What are the most commonly used NumPy mathematical functions in data science?

NumPy ships a comprehensive set of universal functions (ufuncs) — compiled, vectorised operations that apply element-wise across the full array without Python loops. Knowing these avoids writing slow manual loops for standard computations.

import numpy as np

a = np.array([1.0, 4.0, 9.0, 16.0, 25.0])

# Element-wise math
np.sqrt(a)          # [1.  2.  3.  4.  5.]
np.log(a)           # natural log
np.log2(a)          # base-2 log
np.log10(a)         # base-10 log
np.exp(a)           # e^x
np.abs(np.array([-3, 4, -1]))  # [3 4 1]

# Aggregation
a.sum()             # 55.0
a.mean()            # 11.0
a.std()             # standard deviation
a.var()             # variance
a.min(); a.max()    # extremes
a.argmin(); a.argmax()  # INDEX of min/max
np.median(a)        # 9.0
np.percentile(a, 75)   # 75th percentile

# Linear algebra
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
np.dot(A, B)        # matrix multiplication (also A @ B in Python 3.5+)
np.linalg.inv(A)    # matrix inverse
np.linalg.det(A)    # determinant
vals, vecs = np.linalg.eig(A)  # eigenvalues and eigenvectors

# Sorting
unsorted = np.array([3, 1, 4, 1, 5])
np.sort(unsorted)   # returns sorted copy: [1 1 3 4 5]
np.argsort(unsorted)  # indices that would sort: [1 3 0 2 4]

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