1. COMPSCI 101 Principles of Programming
Lecture 3 – Expressions, Mathematical Operators & the math module

2. Review Which of the following code is correct? A: B: C: D:
print("Programming is fun")
print("Python is fun")
print("Programming is fun")
print("Python is fun")
print("Programming is fun)
print("Python is fun")
print("Programming is fun)
print("Python is fun")
CompSci 101

3. Review Which of the following is/are a valid identifier(s)? A. $343
B. mile
C. 9X
D. 8+9
E. max_radius
CompSci 101

4. Learning outcomes
At the end of this lecture, students should be able to:
import modules and use the functions defined in the module
use integer division and modulus operators
use comments. Include a docstring at the top of a program
use self-documenting code to make the program easy to understand
understand that an expression evaluates to one value
understand the order of operations when an expression is evaluated
understand how to develop a program in steps
CompSci 101

5. Docstrings
A docstring is a special kind of string (text) used to provide documentation
Appears at the top of every program
three double-quotes are used to surround the docstring
All programs should include a docstring at the beginning of the program
The docstring contains the author and a description of what the program does
"""Calculates the area of a circle.
Author: Adriana Ferraro
"""
radius = 10
area = * radius ** 2
print("Area of circle", area)
CompSci 101

6. Skeleton of a Python program
Example01.py
DEMO
In general the format of a Python program is:
"""Calculates the area of a rectangle.
Author: Adriana Ferraro
"""
width = 3.56
height = 8.4
area = width * height
print("Area of rectangle", area)
docstring
initialisation
calculation
output
Area of rectangle
Every Python program is stored in a file which has .py at the end of the file name, e.g., CalculateArea.py, CompoundInterest.py
CompSci 101

7. Comments
Example02.py
DEMO
As well as the docstring describing the purpose of the program at the top of all our programs, comments can be added to the program code.
A programming comment is a note to other programmers who need to understand the code.
Anything between a # and the end of the line is a comment and is ignored by the interpreter
"""Converts a length in inches to a length in centimetres.
Author: Adriana Ferraro
"""
length_in_inches = 100 #Change value to convert different lengths
length_in_cm = length_in_inches * 2.54
print("Length", length_in_cm)
CompSci 101
Length 254.0

8. Use self documenting code
Add comments sparingly to explain code that is difficult, or to tell other programmers something they need to know about the code. It is always important to use good variable names.
The program below does the same job as the program on the previous slide but it uses very poor variable names which makes the program difficult to understand.
"""Converts a length
Author: Adriana Ferraro
"""
a = 100
b = a * 2.54
print("Length", b)
Length 254.0
CompSci 101

9. Python libraries
CalculateArea.py
DEMO
Python has libraries of code which contain definitions and functions which perform useful tasks and calculations.
The files in these libraries are called modules. The name of a module is the name of the file without the .py extension.
The math module contains many useful math functions, e.g., math.sin(), math.cos(), math.pow(), math.sqrt(), math.floor(), …
In order to be able to use the functions of a module, we need to import the module. Importing a module means that we can then use all the functions defined inside that module, e.g.,
"""Calculates the radius of a circle, given the area.
"""
import math
area =
radius = math.sqrt(area / math.pi)
print("Radius of circle", radius)
Radius of circle
CompSci 101

10. https://docs.python.org/3/library/math.html#module-math
This website contains the documentation about all the Python modules.
CompSci 101

11. Expressions – order of operations
Expressions using numbers are evaluated in the same way as in mathematical expressions, i.e., BEDMAS applies:
Note:
Work from left to right.
The / operator always results in a float, e.g., 8 / 4 is 2.0
B - Brackets
Exponents
Division, multiplication
Addition, subtraction
CompSci 101

12. Expressions – order of operations
Example03.py
DEMO
What is the output?
18 * / 3
/ 3
result1 = (25 - 7) * / 3
result2 = * /
result3 = 32 / 4 ** (3 + 2 * 3 - 7) / 5
print(result1, result2, result3)
17 – 6 – 12 /
17 – 6 –
23.0
32 / 4 ** 2 / 5
32 / 16 / 5
2 / 5
Remember to work from left to right.
CompSci 101

13. More arithmetic operators
Two more mathematical operators:
Floor division (integer division) //
Modulus (remainder) %
Floor division (integer division) performs the division and throws away the part after the decimal point, e.g.,
16 // 5 gives 3
17 // 5 gives 3
34 // 5 gives 6
CompSci 101

14. More arithmetic operators
Modulus performs the division and gives the remainder, e.g.,
16 % 5 gives 1
17 % 5 gives 2
34 % 5 gives 4
16 % 30 gives 16
CompSci 101

15. Exercise 1 Give the output Integer! result1 = 25 % 3 result2 = 20 % 34
print(result1, result2, result3, result4, result5)
Integer!
CompSci 101

16. Exercise 2 Give the output when the following code is executed
B - Brackets
Exponents (**)
Multiplication, Division, Modulus, Integer division
Addition, Subtraction
Give the output when the following code is executed
result1 = 25 / 4 // * 10 % 3
result2 = // 3 * % 5 / 5 * 2
result3 = 17 % 3 * ** 2 * // 2
print(result1, result2, result3)
CompSci 101

17. Exercise 3: Finding the distance between two cities
We want to find the distance between two cities given the latitude and longitude of the two cities.
Auckland ,
Sydney ,
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18. Finding the distance between two cities
The formula (thank you Internet) for finding the distance between two points on the earth:
where:
φ is latitude
λ is longitude
R is the earth's radius (6371 km or miles)
distance =
Auckland ,
Sydney ,
Note that for this formula the angles need to be in radians to pass to trig functions!
CompSci 101

19. Algorithm Break the problem up into manageable sections
2: Sydney
1: Auckland
Break the problem up into manageable sections
part1
part2
distance =
Auckland ,
Sydney ,
Get lamba_longitude_sydney
Get lamba_longitute_auckland
Get theta_latitude_Sydney
Get theta_latitude_auckland
longitude
in radians
CompSci 101

20. The Math Module
In the math module we can find all the functions we need:
math.sin(), math.cos(), math.asin(), math.sqrt(), math.radians()
distance =
part1
#part 1
part1 = (math.sin((lamba_longitude_sydney - lamba_longitute_auckland)/2)) ** 2
part1 = part1 * math.cos(_____________________) *
math.cos(_____________________)
CompSci 101

21. The Math Module distance = part2
part2 = (math.sin((theta_latitude_sydney - theta_latitude_auckland)/2)) ** 2
part3 =
distance_in_miles = 2 * earth_miles_radius * math.______(part3)
CompSci 101

22. Summary In a Python program we can:
import modules and use the functions defined in the imported module
use integer division and modulus operators
use comments. Every program contains a docstring at the top of the program
use self-documenting code to make the program easy to understand
understand that an expression evaluates to one value
understand the order of operations when an expression is evaluated
understand how to develop a program in steps
CompSci 101