Introduction to Mathematical Functions / Sequences

Python is known for its simplicity and versatility, making it a popular choice for a wide range of applications, including mathematical computations. The language offers comprehensive support for mathematical functions and sequences, providing both built-in features and specialized libraries that streamline the process of working with numbers.

Basic Math Functions

Python’s basic math functions, such as addition, subtraction, multiplication, and division, are intuitive and follow conventional mathematical rules. With Python’s built-in math module, you gain access to more advanced operations like absolute values (abs), square roots (sqrt), and power calculations (pow).

Math Rounding

When working with numbers, rounding plays a critical role in presenting data cleanly or performing approximations. Python’s round function offers straightforward rounding to the nearest integer or specified decimal places. The math module extends this functionality with floor and ceil for rounding down or up to the nearest integer, respectively.

Exponential, Logarithmic, and Trigonometric Functions

Python’s math module provides a suite of functions for advanced mathematical calculations:

• Exponential Functions: Includes exponential growth (exp) and power calculations.
• Logarithmic Functions: Supports natural logarithms (log), base-10 (log10), and base-2 (log2).
• Trigonometric Functions: Covers sine (sin), cosine (cos), and tangent (tan), along with their inverses, to work with angles and periodic phenomena.

Arithmetic Sequences, Fibonacci, and Prime Numbers

Python’s expressive syntax makes it easy to generate and manipulate numerical sequences:

• Arithmetic Sequences: You can create sequences with a constant difference between consecutive terms using basic loops or list comprehensions.
• Fibonacci Sequence: Python allows you to generate the Fibonacci sequence with ease using loops or recursion, thanks to its dynamic typing and simple syntax.
• Prime Numbers: Python’s control structures and functions enable the development of efficient algorithms for identifying prime numbers, such as the Sieve of Eratosthenes.