# abelian groups Published articles for abelian groups. 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. ## Homology Theory -- A Primer DevFeed: [Homology Theory -- A Primer]() Original publisher: [Read original article]() Published: 2013-04-03T20:07:46Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Computing]() Tags: [abelian-groups](), [algebraic-topology](), [fundamental-group](), [groups](), [homology](), [homotopy](), [linear-algebra](), [mathematics](), [matrices](), [primer](), [row-reduction](), [series](), [simplicial-complex](), [topological-invariant](), [topology](), [tor](), [vector-spaces]() ### AI overview A primer on homology theory that introduces homology groups as computable algebraic invariants of topological spaces. It emphasizes linear algebra, row reduction, vector spaces, and the mathematical background needed to implement related programs. ### Source excerpt This series on topology has been long and hard, but we're are quickly approaching the topics where we can actually write programs. For this and the next post on homology, the most important background we will need is a solid foundation in linear algebra, specifically in row-reducing matrices (and the interpretation of row-reduction as a change of basis of a linear operator). Last time we engaged in a whirlwind tour of the fundamental group and homotopy theory.