For centuries, the Pythagorean Theorem has occupied a unique position in mathematics: both elementary and profound. Its ...

Overview of the Thought Leap phenomenon and our bridging approach. (a) Thought Leaps in CoT; (b) Negative impact on training; (c) Bridging leaps improves reasoning performance. In this work, we ...

Learn how backpropagation works by building it from scratch in Python! This tutorial explains the math, logic, and coding behind training a neural network, helping you truly understand how deep ...

Abstract: The term substitution theorem is a vital theorem in mathematical logic that concerns the replacement operation of variables within terms. In this study, we present a comprehensive ...

Abstract: In this paper, we first present the significance of information theory and several commonly referred concepts associated with it. Then, the communication channel models constructed by ...

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School ...

Notes for MATH700132 (Mathematical Logic) taught by David Evans at Imperial in Spring 2025. They are a work in progress. These notes are primarily based on the content covered in lectures, with some ...

The PhD Programme in Mathematics is run within the "Tullio Levi-Civita" Department of Mathematics, that has a long tradition and about 100 faculty. It offers a wide range of research topics, from the ...