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Master Math by Coding in Python


Introductions and installations :
(Important) How to get the most out of this course!
What are your goals for this course?
2 questions
Using Python through Jupyter (installing Anaconda)
Using Python online (no installation!)
Getting help in Python

Arithmetic :
Python code for this section
Addition, subtraction, multiplication, division
Using variables in place of numbers
Printing out equations in Jupyter notebook
Writing comments in Python
Exponents (powers)
Using for-loops to compute powers
Order of operations
Testing inequalities and Boolean data type
Using if-statements and logical operators
Absolute value
Remainder after division (modulus)
Create interactive math functions, part 1
Create interactive math functions, part 2
Create interactive math functions, part 3
Arithmetic bug hunt!

Introduction to Sympy and LaTeX :
Python code for this section
Intro to Sympy, part 1
Intro to LaTeX
Intro to Sympy, part 2
Example: Use Sympy to understand the law of exponents
Sympy/Latex bug hunt!

Algebra 1 :
Python code for this section
Solving for x
Solving for x: exercises
Expanding terms
Creating and accessing matrices with numpy
Exercise: Create a multiplication table
Associative, commutative, and distributive properties
Creating and working with Python lists
More on "slicing" in Python
Greatest common denominator
Greatest common denominator: exercises
Introduction to Python dictionaries
Prime factorization
Solving inequalities
Adding polynomials
Multiplying polynomials
Dividing by polynomials
Factoring polynomials
Algebra 1 bug hunt!

Graphing and visualization :
Python code for this section
Plotting coordinates on a plane
Plotting coordinates on a plane: exercise
Graphing lines part 1: start/end notation
Graphing lines part 2: slope-intercept form
Graphing rational functions
Plotting with Sympy
Plotting with Sympy: exercises
Making images from matrices
Images from matrices: exercise
Drawing patches with polygons
Exporting graphics as pictures
Graphing bug hunt!

Algebra 2 :
Python code for this section
Summation and products
Differences (discrete derivative)
Roots of polynomials
Roots of polynomials: exercise
The quadratic equation
Complex numbers: addition and subtraction
Complex numbers: conjugate and multiplication
Complex numbers: division
Graphing complex numbers
Revisiting the quadratic equation with complex numbers
The unit circle
Natural exponent and logarithm
Graphing the complex roots of unity
Log-spaced and linearly spaced numbers
Arithmetic and geometric sequences
Orders of magnitude and scientific notation
Maxima and minima of functions
Even and odd functions
Algebra 2 bug hunt!

Graphing conic sections :
Python code for this section
Graphing parabolas
Creating contours from meshes in Python
Graphing circles
Graphing ellipses
Graphing hyperbolas
Conic bug hunt!

Trigonometry :
Python code for this section
Introduction to random numbers
Introduction to random numbers: exercise
Exercise: Plotting random phase angles
Converting between radians and degrees
Converting angles: exercise
The Pythagorean theorem
Graphing resolution for sine, cosine, and tangent
Graphing and resolution: Exercise
Euler's formula
Euler's formula: exercise
Exercise: random exploding Euler
Exercise: random snakes with cosine and sine
Trigonometry bug hunt!

Calculus :
Python code for this section
Mathematical proofs vs. intuition with examples
Computing limits of a function
Computing limits: exercise
Piecewise functions
Derivatives of polynomials
Derivatives of polynomials: exercise
Derivatives of trig functions
Derivatives of trig functions: exercise
Graphing a function tangent line
Graphing tangent lines: exercise
Finding critical points
Finding critical points: exercise
Partial derivatives
Indefinite and definite integrals
Exercise: The fundamental theorem of calculus
Area between two curves
Area between two curves: exercise
Calculus bug hunt!

Linear algebra :
Python code for this section
Row and column vectors
Adding and scalar-multiplying vectors
The dot product
Dot product application: Correlation coefficient
The outer product
Matrix multiplication
Transposing vectors and matrices
Various special matrices
Matrix inverse
Matrix pseudoinverse: exercise
Solving a system of equations
Visualizing matrix-vector multiplication
Eigenvalues and eigenvectors
Eigendecomposition: Exercise
Singular value decomposition
SVD of Einstein: exercise
Linear algebra BUG HUNT!

Probabilities and histograms :
Python codes for this section
Histograms and probability densities
Probability exercise: math functions
Virtual coin tosses
Exercise: Virtual weighted dice
Building distributions from random numbers
Exercise: Normalize any distribution to Gaussian
The central limit theorem
Exercise: the central limit theorem
Joint probability distributions
Probability bug hunt!

Bonus section :
Join the community!
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