Ordinary differential equations (ODEs) play a pivotal role across the mathematical sciences, modelling phenomena from celestial mechanics to population dynamics. An algebraic solution of an ODE is one ...

Algebra can be tough to figure out, and textbook answer keys often don't display the step-by-step solutions so crucial to learning. Mathpapa is a website that walks you through each step of an ...

The Yang–Baxter equation is a foundational relation in mathematical physics and algebra, originally arising in studies of integrable models and low-dimensional topology. In its set-theoretic form, it ...

Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials.

A UNSW Sydney mathematician has discovered a new method to tackle algebra’s oldest challenge – solving higher polynomial equations. Polynomials are equations involving a variable raised to powers, ...

§7.1 I HAVE DESCRIBED HOW SOLUTIONS to the general cubic and quartic equations were found by Italian mathematicians in the first half of the 16th century. The next obvious challenge was the general ...

You scrambled up a Rubik’s cube, and now you want to put it back in order. What sequence of moves should you make? Surprise: You can answer this question with modern algebra. You might remember ...

§CQ.1 THE FIRST GREAT ADVANCE in algebra after the Middle Ages was the general solution of the cubic equation, immediately followed by a solution for the quartic. I tell the full story in the next ...