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Variables, expressions and statements: operators

Learning outcomes

  • Practice using the documentation of your HPC cluster
  • Practice using the Python book How to Think Like a Computer Scientist: Learning with Python 3
  • Get the type of an object
  • Create a variable
  • Use a variable
  • Practice converting an equation to Python code
  • Find and use the operator for exponentiation
  • Practice the modulo operator
  • Practice converting a simple text question to Python code
For teachers

Teaching goals are:

  • Learners have worked with variables
  • Learners understand the purpose of variables
  • Learners have obtained the data type of a variable
  • Learners have heard about what a data type is
  • Learners have practiced converting an equation and a text question to Python
  • Learners have read about operators
  • Learners have worked with the modulo operator

Lesson plan:

Exercises:

  • 5 mins: prior knowledge
  • 5 mins: presentation
  • 15 mins: challenge
  • 5 mins: feedback

Prior questions:

  • What is an operator?
  • If I ask you: 'What time is it 10 hours later, what is the calculation you do in your head?'
  • What is the modulo operator?

Overview

In any non-trivial calculation, we want to let our computer remember things, such as the content of a data file or the parameters/settings we use in our program. Variables allows one to make a computer store ('remember') information. Here we use our first simple variables.

Also we practice converting an equation and a mathematical problem to Python code. We will discover the helpful modulo operator.

Exercises

Exercise 1: an equation with exponentiation

Learning outcomes

  • practice converting an equation to Python code
  • find and use the operator for exponentiation

Read the following sections of How to Think Like a Computer Scientist: Learning with Python 3:

  • 2.6. Operators and operands

Then in section 2.14, do exercise 5 except for asking for input: use a hardcoded value as input, for example:

t = 3.14

2.14.5

The formula for computing the final amount if one is earning compound interest is given on Wikipedia as

Equation for compound interest

Write a Python script that assigns the principal amount of $10000 to variable P, assign to n the value 12, and assign to r the interest rate of 8%. Set the value of t to any positive value. Calculate and print the final amount after t years.

Answer

Here is a possible implementation:

p = 10000 # principal amount, in dollar
r = 1.08 # yearly anual interest rate
n = 12 # monthly compounding
t = 3.14 # number of years
a = p * ((1 + (r/n)) ** (n * t))
print(a)

Note that p (and not P) was used, as this follows the PEP 8 Python coding standard.

Additionally, to make sure the equation is calculated correctly, plenty of parentheses were used.

Exercise 2: the modulo operator

Learning outcomes

  • practice the modulo operator
  • practice converting a simple text question to Python code

Read the following sections of How to Think Like a Computer Scientist: Learning with Python 3:

  • 2.8. Order of operations
  • 2.12. The modulus operator

Then in section 2.14, do exercises 6 and 7.

2.14.6

Evaluate the following numerical expressions in your head, then use the Python interpreter to check your results:

>>> 5 % 2
>>> 9 % 5
>>> 15 % 12
>>> 12 % 15
>>> 6 % 6
>>> 0 % 7
>>> 7 % 0

What happened with the last example? Why? If you were able to correctly anticipate the computer’s response in all but the last one, it is time to move on. If not, take time now to make up examples of your own. Explore the modulus operator until you are confident you understand how it works.

Answer 
>>> 5 % 2
1
>>> 9 % 5
4
>>> 15 % 12
3
>>> 12 % 15
12
>>> 6 % 6
0
>>> 0 % 7
0
>>> 7 % 0
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ZeroDivisionError: integer modulo by zero
>>>

The last error is the result from a division by zero: 7 % 0 means: 'calculate the remainder after dividing seven by zero'. One cannot divide a number by zero.

2.14.7

You look at the clock and it is exactly 2 pm. You set an alarm to go off in 51 hours. At what time does the alarm go off? (Hint: you could count on your fingers, but this is not what we’re after. If you are tempted to count on your fingers, change the 51 to 5100.)

Answer

Here is a possible implementation:

t_now = 14 # 2 pm
t_future = (t_now + 51) % 24
print(t_future)

The result is 17, i.e. 5 pm.