# group actions Published articles for group actions. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Two's Complement and Group Theory DevFeed: [Two's Complement and Group Theory]() Original publisher: [Read original article]() Published: 2023-07-10T07:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [math](), [Mathematics](), [Computer science](), [Programming]() Tags: [abelian-groups](), [arithmetic](), [bits](), [boolean](), [circuits](), [computer-science](), [group-actions](), [groups](), [math](), [mathematics](), [programming](), [quotients](), [symmetry](), [twos-complement]() ### AI overview The article explains two's-complement signed integer arithmetic using group theory. It presents signed and unsigned n-bit integers as representations of the quotient group of integers modulo 2^n, clarifying why the same arithmetic circuits can operate on both. ### Source excerpt Before I discovered math, I was a first year undergrad computer science student taking Electrical Engineering 101. The first topic I learned was what bits and boolean gates are, and the second was the two's complement representation of a negative n-bit integer. At the time two's complement seemed to me like a bizarre quirk of computer programming, with minutiae you just had to memorize. If the leading bit is 1, it's negative, and otherwise it's positive. ## Group Actions and Hashing Unordered Multisets DevFeed: [Group Actions and Hashing Unordered Multisets]() Original publisher: [Read original article]() Published: 2021-10-14T08:00:00Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [hashing](), [Programming]() Tags: [abelian-groups](), [group-actions](), [group-theory](), [groups](), [hashing](), [mathematics](), [multiset](), [multisets](), [practical](), [programming](), [xor]() ### AI overview The article introduces a result by Kevin Ventullo that applies group actions to hash functions for unordered sets and multisets. It explains why incremental, order-independent hashing is useful and describes collision-related weaknesses of addition and XOR approaches. ### Source excerpt I learned of a neat result due to Kevin Ventullo that uses group actions to study the structure of hash functions for unordered sets and multisets. This piqued my interest because a while back a colleague asked me if I could think of any applications of "pure" group theory to practical computer programming that were not cryptographic in nature. He meant, not including rings, fields, or vector spaces whose definitions happen to be groups when you forget the extra structure. ## Groups -- A Primer DevFeed: [Groups -- A Primer]() Original publisher: [Read original article]() Published: 2012-12-08T23:42:10Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Mathematics](), [structure](), [Math and Logic](), [Cryptography]() Tags: [applications](), [group-actions](), [groups](), [lagrange](), [mathematics](), [public-key](), [set-theory](), [structure](), [symmetry](), [theory]() ### AI overview This primer introduces group theory as the study of algebraic structures that can describe operations beyond ordinary numbers. It motivates the subject through examples involving symmetry, squares, and Rubik's Cube, and notes applications including public-key cryptography, error detection, crystal structures, particle physics, and mathematical biology. ### Source excerpt The study of groups is often one's first foray into advanced mathematics. In the naivete of set theory one develops tools for describing basic objects, and through a first run at analysis one develops a certain dexterity for manipulating symbols and definitions. But it is not until the study of groups that one must step back and inspect the larger picture. The main point of that picture (and indeed the main point of a group) is that algebraic structure can be found in the most unalgebraic of settings.