding the Maxima and MinimaFinding the Global Maximum Using Gradient AscentA Generic Program for Gradient AscentA Word of Warning About the Initial ValueThe Role of the Step Size and EpsilonFinding the Integrals of FunctionsProbability Density FunctionsWhat You LearnedProgramming Challenges#1: Verify the Continuity of a Function at a Point#2: Implement the Gradient Descent#3: Area Between Two Curves#4: Finding the Length of a Curve
Things to Explore NextProject EulerPython DocumentationBooksGetting HelpConclusion
Microsoft WindowsUpdating SymPyInstalling matplotlib-vennStarting the Python ShellLinuxUpdating SymPyInstalling matplotlib-vennStarting the Python ShellMac OS XUpdating SymPyInstalling matplotlib-vennStarting the Python Shell
if __name__ == '__main__'List ComprehensionsDictionary Data StructureMultiple Return ValuesException HandlingSpecifying Multiple Exception TypesThe else BlockReading Files in PythonReading All the Lines at OnceSpecifying the Filename as InputHandling Errors When Reading FilesReusing Code
Chapter 3: Describing Data with StatisticsChapter 6: Drawing Geometric Shapes and FractalsChapter 7: Solving Calculus ProblemsAfterword

Content preview from Doing Math with Python

4Algebra and Symbolic Math with SymPy

The mathematical problems and solutions in our programs so far have all involved the manipulation of numbers. But there’s another way math is taught, learned, and practiced, and that’s in terms of symbols and the operations between them. Just think of all the xs and ys in a typical algebra problem. We refer to this type of math as symbolic math. I’m sure you remember those dreaded “factorize x³ + 3x² + 3x + 1” problems in your math class. Fear no more, for in this chapter, we learn how to write programs that can solve such problems and much more. To do so, we’ll use SymPy—a Python library that lets you write ...