import numpy as np

# Mathematical functions overview
data = np.array([1, 4, 9, 16, 25])
print(f"Data: {data}")

# Universal functions
print(f"Square roots: {np.sqrt(data)}")
print(f"Logarithms: {np.log(data)}")
print(f"Statistics: mean={np.mean(data)}, std={np.std(data):.2f}")

import numpy as np

# Vectorized operations are fast
numbers = np.arange(100000)

# All operations happen instantly - no loops!
squares = numbers ** 2
roots = np.sqrt(numbers)

print(f"Processed {len(numbers)} numbers instantly!")
print(f"First 5 squares: {squares[:5]}")

import numpy as np

x = np.array([1, 2, 3, 4, 5])

# Mathematical ufuncs
print(f"Exponential: {np.exp(x)}")
print(f"Square root: {np.sqrt(x)}")
print(f"Trigonometry: {np.sin(x)}")

import numpy as np

scores = np.array([85, 92, 78, 96, 89, 74, 88, 93])

# Statistical operations
print(f"Mean: {np.mean(scores):.1f}")
print(f"Median: {np.median(scores):.1f}")
print(f"Std Dev: {np.std(scores):.2f}")

import numpy as np

# Matrix operations
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])

print(f"Matrix multiplication: \n{A @ B}")
print(f"Determinant: {np.linalg.det(A):.2f}")

import numpy as np

# Temperature conversion
celsius = np.array([0, 20, 30, 100])
fahrenheit = celsius * 9/5 + 32

print(f"°C: {celsius}")
print(f"°F: {fahrenheit}")

import numpy as np

# Compound interest
principal = 1000
rate = 0.05
years = np.array([1, 5, 10, 20])

amounts = principal * (1 + rate) ** years
print(f"Investment growth: {amounts.round(0).astype(int)}")