Python Standard Library Core

Python follows a philosophy known as "Batteries Included". This means the standard library ships with an immense collection of battle-tested, high-performance C-optimized modules ready for immediate use without installing external packages.

The math module provides access to mathematical functions defined by the C standard library:

• Constants: math.pi (3.14159...), math.e (2.71828...), math.tau ($2\pi$), math.inf, math.nan.
• Rounding: math.floor() (rounds down), math.ceil() (rounds up), math.trunc() (truncates decimals).
• Power & Logarithms: math.sqrt(), math.pow(), math.log() (natural log), math.log10(), math.log2().
• Combinatorics: math.factorial(n), math.comb(n, k) (combinations), math.gcd(a, b) (greatest common divisor).

import math

# 1. Rounding operations
print("Ceil of 4.2: ", math.ceil(4.2))   # 5
print("Floor of 4.8:", math.floor(4.8))  # 4

# 2. Factorial and Combinations
print("\n5! (Factorial):", math.factorial(5)) # 120
print("Combinations of 5 choose 2:", math.comb(5, 2)) # 10

# 3. Trigonometry and Geometry (Angles in Radians)
angle_rad = math.radians(90) # Convert 90 degrees to pi/2 radians
print("sin(90 degrees):", math.sin(angle_rad))
print("Hypotenuse of 6 and 8:", math.hypot(6, 8)) # 10.0

The random module implements a Pseudo-Random Number Generator (PRNG) based on the famous Mersenne Twister algorithm (period of $2^{19937}-1$).

• random.randint(a, b): Returns a random integer $N$ such that $a \le N \le b$ (both endpoints inclusive!).
• random.random(): Returns a random float in the range $[0.0, 1.0)$.
• random.choice(sequence): Picks a single random element from a list, string, or tuple.
• random.choices(seq, k=n): Selects $n$ items with replacement (duplicates possible).
• random.sample(seq, k=n): Selects $n$ unique items without replacement.
• random.shuffle(list): Randomizes list elements in place.
• random.seed(x): Initializes the PRNG with a fixed seed, making randomized outputs 100% deterministic and reproducible for scientific experiments.

import random

# 1. Generating random integers and floats
dice_roll = random.randint(1, 6)
random_prob = random.random()
print(f"🎲 Rolled a dice: {dice_roll} | Probability: {random_prob:.4f}")

# 2. Random selection from lists
participants = ["Alex", "Balaji", "Chloe", "David", "Elena", "Faisal"]
winner = random.choice(participants)
print(f"🏆 Lucky Winner (choice): {winner}")

# 3. Unique sampling without replacement (Lottery / Team selection)
team = random.sample(participants, k=3)
print(f"👥 Selected Team (3 unique members): {team}")

# 4. In-place shuffling of a deck of cards
cards = ["A♠", "K♥", "Q♦", "J♣", "10♠"]
random.shuffle(cards)
print(f"🃏 Shuffled Cards: {cards}")

The datetime module provides classes for manipulating dates, times, and intervals:

• datetime.date(year, month, day): Represents a calendar date.
• datetime.time(hour, minute, second): Represents time of day independent of date.
• datetime.datetime.now(): Returns current date and time.
• datetime.timedelta(days, hours, minutes): Represents duration / time difference for arithmetic (e.g. adding 30 days to a date).
• Formatting:
  • strftime(format): String Format Time (Converts datetime object to formatted string).
  • strptime(string, format): String Parse Time (Parses raw text string into datetime object).

import datetime as dt

# 1. Current timestamp
now = dt.datetime.now()
print("Current Timestamp:", now)

# 2. Custom date formatting with strftime
formatted_date = now.strftime("%A, %d %B %Y | %I:%M:%S %p")
print("Formatted Date:   ", formatted_date)

# 3. Date Arithmetic using timedelta
today = dt.date.today()
expiry_date = today + dt.timedelta(days=30)
days_remaining = (expiry_date - today).days

print(f"\nSubscription Start: {today}")
print(f"Subscription Expiry: {expiry_date} ({days_remaining} days left)")

# 4. Parsing a date string with strptime
user_input_str = "2026-12-25"
parsed_date = dt.datetime.strptime(user_input_str, "%Y-%m-%d").date()
print("Parsed Holiday Date:", parsed_date)

The statistics module provides built-in functions for calculating mathematical statistics of numeric datasets without needing heavy third-party libraries like NumPy for basic tasks:

• mean(data): Arithmetic mean (average).
• median(data): Middle value (robust against extreme outliers).
• mode(data): Most frequently occurring value.
• stdev(data): Sample standard deviation (measures variance spread).
• quantiles(data, n=4): Divides dataset into $n$ continuous intervals (quartiles).

import statistics as stats

exam_scores = [78, 85, 92, 85, 99, 64, 85, 90, 72, 88]

avg_score = stats.mean(exam_scores)
median_score = stats.median(exam_scores)
most_common = stats.mode(exam_scores)
spread = stats.stdev(exam_scores)

print("Dataset:", exam_scores)
print("=" * 40)
print(f"• Mean (Average):     {avg_score:.2f}")
print(f"• Median (Midpoint):  {median_score}")
print(f"• Mode (Most Common): {most_common}")
print(f"• Standard Deviation: {spread:.2f}")