Hopf algebras constitute a central framework in modern algebra, merging structures from both algebra and coalgebra with an antipode map that renders them amenable to duality considerations. These ...

Abstract: This work investigated the post-quantum digital signature algorithm based on Finite Non-commutative Associative Algebras and also provides a brief analytical overview of certain post-quantum ...

Abstract: In cloud storage, selectively sharing encrypted data is becoming increasingly important. One key design challenge is the management of encryption keys. Traditionally, a large quantity of ...

The SNEG library is a package for Mathematica computer algebra system. It provides a framework for performing calculations using the operators of the second quantisation with an emphasis on the ...

Noncommutative geometry offers a radical reformulation of traditional geometrical concepts by replacing the classical notion of a manifold with a noncommutative algebra of coordinates. This approach ...

Practise your 2 times tables with this quiz. The 5 times table Learn all about the 5 times table and find out about multiples of 5. The 10 times table Discover the 10 times tables and try this quiz.

Multiplication is working out how many groups of something you have altogether. Division is working how many you get, after sharing a number between another number. You can use place value charts to ...

The general-purpose drawing package TikZ can be used to typeset commutative diagrams and other kinds of mathematical pictures, generating high-quality results. This TikZ library facilitates the ...

Thank you so much for helping us close out our 2025 fundraiser. With your support, we'll accomplish even more in 2026. Have a wonderful New Year, and enjoy the archive! By submitting, you agree to ...

I will never forget this one day when Kevin was a preschooler. We had an IEP meeting, and one of his proposed math IEP goals was to be able to visualize and identify what 2 of something looks like or ...