Articles

Explore the world of mathematics with in-depth articles designed to challenge and inspire. while being engaging and approachable. To stay up to date on the latest content, please join our email list.

Categories
Tags
1-10 of 29 results
  • A Beginner-Friendly Approach to Understanding Vector Spaces and Subspaces

    By Joseph W Barnett • October 31, 2025
    Gain a solid foundation in linear algebra with this guide to understanding vector spaces and subspaces featuring definitions, properties, and examples.
    learn More
  • Step-by-Step Solutions to Common Examples of Linear Transformations in Linear Algebra

    By Joseph W Barnett • October 24, 2025
    Learn common examples of linear transformations in linear algebra including reflections, rotations, dilations, projections, and composition.
    learn More
  • Vector Operations Tutorial for Beginners: A Complete Step-by-Step Guide

    By Joseph W Barnett • October 21, 2025
    Learn vector addition, vector subtraction, scalar multiplication, dot product, cross product, and projection in this vector operations tutorial for beginners.
    learn More
  • How to Find the Inverse of a Matrix Step by Step: A Complete Beginner’s Guide

    By Joseph W Barnett • October 16, 2025
    Learn how to find the inverse of a matrix step by step using formulas, row operations, and determinants with examples.
    learn More
  • The Ultimate Step-by-Step Guide to Basic Matrix Operations for Beginners

    By Joseph W Barnett • October 12, 2025
    Learn matrix addition, subtraction, multiplication, scalar multiplication, transpose, and trace in this step-by-step guide to basic matrix operations.
    learn More
  • Euler Substitution Examples with Solutions: A Complete Step-by-Step Beginner’s Guide

    By Joseph W Barnett • October 9, 2025
    Learn how to solve integrals involving radicals with this complete beginner’s guide providing Euler substitution examples with solutions.
    learn More
  • How to Use the Weierstrass Substitution Step by Step with Examples

    By Joseph W Barnett • October 7, 2025
    This guide explains how to use the Weierstrass substitution step by step to solve trigonometric integrals with examples.
    learn More
  • Beginner’s Guide to Changing Variables in Double and Triple Integrals: Everything You Need to Know

    By Joseph W Barnett • July 5, 2025
    This beginner’s guide to changing variables in double and triple integrals explains the process for change of variables with examples.
    learn More
  • How to Find the Determinant of a Matrix Step by Step: A Complete Beginner’s Guide

    By Joseph W Barnett • June 28, 2025
    Learn how to find the determinant of a matrix step by step with this guide including 2×2 and 3×3 determinants, cofactor expansion, and row operations.
    learn More
  • Step-by-Step Tutorial on How to Use Polar, Cylindrical, and Spherical Coordinates in Integrals

    By Joseph W Barnett • June 21, 2025
    Learn how to use polar, cylindrical, and spherical coordinates in integrals with this tutorial featuring detailed solutions for double and triple integrals.
    learn More