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2. NumPy – Foundation of Numerical Computing

NumPy (Numerical Python) is the most important library for numerical and scientific computing in Python. Almost every data science library (Pandas, Scikit-learn, Matplotlib, TensorFlow, PyTorch, etc.) is built on top of NumPy.

Why NumPy is essential in 2026:

• Extremely fast (written in C, vectorized operations)

• Memory-efficient multi-dimensional arrays

• Broadcasting (no loops needed for many operations)

• Basis for all modern data science & machine learning

Install NumPy (if not using Anaconda)

Bash

pip install numpy

Import convention (standard in data science):

Python

import numpy as np

2.1 NumPy Arrays vs Python Lists

Python lists are flexible but slow for numerical work.

NumPy arrays (ndarray) are homogeneous, fixed-type, multi-dimensional arrays optimized for math.

FeaturePython ListNumPy Array (ndarray)WinnerData typesMixed (int, str, float, etc.)Homogeneous (all same type)NumPySpeed (math operations)Slow (loops in Python)Very fast (vectorized, C-level)NumPyMemory usageHigh (objects + pointers)Low (contiguous memory block)NumPyMulti-dimensional supportManual (list of lists)Native (ndarray with shape)NumPyBroadcastingNot supportedAutomatic (shape rules)NumPyMathematical functionsManual or loopBuilt-in (np.sum, np.mean, etc.)NumPy

Quick comparison example

Python

# Python list (slow) lst = list(range(1000000)) %timeit [x**2 for x in lst] # ~100–150 ms # NumPy array (fast) arr = np.arange(1000000) %timeit arr**2 # ~1–5 ms

2.2 Array Operations, Broadcasting & Vectorization

Vectorization = performing operations on entire arrays without explicit loops.

Basic array creation

Python

import numpy as np a = np.array([1, 2, 3, 4]) # 1D array b = np.array([[1, 2], [3, 4]]) # 2D array zeros = np.zeros((3, 4)) # 3×4 array of zeros ones = np.ones(5) # [1. 1. 1. 1. 1.] arange = np.arange(0, 10, 2) # [0 2 4 6 8] linspace = np.linspace(0, 1, 5) # 5 evenly spaced points rand = np.random.rand(3, 2) # random values [0,1)

Vectorized operations

Python

a = np.array([10, 20, 30, 40]) b = np.array([1, 2, 3, 4]) print(a + b) # [11 22 33 44] print(a 2) # [20 40 60 80] print(a * 2) # [100 400 900 1600] print(np.sqrt(a)) # square root of each element

Broadcasting – automatic shape alignment

Python

a = np.array([[1, 2, 3], [4, 5, 6]]) # shape (2,3) b = np.array([10, 20, 30]) # shape (3,) print(a + b) # adds b to each row # [[11 22 33] # [14 25 36]] c = np.array([[100], [200]]) # shape (2,1) print(a + c) # adds c to each column

Rule of thumb: Broadcasting works when dimensions are compatible (equal or one is 1).

2.3 Indexing, Slicing & Advanced Array Manipulation

Basic indexing & slicing

Python

arr = np.array([10, 20, 30, 40, 50]) print(arr[0]) # 10 print(arr[-1]) # 50 (last element) print(arr[1:4]) # [20 30 40] print(arr[::2]) # [10 30 50] (every second) print(arr[::-1]) # [50 40 30 20 10] (reverse)

2D array indexing

Python

matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) print(matrix[0, 2]) # 3 print(matrix[:, 1]) # [2 5 8] (second column) print(matrix[1:, :2]) # [[4 5] # [7 8]] (rows 1–2, columns 0–1)

Boolean indexing (very powerful)

Python

arr = np.array([10, 25, 7, 40, 15]) print(arr[arr > 20]) # [25 40]

Advanced manipulation

Python

# Reshape a = np.arange(12) print(a.reshape(3, 4)) # 3×4 matrix # Flatten / ravel print(a.ravel()) # back to 1D # Transpose matrix.T # rows ↔ columns # Concatenate & stack np.concatenate([a, b]) np.vstack([a, b]) # vertical stack np.hstack([a, b]) # horizontal stack

2.4 Mathematical & Statistical Functions

NumPy provides fast, vectorized versions of almost all math operations.

Basic math

Python

a = np.array([1, 4, 9, 16]) print(np.sqrt(a)) # [1. 2. 3. 4.] print(np.exp(a)) # exponential print(np.log(a)) # natural log print(np.sin(np.deg2rad(30))) # sin(30°) = 0.5

Statistical functions

Python

data = np.random.randn(1000) # 1000 random normal values print(np.mean(data)) # ≈ 0 print(np.median(data)) print(np.std(data)) # standard deviation print(np.var(data)) # variance print(np.min(data), np.max(data)) print(np.percentile(data, 25)) # 25th percentile

Axis-wise operations (very important)

Python

matrix = np.random.randint(1, 100, size=(4, 5)) print(matrix.mean(axis=0)) # mean of each column print(matrix.sum(axis=1)) # sum of each row print(matrix.max(axis=0)) # max per column

Mini Summary Project – Basic Data Analysis with NumPy

Python

import numpy as np # Simulate student marks marks = np.random.randint(40, 100, size=50) print("Average marks:", np.mean(marks)) print("Highest marks:", np.max(marks)) print("Lowest marks:", np.min(marks)) print("Top 10% percentile:", np.percentile(marks, 90)) # Students above 80 above_80 = marks[marks >= 80] print(f"{len(above_80)} students scored 80+")

This completes the full NumPy – Foundation of Numerical Computing section — the true backbone of all data science in Python!

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