Master Math by Coding in Python

Learn to perform basic arithmetic in Python as a calculator in a Jupyter notebook, using the asterisk for multiplication, the forward slash for division, and parentheses for order of operations.

Learn how to use variables as placeholders for numbers in Python, assign and reassign values, and print multiple results in a cell to see how equations behave.

Explore printing equations in a Jupyter notebook by using IPython display and math, combine Python strings, and apply latex coding for fractions to format clear, math-ready outputs.

Learn how to use comments in Python to document and organize code for readability, either on a line or after code, and how the Ctrl+/ shortcut toggles them.

Master math by coding in Python covers exponents and the law of exponents, using Python and LaTeX to print and explore powers clearly, including order of operations.

Master how to use for loops in Python to compute powers, including range basics and proper indentation. Use a base variable to calculate base^i from 0 to 9.

Master the order of operations in Python, including spacing, parentheses, and the please excuse my dear Aunt Sally mnemonic, with multiplication and division before addition and subtraction.

Explore how to test inequalities in Python and work with the boolean data type, including greater than, less than, greater than or equal to, and equality, using true/false values.

Master python if statements and logical operators like and or, learn elif and else, and see examples that teach boolean conditions, indentation, and printing.

Explain the absolute value concept as distance from zero, demonstrate using Python's abs, print results, and practice with for loops and if statements in a hands-on coding exercise.

Learn how the modulus, or remainder after division, is used in Python to determine odd or even numbers by looping through minus five to plus five and printing results.

Learn to create and call Python functions with def, accept interactive user input, and print division results with remainder using the modulus operator and string formatting.

Create three Python functions that take inputs x and y and a switch to compute either x to the power of y or x divided by y, with error handling.

Learn to build an interactive Python function, guess the number, using random integers and a while loop to guide the user with higher or lower hints, starting with planning comments.

Join the arithmetic bug hunt to practice debugging Python code, fixing type and formatting errors, imports, and control-flow issues while learning how small changes affect output.

Learn to use the sympy Python module for symbolic math, create symbol variables, print expressions with display, compare symbolic vs numeric representations such as numpy, and introduce LaTeX formatting.

Explore how LaTeX coding integrates with Python to print mathematical expressions using display and math, including Greek letters, subscripts, superscripts, fractions, and markdown in notebooks.

Explore how to use the sympy module with latex in Python notebooks, creating symbolic variables (including Greek letters), printing equations, and performing substitutions with subs and dictionaries.

Explore f-strings in Python, learn basic usage with variables, compare to percent formatting, and see how to embed f-strings with latex, including handling braces and readability.

Explore the law of exponents using SymPy and Python to simplify expressions with the same base, show multiplication and division rules, and render results with LaTeX.

Fix a series of sympy and latex bugs by correcting imports, latex conversion, and Python syntax. Learn to use display and subs to render mathematical expressions clearly.

Explore Python data types through numbers and strings, including integers, floats, and string operations like concatenation and replication. Convert between strings and numbers using int, float, and str.

Investigate lists and numpy arrays in Python, highlighting differences in concatenation and elementwise operations, and practice converting lists to arrays and inspecting elements with for loops.

Explore algebra by solving for x with sympy in python, including single and multi-variable equations, homogeneous forms, lists and loops, and imaginary and complex numbers.

Three progressively harder exercises guide you to solve for q in Python using SymPy, comparing sympify, simplify, and cancel, and verifying results by substitution and algebraic simplification.

Learn how to expand terms with Python and sympy, apply the distributive property, work with symbolic variables like x and y, and render results with LaTeX and display.

Learn to create and index matrices in Python with NumPy, explore rows and columns, 0-based indexing, use zeros arrays and for loops, and generate a checkerboard pattern with latex.

Build a 10 by 10 multiplication matrix in Python using for loops and correct indexing, then convert the numpy result to a sympy object for latex display.

Explore the associative, commutative, and distributive properties with numeric and symbolic examples, then verify them in Python using the SymPy toolbox.

Master lists in Python by creating and slicing them, using zero-based indexing to access elements, and iterating with for loops. Explore lists of numbers, strings, and lists, including SymPy expressions.

Master indexing and slicing in Python by converting ranges to lists, accessing elements with zero-based indices, using the colon syntax and steps, and reversing with [:: -1].

The greatest common denominator, also called the greatest common factor, is the largest integer that divides two numbers without remainder; learn examples and how to reduce fractions with Python's math.gcd.

Demonstrate the greatest common denominator with symbolic variables in sympy to prove gcd(CA, CB) = C gcd(A,B), then build a 10x15 matrix and fill gcd(i+1, j+1) via a loop.

Learn to create and access Python dictionaries with dict function, keys, and values, getting items and looping over keys. Group equations by X and Y and solve with sympy.

Explore prime factorization and implement it in python using sympy's factorint. Learn how dictionaries store prime factors, distinguish primes from composites, and print factor lists.

Learn to solve inequalities with Python using SimPy, including representing infinity, handling two-term and quadratic inequalities, and verifying results such as X>2 and X>=22/7.

Explore polynomials in Python by adding polynomials with SymPy, align like terms by degree, and display results with LaTeX and coeffs, inspecting poly objects.

Multiply polynomials in Python by expanding terms, applying the law of exponents, and using SymPy to expand, print, and compare product expansion with separate substitutions.

Divide polynomials in python using sympy, expanding and simplifying to show how computers solve polynomial division and an exercise finding y between 5 and 15.

Learn to factor polynomials with Python and sympy, from simple x squared plus four x plus three to multi-variable expressions, and identify factorable cases with the factor function.

Jump into a bug hunt for algebra in Python, running and debugging code cells, fixing import errors and type issues, and exploring sympy, math, and numpy.

Explore plotting coordinates on a plane with Python and matplotlib, building intuition through single and multiple point graphs, a grid, axis limits, and legends.

Apply your Python plotting skills to plot y = x^2 - 3x for integer x from -10 to 11, with axes labeled. Practice plotting points as dots.

Plot lines in Python by connecting two points using start and end coordinates with matplotlib. Define lines with two points, specify x and y coordinates, adjust color and line width.

Learn to plot lines in Python using slope-intercept form y = mx + b with matplotlib, handling list vs array data, and add a legend for multiple lines.

Learn that a rational function is a ratio of polynomials and plot it in Python using numpy and matplotlib, adjusting resolution with linspace and x ranges.

Master math by coding in Python shows how to plot symbolic functions with the sympy module, compare with matplotlib, and adjust axes, colors, legends, and latex labels for clear visualization.

Define the function y = x/(x^2 - a) in Sympy, substitute a values 1–4 to generate multiple plotted lines with a legend, and distinguish lines using random colors.

This lecture examines accountability in online learning and its contrast with traditional classrooms. It explains how learners rely on self-motivation to maintain consistent progress and discusses practical strategies.

Map matrix values to colors to create images from matrices in Python using NumPy and Matplotlib, displaying pixels with imshow and adjusting the color map.

Create a 10 by 10 checkerboard from a matrix using (-1)^(i+j) in python, visualize with imshow in greyscale, and adjust tick_params to hide labels while keeping tick marks.

Learn how to draw patches with polygons in Python using matplotlib's Polygon, specify points as x,y pairs, and customize colors and transparency to create shapes like triangles and hobbit houses.

Export Python figures with savefig, saving as PNG or PDF for crisp or scalable results. Adjust figure size, save order, and options like orientation or transparency to tailor exported graphics.

Develop plotting and debugging skills in Python by guiding students through a hands-on graphing bug hunt. Fix common mistakes in Matplotlib plots, legends, array indexing, and text annotations.

Explore summation and products in algebra using Python, including the cumulative sum and list basics with NumPy. Learn how to compute sums with sum and prod, and to plot results.

Explore the discrete difference operator, a discrete derivative for time series, compute y(t)=x(t+1)−x(t), and illustrate first and second order differences in python with numpy.

Learn how polynomials have roots by setting the polynomial equal to zero, identify coefficients and the variable, and compute roots with numpy and sympy while noting computer rounding error.

Explore the fundamental theorem of algebra by generating degree n polynomials in Python, counting their roots with numpty, and confirming that a degree n polynomial has n roots.

Explore the quadratic equation, a degree-2 polynomial, solved in Python with the quadratic formula using A, B, and C by a function that returns the two solutions.

Explore complex numbers and the imaginary unit in Python, learn to represent i or j, and add and subtract complex numbers by combining real and imaginary parts.

Multiply complex numbers using the complex conjugate, where z times its conjugate equals a squared plus b squared, with a as the real part and b as the imaginary part.

Learn to divide complex numbers using the conjugate trick, turning the denominator real, and apply this in Python with numpy and sympy while breaking long expressions into readable lines.

Explore the view of complex numbers by plotting them on the complex plane, using the real part on the x-axis and the imaginary on the y-axis in Python with Matplotlib.

Explore the quadratic equation with complex numbers by separating the real and imaginary parts and plotting their magnitude across varying B and C.

Learn how to create and plot the unit circle in Python using cosine and sine, with numpy pi, and plot with matplotlib while setting square axes and adding axis labels.

Explore the natural exponent e^x and natural logarithm ln x, and visualize their inverse relationship using Python with numpy and matplotlib.

Learn the gaussian function and its bell curve, including the full width at half maximum H. Find T values for a given Y in Python using logarithms and exponentials.

Generate a color-mapped image of a family of gaussians along a time axis, with color representing amplitude and each row using a distinct full width at half maximum.

Explore the complex roots of unity and plot them on the unit circle using Z = e^{2 pi i k / N}, linking algebra to Python visualizations and signal processing.

Compare linearly spaced and logarithmically spaced numbers, and show how linear functions approximate nonlinear ones at close boundaries using Python with NumPy and Matplotlib.

Explore how the logarithm converts multiplication to addition, division to subtraction, and exponentiation to multiplication, with Python demonstrations and LaTeX formatting to visualize these properties.

Learn arithmetic and geometric sequences and how to convert their formulas into Python code. Compare parameter effects, index the nth term, and plot sequences to visualize growth.

Explore orders of magnitude and scientific notation, and learn how to print and decode scientific notation in Python using string formatting, E notation, and precision control.

Identify maxima and minima of functions with numpy and locate their positions for plotting, then find peaks with scipy.signal.find_peaks on minus cosine x minus sqrt x over 0 to 12π.

Explore even and odd functions through visual intuition and Python coding, using NumPy and matplotlib to test definitions and confirm cosine is even and sine is odd.

Engage in a hands-on Python bug hunt, debugging syntax, imports, and math functions while exploring NumPy, SymPy, and Matplotlib to validate complex plotting and polynomial roots.

Learn to graph parabolas using Python by applying the general parabola formula, plotting vertical and horizontal forms, and visualizing the vertex, focus, and directrix.

Create contours from meshes in Python using NumPy and Matplotlib to build a grid, visualize with pcolormesh and imshow, and explore a two-dimensional Gaussian smoothing kernel.

Explore circle graphs in Python using mesh grids to plot circles. Visualize circle centers, radii, contours, and dynamic axis scaling.

Demonstrate the ellipse formula by plotting ellipses with radii a and b around center h, k using a mesh grid and contour plots, and compare to circles when a=b.

Explore hyperbolas through their formula and visualize them in Python using the Numpty and Matplotlib pipeline modules, plotting centered hyperbolas with parameters a, b, h, k.

Master math by coding in Python guides a step-by-step conic bug hunt: fix gaussian formula, draw a circle with meshgrid, center an ellipse, and correct the hyperbola.

Learn to generate random numbers in Python using NumPy and matplotlib, compare normal and uniform distributions, and adjust centers and minimum and maximum values through shifting and stretching.

Learn to generate a normal distribution in Python by scaling and shifting random numbers to achieve a mean of 15 and a standard deviation of 4.3, with normalization.

Plot unit vectors on the unit circle with random phase angles in Python. Compare normally distributed and uniform distributions and convert angles to radians (and degrees) for broader understanding.

Explore radians and degrees, their relationship on the unit circle, and use simple conversion formulas in Python with numpy.pi to switch between these angle measures and wrap them with modulus.

Create a Python function that converts between radians and degrees, handles invalid units, and plots a vector with a reference along x axis showing the angle in radians and degrees.

Master the Pythagorean theorem in Python by building and drawing a right triangle from first principles. Apply the theorem to complex numbers to compute magnitude and angle.

Explore plotting sine, cosine, and tangent in Python, and learn how resolution and sampling affect smoothness, including tan as sin over cos and cos squared plus sin squared equals one.

Translate two trig formulas into Python plots, explore embedding sine and cosine, plot the unit circle arc, and use symbolic pi for clear theta labeling.

Explore Euler's formula and its identity, linking e^(i k) to cosine k plus i sine k on the unit circle, with magnitude and angle in the plane.

Learn to implement a function that accepts cosine and sine parts, computes magnitude and angle, and plots m e^{i theta} on a polar plot with adjustable theta grids.

Create a randomized exploding oilor visualization in Python by plotting 200 vectors using Euler's formula in polar form, with color probabilities for pink, purple, and green.

Plot x = cos(theta) * r1 and y = sin(theta) * r2 using random r1, r2. Display r1 and r2 to two decimals and connect start to end with np.append.

Engage in a hands-on Python bug hunt on trig graphs, NumPy plots, and unit vectors. Fix radians to degrees, polar plots, spirals, and Euler's formula demonstrations.

Plot asteroid radial curves with x = a cos(t^3) and y = a sin(t^3) in Python, then present nine variants in a 3×3 subplot grid using ravel indexing.

Explore rose curves from the trigonometric formula and the K parameter that determines petals (even 2K, odd K). Implement nine curves in a 3x3 grid using Python, NumPy, and matplotlib.

Derive and plot a squircle by converting x^4 + y^4 = a^4 from Wolfram Math World into x,y coordinates, set a=1, and visualize the two ± solutions in Python.

Explore the logarithmic spiral and its natural occurrences, then build and visualize it in Python by combining cosine with an exponential decay and adjustable parameters.

Explore the logistic map and its chaotic, bifurcating dynamics by plotting the unique values from the last 10 percent of x as r runs from 1 to 4 in Python.