Modules & Importing Libraries

Why read this? Python alone gives you the basics. But its real power is the vast ecosystem of libraries — pre-written code that handles everything from advanced math to generating random numbers. Modules are how you tap into that power.

🎯 Learning Objectives

1. Import modules using import, from...import, and import...as
2. Use functions from the math module (sqrt, ceil, floor, sin, cos, etc.)
3. Use functions from the random module (randint, choice, shuffle)
4. Understand the difference between absolute and relative imports
5. Write portable import statements following Python conventions

📋 Prerequisites

• All Week 1-2 topics. Variables, functions, conditionals — all needed here.

📖 Core Content

8.1 What Problem Do Modules Solve?

8.2 Three Ways to Import

python
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import math
print(math.sqrt(25))    # 5.0
print(math.pi)           # 3.141592653589793

python
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from math import sqrt, pi
print(sqrt(25))          # 5.0 (no need for math.sqrt)
print(pi)                # 3.141592653589793

python
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import math as m
print(m.sqrt(25))        # 5.0 (using alias)

8.3 The math Module

python
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# runnable
import math
# Constants
print("pi:", math.pi)
print("e:", math.e)
# Rounding
print("ceil(4.2):", math.ceil(4.2))    # 5 (ceiling — round UP)
print("floor(4.9):", math.floor(4.9))  # 4 (floor — round DOWN)
# Powers and roots
print("sqrt(144):", math.sqrt(144))    # 12.0
print("pow(2, 10):", math.pow(2, 10))  # 1024.0
# Trigonometry (angles in radians)
print("sin(pi/2):", math.sin(math.pi/2))  # 1.0
print("cos(0):", math.cos(0))             # 1.0
# Log and exp
print("log(100, 10):", math.log(100, 10)) # 2.0 (log base 10)
print("log(e):", math.log(math.e))        # 1.0 (natural log)

pseudo
pi: 3.141592653589793
e: 2.718281828459045
ceil(4.2): 5
floor(4.9): 4
sqrt(144): 12.0
pow(2, 10): 1024.0
sin(pi/2): 1.0
cos(0): 1.0
log(100, 10): 2.0
log(e): 1.0

8.4 The random Module

python
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# runnable
import random
# Random integer between a and b (INCLUSIVE)
dice = random.randint(1, 6)
print("Dice roll:", dice)
# Random float between 0 and 1
print("Random float:", random.random())
# Random choice from a list
fruits = ["apple", "banana", "cherry", "date"]
print("Random fruit:", random.choice(fruits))
# Shuffle a list (modifies in-place)
cards = ["Ace", "King", "Queen", "Jack"]
random.shuffle(cards)
print("Shuffled cards:", cards)
# Random float between a and b
print("Uniform(10, 20):", random.uniform(10, 20))

pseudo
Dice roll: 4
Random float: 0.7432918374091287
Random fruit: cherry
Shuffled cards: ['Queen', 'Ace', 'Jack', 'King']
Uniform(10, 20): 15.278345190187345

8.5 Worked Example 1: The Birthday Paradox

python
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# runnable
import random
def has_duplicate_birthday(group_size):
    """Return True if at least two people share a birthday."""
    birthdays = []
    for _ in range(group_size):
        bday = random.randint(1, 365)
        if bday in birthdays:
            return True
        birthdays.append(bday)
    return False
# Run simulation 10000 times
trials = 10000
group_size = 23
count = 0
for _ in range(trials):
    if has_duplicate_birthday(group_size):
        count += 1
probability = count / trials * 100
print(f"With {group_size} people, shared birthday probability: {probability:.1f}%")

pseudo
With 23 people, shared birthday probability: 50.7%

8.6 Worked Example 2: Guessing Game

python
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# runnable
import random
secret = random.randint(1, 100)
attempts = 0
print("I'm thinking of a number between 1 and 100.")
while True:
    guess = int(input("Your guess: "))
    attempts += 1
    if guess < secret:
        print("Too low!")
    elif guess > secret:
        print("Too high!")
    else:
        print(f"Correct! You got it in {attempts} attempts.")
        break

8.7 Worked Example 3: GCD and LCM

python
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# runnable
import math
a = int(input("First number: "))
b = int(input("Second number: "))
gcd = math.gcd(a, b)
lcm = abs(a * b) // gcd
print(f"GCD({a}, {b}) = {gcd}")
print(f"LCM({a}, {b}) = {lcm}")

8.8 Worked Example 4: Password Generator

python
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# runnable
import random
import string
length = int(input("Password length: "))
# Combine all character types
chars = string.ascii_letters + string.digits + "!@#$%^&*"
password = ""
for _ in range(length):
    password += random.choice(chars)
print(f"Generated password: {password}")

8.9 Worked Example 5: Scientific Calculator

python
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# runnable
import math
print("Scientific Calculator")
print("1. Square root")
print("2. Sine (degrees)")
print("3. Cosine (degrees)")
print("4. Logarithm (base 10)")
choice = int(input("Choose (1-4): "))
value = float(input("Enter value: "))
if choice == 1:
    if value >= 0:
        print(f"√{value} = {math.sqrt(value):.4f}")
    else:
        print("Cannot compute sqrt of negative number")
elif choice == 2:
    rad = math.radians(value)
    print(f"sin({value}°) = {math.sin(rad):.4f}")
elif choice == 3:
    rad = math.radians(value)
    print(f"cos({value}°) = {math.cos(rad):.4f}")
elif choice == 4:
    if value > 0:
        print(f"log({value}) = {math.log10(value):.4f}")
    else:
        print("Cannot compute log of non-positive number")

📐 Key Concepts Reference

⚠️ Common Pitfalls

Pitfall 1: Name Conflicts with from import

Pitfall 2: Shadowing Standard Modules

Pitfall 3: Forgetting math. Prefix

Pitfall 4: random.randint Upper Bound

📝 Practice Questions

Q1: What does math.ceil(-3.7) return?

Answer: -3

ceil() rounds UP (toward positive infinity). -3.7 rounded up is -3 (because -3 > -3.7). Q2: What's the output?

python
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import math
print(math.floor(3.999))

Answer: 3

floor() rounds DOWN (toward negative infinity). 3.999 floored is 3. Q3: Fix this code:

python
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import random
print(randint(1, 10))

Answer: Error: NameError: name 'randint' is not defined Fix: Either print(random.randint(1, 10)) or from random import randint. Q4: Write code to simulate rolling two dice and printing their sum.

Answer:

python
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# runnable
import random
die1 = random.randint(1, 6)
die2 = random.randint(1, 6)
print(f"Dice: {die1} + {die2} = {die1 + die2}")

Q5: What's the output?

python
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from math import pi, sqrt
print(sqrt(pi))

Answer:

pseudo
1.772453850905516

sqrt(pi) = √3.14159... ≈ 1.772 Q6: Write code using math.gcd to find if two numbers are coprime (GCD = 1).

Answer:

python
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# runnable
import math
a, b = 15, 28
if math.gcd(a, b) == 1:
    print(f"{a} and {b} are coprime")
else:
    print(f"{a} and {b} are not coprime")

Q7: What does random.shuffle() return?

Answer: None

shuffle() modifies the list IN PLACE and returns None. It does NOT create a new list. If you do new_list = random.shuffle(my_list), new_list will be None. Q8: Write a program that picks a random card from a standard 52-card deck.

Answer:

python
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# runnable
import random
suits = ["Hearts", "Diamonds", "Clubs", "Spades"]
ranks = ["Ace", "2", "3", "4", "5", "6", "7", "8", "9", "10", "Jack", "Queen", "King"]

suit = random.choice(suits)
rank = random.choice(ranks)
print(f"{rank} of {suit}")

*Q9: What's the difference between import math and from math import ?

Answer:

• import math loads math into a namespace. You access functions via math.sqrt(25).
• from math import * loads ALL math names directly into your namespace. You can use sqrt(25) directly, but it may override your existing variables/functions.

Use import math unless you have a good reason not to. Q10: Write a program that calculates the distance between two points (x1,y1) and (x2,y2) using math.hypot or math.sqrt.

Answer:

python
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# runnable
import math
x1, y1 = 0, 0
x2, y2 = 3, 4
distance = math.sqrt((x2 - x1)**2 + (y2 - y1)**2)
print(f"Distance: {distance}")  # 5.0
# Or: distance = math.hypot(x2-x1, y2-y1)

🔗 Cross-References

• Next Topic: While Loops
• Previous Topic: Nested Conditionals & Logical Operators
• BSCS1001 Computational Thinking: Modular design is key to managing complexity.
• Reference: Python for Everybody, Chapter 1 (Section 1.5)
• Video: L23: Different ways to import a library, L27: Introduction to import library Join Discord Previous7. Nested ConditionalsNext9. While Loops