Learn Python variables with this beginner-friendly guide. Understand variable naming rules, assignments, and operations with examples and exercises. Perfect for students and professionals starting their Python journey.
Python is widely used in mathematics for calculations, data analysis, and visualization due to its simple syntax and powerful libraries. Here’s a quick overview of how Python can help in different areas of mathematics:
Python can perform basic arithmetic operations, making it ideal for solving algebraic equations and expressions.
# Basic operations
addition = 3 + 5
subtraction = 10 - 4
multiplication = 7 * 3
division = 20 / 5
exponent = 2 ** 3 # 2 to the power of 3
Python lets you define variables to represent unknown values, which is helpful when solving equations.
x = 10
y = 5
result = (x + y) * (x - y)
The math library offers functions for more advanced calculations like square roots, logarithms, trigonometry, and more.
import math
square_root = math.sqrt(25)
log_val = math.log(10) # Natural logarithm
sin_val = math.sin(math.pi / 2) # sine of 90 degrees
For higher-level math, such as linear algebra, the NumPy library is very useful. It can handle matrices, arrays, and operations on them.
import numpy as np
# Creating a matrix
A = np.array([[1, 2], [3, 4]])
B = np.array([[2, 0], [1, 3]])
# Matrix operations
addition = A + B
multiplication = np.dot(A, B) # Matrix multiplication
inverse = np.linalg.inv(A) # Inverse of a matrix
Visualizing mathematical functions and data is easy with libraries like matplotlib. It allows you to create graphs for a range of mathematical functions.
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(-10, 10, 100)
y = x ** 2 # y = x^2, a parabola
plt.plot(x, y)
plt.xlabel("x")
plt.ylabel("y")
plt.title("Graph of y = x^2")
plt.grid(True)
plt.show()
For advanced statistical and probability functions, the SciPy library provides tools for distribution, statistical tests, and probability functions.
from scipy import stats
# Mean, median, and mode
data = [1, 2, 2, 3, 4, 4, 4, 5]
mean_val = np.mean(data)
median_val = np.median(data)
mode_val = stats.mode(data)
For symbolic computation (e.g., solving equations, differentiation, and integration), the SymPy library is ideal.
from sympy import symbols, solve, diff, integrate
x = symbols('x')
equation = x ** 2 - 5 * x + 6
solutions = solve(equation, x)
# Differentiation
diff_eq = diff(x ** 2 + 3 * x, x)
# Integration
integral_eq = integrate(x ** 2 + 3 * x, x)