Wednesday, February 4th, 2026

On Monday, we started working with lists and for loops.

Constructing lists

So far, we've explicitly generated lists using square brackets and comma-separated inputs (which we've had to manually type in). Suppose we want to generate a list containing the cubes of the first 50 positive integers. Our current strategy is not reasonable for this sort of task.

The .append method (attached to a list) can be used to add an element to a list. That is, we can write something like <some list>.append(<some new element>) to add <some new element> to <some list>.

my_list = ['a', 'b', 'c', 'd', 'e']
print(my_list)

['a', 'b', 'c', 'd', 'e']

my_list.append('x')
print(my_list)

['a', 'b', 'c', 'd', 'e', 'x']

my_list.append('g')
print(my_list)

['a', 'b', 'c', 'd', 'e', 'x', 'g']

To build a list of the cubes of the first 50 positive integers, we can start with an empty list [] and then iteratively use the .append method to add elements to that list.

cubes = []

for i in range(1,51):
    cube = i**3
    cubes.append(cube)

    print(cubes[-1])

1
8
27
64
125
216
343
512
729
1000
1331
1728
2197
2744
3375
4096
4913
5832
6859
8000
9261
10648
12167
13824
15625
17576
19683
21952
24389
27000
29791
32768
35937
39304
42875
46656
50653
54872
59319
64000
68921
74088
79507
85184
91125
97336
103823
110592
117649
125000

for cube in cubes:
    print(cube)

1
8
27
64
125
216
343
512
729
1000
1331
1728
2197
2744
3375
4096
4913
5832
6859
8000
9261
10648
12167
13824
15625
17576
19683
21952
24389
27000
29791
32768
35937
39304
42875
46656
50653
54872
59319
64000
68921
74088
79507
85184
91125
97336
103823
110592
117649
125000

print(cubes)

[1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728, 2197, 2744, 3375, 4096, 4913, 5832, 6859, 8000, 9261, 10648, 12167, 13824, 15625, 17576, 19683, 21952, 24389, 27000, 29791, 32768, 35937, 39304, 42875, 46656, 50653, 54872, 59319, 64000, 68921, 74088, 79507, 85184, 91125, 97336, 103823, 110592, 117649, 125000]

Exercise: Generate a list of the squares of the first $40$ positive integers. Then print the remainder of each after division by $7$.

squares = []
for i in range(1,41):
    squares.append(i**2)

for square in squares:
    print(square % 7)

1
4
2
2
4
1
0
1
4
2
2
4
1
0
1
4
2
2
4
1
0
1
4
2
2
4
1
0
1
4
2
2
4
1
0
1
4
2
2
4

Boolean expressions

There are two Boolean values, namely True and False.

We can write statements that evalute to either True or False called Boolean expressions. For example, we can compare two numbers using < or > to see if one is less than the other or one is greater than the other.

7 > 3

True

3 > 7

False

10 < 10.1

True

Similarly, we can use <= or >= for less than/greater than or equal to.

10 <= 10

True

9 <= 9.1

True

Inequality checks can also be chained together.

2 < 3 < 5

True

-1 <= -1 < -1

False

We can use a double equality == to check whether two objects are equal to one another.

5 == 5

True

3.0 == 3

True

We can also check whether two lists are equal to one another (i.e. if they contain equal objects in the same order).

my_list1 = [1,2,3,4,5]
my_list2 = [1,2,3,4,5]

my_list1 == my_list2

True

my_list1 = [1,2,3,4,5]
my_list2 = [1,2,3,4,6]

my_list1 == my_list2

False

We can construct more complicated Boolean expressions using the and, or, and not operators. That is:

• (some expression) and (some other expression) will evaluate as True if (some expression) and (some other expression) are both True.
• (some expression) or (some other expression) will evaluate as True if either (some expression) or (some other expression) are True (or both).
• not (some expression) will evaluate as True if (some expression) is False.

Note: A number $n$ is even if it has remainder $0$ after division by $2$.

A number $n$ is a multiple of $3$ if it has remainder $0$ after division by $3$.

Can we check if a given number n is both even and a multiple of $3$?

for n in range(1,21):
    print(n, (n % 2 == 0) and (n % 3 == 0))

1 False
2 False
3 False
4 False
5 False
6 True
7 False
8 False
9 False
10 False
11 False
12 True
13 False
14 False
15 False
16 False
17 False
18 True
19 False
20 False

(5 < 6) or (6 < 5)

True

not (True)

False

Using if statements

We can use an if statement to perform some operations only when a Boolean expression is True. The syntax for writing an if statement is: if (some Boolean expression): (do something)

Again, spacing is CRITICAL, as it indicates which operations are part of the if statement (which will only run when the Boolean expression is True), and which operations are outside of the if statement (which will run regardless).

n = 12

if n % 2 == 0:
    print('{} is even.'.format(n))
if n % 2 == 1:
    print('{} is odd.'.format(n))
print('Done!')

12 is even.
Done!

for n in range(1,21):
    if n % 2 == 0:
        print('{} is even.'.format(n))
    if n % 2 == 1:
        print('{} is odd.'.format(n))
print('Done!')

1 is odd.
2 is even.
3 is odd.
4 is even.
5 is odd.
6 is even.
7 is odd.
8 is even.
9 is odd.
10 is even.
11 is odd.
12 is even.
13 is odd.
14 is even.
15 is odd.
16 is even.
17 is odd.
18 is even.
19 is odd.
20 is even.
Done!

evens = []
odds = []

for n in range(1,21):
    if n % 2 == 0:
        evens.append(n)
    if n % 2 == 1:
        odds.append(n)
print('Done!')

Done!

evens

[2, 4, 6, 8, 10, 12, 14, 16, 18, 20]

odds

[1, 3, 5, 7, 9, 11, 13, 15, 17, 19]

Optionally, we can include an else block immediately following an if block. In this case, the code inside the else block will only occur if the Boolean expression in the if statement was False.

n = 11

if n % 2 == 0:
    print('{} is even.'.format(n))
else:
    print('{} is not even.'.format(n))

11 is not even.

Exercise: Use an if/else pair to print a string stating whether an integer n is even or odd.

We very often want to perform different operations based on several Boolean expressions. We can supplement an if statement with an elif statement (which is short for "else if") with a new Boolean expression to perform operations only in the case that the first if expression was False and the new expression is True.

n = 13

if n % 3 == 0:
    print('{} is a multiple of 3.'.format(n))
elif n % 3 == 1:
    print('{} is one more than a multiple of 3.'.format(n))
elif n % 3 == 2:
    print('{} is two more than a multiple of 3.'.format(n))
else:
    print('{} is not zero, one, or two more than a multiple of 3.'.format(n))

13 is one more than a multiple of 3.

We can include many elif blocks to check different cases.

Exercise: Use an if/elif/else triple to print a string stating whether an integer n is a multiple of $3$, one more than a multiple of $3$, or two more than a multiple of $3$.

In-class exercise

Exercise: Out of the squares of the first $40$ positive integers, count how many have remainder $1$ after division by $7$.