• Install packages in Python using conda install
• Create, access, and modify variables
• Manipulate lists
• Use the print() function to display information

• Assignment 01 is due today! 🚨
• Assignment 02 is already online on Canvas and GitHub
• Feel free to email your assignments to me at danilo.freire@emory.edu or submit it via Canvas (hopefully it is working now!)
• We will mark them and provide feedback on your work soon

• The QTM Open House is an event where you can learn more about the QTM major
• You can meet the faculty, staff, and students
• It is this Friday, September 13th, from 1:30 to 3:30 PM at PAIS 290

• A brief overview of Matplotlib and NumPy
• NumPy (short for “Numerical Python”) is a library that provides support for large, multi-dimensional arrays and matrices
• An array is a collection of numbers that are arranged in a regular grid (vector, matrix, high-dimensional array - tensors)
• In simpler terms, NumPy arrays are a “super-powered list of numbers”
• NumPy is the backbone of many other libraries in Python, such as pandas and scikit-learn
• We will also learn about the random module, which generates random numbers

• NumPy already comes with Anaconda, so you don’t need to install it
• In case you are using a different Python distribution, you can install NumPy using conda install numpy or pip install numpy
• The alias for NumPy is np, so you can import it using import numpy as np
• The random module is part of the Python Standard Library, so you don’t need to install it
• You can just import it using import random
  • Interestingly, the random module does not have an alias 🤷🏻‍♂️

• We can use the matplotlib package to create plots
• The hist() function creates a histogram
• We can pass a list as an argument to the hist() function
• We can also customise the plot by adding labels, titles, and changing the colour (more on that later)
• You print the graph by using the show() function

• Try it yourself!
• Create a list with repeated string values (maybe repeat the movies you like a few times?) and compute your own histogram Appendix 01

• We can also create scatter plots using the scatter() function
• The scatter() function takes two lists as arguments
  • The first list contains the x-coordinates
  • The second list contains the y-coordinates
• We use them to visualise the relationship between two continuous variables
• Here, we will use the xlabel() and ylabel() functions to label the axes

• As usual, we start by importing the libraries we will use
• NumPy has several functions
• For instance, \(ln(x), e^x, sin(x), cos(x), \sqrt{x}\)
• Remember that exponentiation in Python is done using **, not ^

• You can check a list of NumPy functions here (there are many!)

• Create an array from a list

• \(a = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}\)

• \(b = \begin{pmatrix} 0 \\ 1 \\ 0\end{pmatrix}\)

• \(c = \begin{pmatrix} 10 \\ 100 \\ 1000 \\ 2000 \\ 5000 \end{pmatrix}\)

• \(d = \begin{pmatrix} 4 \\ 2 \end{pmatrix}\)

• We can perform operations with a single array and a scalar
• For instance, we can add or multiply a scalar to an array

• Add 2 to each element of \(a\)
• \(a + 2 = \begin{pmatrix} a_1 + 2 \\ a_2 + 2 \\ a_3 + 2 \end{pmatrix}\)

# Print the original array
print(vec_a)

# Adding 2 to each element of a
print(vec_a + 2)

[1 2 3]
[3 4 5]

• A scalar refers to either an int or float
• We can do many common operations with

print(vec_a * 2)
print(vec_a / 2)
print(vec_a + 2)
print(vec_a ** 2)

[2 4 6]
[0.5 1.  1.5]
[3 4 5]
[1 4 9]

\(a + b = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix} +\) \(\begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix} =\) \(\begin{pmatrix} a_1 + b_1 \\ a_2 + b_2 \\ a_3 + b_3 \end{pmatrix}\)

\(a * b = \begin{pmatrix} a_1 * b_1 \\ a_2 * b_2 \\ a_3 * b_3 \end{pmatrix}\)

• NumPy provides several functions to compute summary statistics of an array
• For instance, we can compute the mean, median, standard deviation, variance, minimum, and maximum
• We can also compute the sum, product, and cumulative sum

print(np.mean(vec_a))
print(np.std(vec_a))
print(np.min(vec_a))
print(np.median(vec_a))
print(np.max(vec_a))

2.0
0.816496580927726
1
2.0
3

• Try it yourself! Compute the mean of

\(e = \begin{pmatrix} 10 \\ 8 \\ 15 \\ 0 \\ 24 \end{pmatrix}\)

Appendix 05

• Why randomness?
  • Simulate different scenarios: high risk or low risk
  • Study properties of a complex system and/or estimator
  • In medicine, randomly assign subjects to treatment or control
  • In finance, simulate stock prices
  • In sports, simulate outcomes of games, etc

• This code creates a vector of random variables generated from a normal distribution
• It has the mean “loc” (location) and standard deviation “scale”
• The number of distinct variabels is “size”

# Generate 10 random variables from a normal distribution
# with mean 0 and standard deviation 1
randomvar_a = np.random.normal(loc=0, scale=1, size=10)
print(randomvar_a)

[-8.38647682e-01  9.71999306e-05  1.46042152e+00 -2.74959772e-01
 -2.38994851e-01  1.32189637e+00 -6.06496387e-01 -7.17636488e-01
  2.57737110e+00  7.03601606e-02]

• Today we larned to:
  • Use mathematical functions in NumPy
  • Create arrays from lists
  • Access elements of an array
  • Perform operations with a single array and a scalar
  • Perform element-by-element operations between two arrays
  • Compute summary statistics of an array
  • Generate random numbers
  • Create histograms of random variables

• In our next lecture, we will learn how to:
  • Introduce boolean types
  • Test different categories of expressions with text and numbers
  • Study if/else statements