This book offers a clear, self-contained introduction to algebraic number theory, guiding readers from foundational concepts to a largely unexplored research topic: the distribution of units in ...

08 Divisibility §9.1–9.2 materials/lecture-notes/lec08.pdf materials/recitations-f10/rec08.pdf 09 Modular Arithmetic §9.6–9.7, 9.9 materials/lecture-notes/lec09.pdf materials/recitations-f10/rec09.pdf ...

1 UMRI MSN, Felix Houphouet-Boigny National Polytechnic Institute, Yamoussoukro, Ivory Coast. 2 Nangui Abrogoua University, Applied Fundamental Sciences Department, Abidjan, Ivory Coast. 3 UFRMI, ...

Suppose you were asked to design an abridged computer science (CS) program consisting of just three courses. How would you go about it? The first course would probably be an introduction to computer ...

IBM's Naval Ordnance Research Calculator (NORC) was the first supercomputer (1) and the most powerful computer on earth from 1954 to about 1963, and remained in service until 1968. Built between 1950 ...

One day in late December, I downloaded a program called Whisper.cpp onto my laptop, hoping to use it to transcribe an interview I’d done. I fed it an audio file and, every few seconds, it produced one ...

Gap: Real implementation of finite automata use the structure of the alphabet, for example, character classes, to enable efficient data structures and algorithms. These aspects are missing in the way ...

Hurwitz class numbers were introduced over 100 y ago, and they impact different areas of mathematics. In particular, their generating function is a so-called mock modular form. Despite their ...

The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.” In the run-up to the presentation of the Fields ...