PDF for mathematics from the official Punjab Board website. Access chapter-wise details for mathematics with the link to download the PDF, and more to plan your studies effectively ...

Mathematics AI could be about to completely change the way we do mathematics Computers can help ensure that mathematical proofs are correct, but translating traditional maths into a machine ...

Abstract: This paper presents three new ensembles of low density generator matrix (LDGM) codes, all of which are systematic codes. We prove that, under the maximum likelihood (ML) decoding, these ...

Fermat’s Last Theorem is a mathematical conjecture about integer numbers, while the 3D Pythagoras’ theorem is a mathematical and geometrical proof about real numbers.

Lean is a functional programming language and interactive theorem prover. Our project strives to revolutionize mathematics by empowering anyone with an interest to grow in the field using Lean as ...

Learning process and inverse H-theorem It is proposed to use the time rate of decrease of the entropy defined by the response probabilities as a measure of the speed of learning.

In this paper, we provide a purely combinatorial proof of this result and new properties of the function σmex(n) σ mex (n). We generalize this combinatorial interpretation to σrmex(n) σ r mex (n), the ...

Get the right documents – Study in CanadaYou need these documents to apply for a study permit: proof of acceptance provincial attestation letter or territorial attestation letter proof of identity ...