#!/usr/bin/env python
# coding: utf-8

# # Exercises for day 1a
# 
# You will be working on a series of exercises for the material covered in lecture 1a. As a reminder, we discussed programming languages and how Python/Jupyter can be used as a powerful calculator.
# 
# The first set of exercises will focus on how to use Python/Jupyter as a calculator.
# 
# The following will be useful:
# - Jupyter consists of a series of cells
# - Use shift + enter to run a cell
# - Remember the order of operations!

# ## Exercise 1
# 
# We will start simple. Calculate the following quantities _using Jupyter_, one per cell:
# - 10 + 20
# - 72 - 123
# - 23 * 67
# - 90 / 30
# - 90 / 27
# - 90 // 27
# 
# Remember to use _shift + enter_ to run cells

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# ## Exercise 2
# 
# Now that you're used to simple arithmetic, we'll make things a bit harder. Python/Jupyter executes statements like `1 + 2 * 3` in a specific order. This is called the _order of operations_. 
# 
# The order of operation is very important! They can change the results dramatically.
# 
# Compute the following quantities by hand. Then, use Jupyter to check if you got the order of operations correct.
# - 1 + 2 * 3
# - 1 * 2 + 3
# - 1 / 2 + 3
# - 1 - 2 * 3
# - 1 * 2 - 3
# 
# Now do the following:
# - 10 * 23 / 5
# - (1 + 2) * 3
# - 1 + (2 * 3)
# - 12 * 5 / 4
# - 12 * 5 // 7
# 
# Remember to use _shift + enter_ to run cells

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# ## Exercise 3
# 
# Beyond addition, subtraction, multiplication, and division, there are other, more complex operations. We will first review exponentiation.
# 
# The _syntax_ for exponentiation is as `a ** b`. IT IS NOT THE `^`!
# 
# Compute the following quantities by hand. Then, use Jupyter to check if you got them correct:
# - 2 ** 2
# - 2 ** 3
# - 5 ** 2
# - 10 ** 5
# - 25 ** 0.5
# - 3 ** -1
# 
# Remember to use _shift + enter_ to run cells

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# ## Exercise 4
# 
# In Python, there are some _invalid operations_. Invalid operations will cause errors. If you see an error, that means that there's a logical issue with your code. These will become increasingly important later in the course to help you debug your code
# 
# See what happens if you run the following:
# - 10 / 0
# - 1 +
# - 2 * * 4
# - 3 x 4
# - 3 a

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# ## Exercise 5
# 
# Now that we've gone over the basic arithmetic operations, let's use them in interesting ways.
# 
# Let's say we have a mathematical function $f(x) = x^3 + 2 x^2 + 3 x + 4$. (Important note: we will see later in the course that _programming function_ are **NOT THE SAME** as _mathematical functions_. You don't need to worry about this for now, but keep this in mind).
# 
# Using Jupyter, compute $f(5)$. Expand the computation so that $x$ is replaced by 5 and you do all of the arithmetic operatoins.
# 
# Do the same for $f(10)$.
# 
# You might notice that this process of substituting the variables is quite annoying. We will revisit this in future lectures.

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# ## Exercise 6
# 
# Use this space to compute free-form arithmetic operations. What are the most interesting things you can compute? If you're willing, bring some to share to class.
# 
# Remember to use _shift + enter_ to run the cells.

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# ## Exercise 7 (medium)
# 
# We will now review the modulus operation. The syntax for modulus is `a % b`
#  
# Compute the following quantities by hand. Then, use Jupyter to check if you got them correct:
# - 1 % 2
# - 10 % 2
# - 10 % 5
# - 67 % 3
# 
# Remember to use _shift + enter_ to run cells

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# ## Exercise 8 (Hard)
# 
# For this exercise, using _only the operations we discussed in class_, do the following:
# - Extract the lowest digit from the number 48756378291
# - Extract the second lowest digit from the number 48756378291
# - Extract the third lowest digit from the number 48756378291
# 
# Do you see a pattern?

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# # Supplementary exercises
# 
# If you've completed all of the exercises so far, congratulations! There are supplementary exercises you can do now. Ask a TA to get access to them.

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