Programming is often thought to be a subject that doesn’t require much mathematical knowledge. However, while you don’t need to be a math expert to become a programmer, some mathematical concepts can greatly enhance your programming and problem-solving skills.
So here are 10 mathematical concepts every programmer should know of:
Numerical Systems
Numeral systems in programming are ways of representing numbers using different symbols and bases. The most common systems are decimal (base-10), binary (base-2), hexadecimal (base-16), and octal (base-8). Each system has its own set of symbols and rules for representing numbers. They are used for different purposes in programming, such as representing data, memory addresses, and byte values.
The possibilities are endless, and as a programmer, you have the power to choose which system to use depending on the needs of your project. Will you stick to the traditional decimal system, or will you explore new and creative ways to represent numbers? The choice is yours!
Linear Algebra
Linear algebra is a powerful mathematical tool used in programming to efficiently manipulate large sets of data. It helps programmers build complex algorithms for machine learning, computer graphics, and cryptography by using techniques like matrix operations, vector addition, and finding eigenvalues and eigenvectors. Linear algebra is like a set of building blocks that programmers can use to create advanced systems that can process and analyze data at scale.
Statistics
In programming, statistics is used in a variety of applications, from fraud detection to medical research. By using statistics to analyze and interpret data, programmers can make more informed decisions and create better systems. It’s like having a detective on your team who can help you solve complex problems and uncover hidden insights.
Boolean Algebra
Boolean algebra is a branch of mathematics that deals with logical operations on binary variables. In simpler terms, it’s a system of mathematics that helps us work with true and false values, represented as 1 and 0, respectively.
In Boolean algebra, there are three key operations: AND, OR, and NOT.
- The AND operation is represented by a dot (.) and it takes two inputs. It outputs 1 only if both inputs are 1, otherwise, it outputs 0.
- The OR operation is represented by a plus sign (+) and it also takes two inputs. It outputs 1 if either one or both inputs are 1, otherwise, it outputs 0.
- The NOT operation is represented by a bar over a variable (¬ or ~) and it takes only one input. It outputs the opposite value of the input, ie if the input is 1, it outputs 0, and if the input is 0, it outputs 1.
Using these operations, we can create logical expressions that represent complex conditions. For example, the expression (A AND B) OR (NOT A AND C) means that we want to output 1 if both A and B are 1, or if A is 0 and C is 1.
Read: How is Boolean Algebra used in ML?
Floating Points
Floating points in programming are like scientific notation for computers. They allow for a wide range of real numbers to be represented using a base and an exponent, The base is a binary number that represents the significant digits of the number, and the exponent is an integer that represents the power of 2 to which the base is raised. Together, they create a floating-point representation of the number.
The representation is not always exact due to limited precision. They’re commonly used for calculations in science, engineering, and graphics, but require careful consideration of potential inaccuracies in code.
Logarithms
Logarithms are like special tools for solving problems involving exponential growth or decay. They help to transform large numbers into smaller, more manageable ones, making calculations more efficient.
For example, a computer program may need to calculate the result of a complex mathematical equation that involves very large numbers. By taking the logarithm of those numbers, the program can transform them into smaller values that are easier to work with. This can significantly reduce the processing time and memory requirements needed to complete the calculation.
Set Theory
Set Theory deals with sets, which are collections of distinct objects. In programming, set theory is used to solve problems that involve grouping or organizing data. A set can be defined as a collection of unique elements. These elements can be anything, such as numbers, strings, or even other sets.
In programming, set theory is used to solve problems such as searching for elements in a collection, comparing sets, and merging or splitting sets. It is often used in database management, data analysis, and machine learning.
Combinatorics
Combinatorics is a magic wand for counting and arranging objects. By using combinatorial techniques, programmers can solve problems related to probability, statistics, and optimization in a wide range of applications.
For example, combinatorics can be used to generate random numbers or to analyze patterns in large datasets.
Graph Theory
In programming, graph theory is used to solve problems such as finding the shortest path between two nodes in a network, detecting cycles or loops in a graph, and clustering nodes into communities. Graph theory is also used in artificial intelligence and machine learning, where it can be used to model decision trees and neural networks.
One of the key benefits of graph theory in programming is its ability to represent complex systems and relationships in a simple and intuitive way. By using graphs to model problems, programmers can analyze and optimize complex systems more efficiently, making graph theory an essential tool for several programming applications.
Read: Top resources to learn graph neural networks
Complexity Theory
Complexity theory is like having a GPS for programming. It helps you navigate the vast landscape of problems and algorithms, and find the most efficient path to your destination. One of the key benefits of complexity theory in programming is its ability to identify the most efficient algo for solving a problem.
The most famous problem in complexity theory is the “P vs NP” problem, which asks whether there are problems that are easy to verify but hard to solve. If such problems exist, then they are considered to be in the class “NP”, while problems that can be solved efficiently are in the class “P”.
