Lesson 3: Discovering your Paths > The math module | Python Programming (70053 Autumn Term 2021/2022) | Department of Computing

Lesson 3

Discovering your Paths

Chapter 7: Using existing functions

The math module

face Josiah Wang

The official documentation for the math module contains a list of functions and variables defined for the module.

Take a quick glance at them, and then try to answer/solve the following problems.

Please try to solve them yourself before peeking at the sample solutions! You will learn better this way!

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Question 1

Given p = 0.7 and q = 0.3, use Python to compute the value of $-p \times log_2(p)-q \times log_2(q)$

Answer

Sample solution:

Here are two possible solutions. To compute $log_2$ , you can either use math.log2(x) or the more generic math.log(x, base).

Tip: you are actually computing the entropy (which will be covered in your Introduction to Machine Learning course)

import math
p = 0.7
q = 0.3
entropy = -p*math.log2(p) - q*math.log2(q)
print(entropy)

import math
p = 0.7
q = 0.3
entropy = -p*math.log(p, 2) - q*math.log(q, 2)
print(entropy)

Question 2

Compute the sigmoid of 0.6 using Python, where $sigmoid(x)$ is defined as $\frac{1}{1 + e^{-x}}$ .

Answer

Sample solution:

Here is a possible solution.

import math
sigmoid = 1 / (1+math.exp(-0.6))
print(sigmoid)

Question 3

Write Python code to compute the cosine of 45 degrees. Use Python to convert 45 degrees to radians if needed.

Answer

Sample solution:

Here are two possible implementations. The first is at a higher-level of abstraction, by making use of the math.radians() function. The second is more low level and computes the radians directly (and abstracting the value of $\pi$ with math.pi instead).

import math
x_deg = 45
x_rad = math.radians(x_deg)
cos_x = math.cos(x_rad)
print(cos_x)

import math
x_deg = 45
x_rad = x_deg / 180 * math.pi
cos_x = math.cos(x_rad)
print(cos_x)

Question 4

How do you represent negative infinity in Python?

Answer

Sample solution:

Here are several ways to represent negative infinity in Python.

>>> import math
>>> -math.inf
-inf
>>> -float("inf")
-inf
>>> float("-inf")
-inf