165 research outputs found
Finite-dimensional algebras with smallest resolutions of simple modules
Let be a finitely generated left module over a left artinian ring ,
and let be the infinite sequence of nonnegative integers where
is the length of the -th term of the minimal projective resolution of
. We introduce a preorder relation on the set and
characterize the elementary finite-dimensional algebras with the
following property. Let be a simple -module, and let be a
finitely generated module over an arbitrary left artinian ring . If the
projective dimension of does not exceed the projective dimension of ,
then . We characterize the indicated algebras by quivers with
relations.Comment: Minor revisions, to appear in Journal of Algebr
Is Speciation Accompanied by Rapid Evolution? Insights from Comparing Reproductive and Nonreproductive Transcriptomes in Drosophila
The tempo and mode of evolutionary change during speciation have remained contentious until recently. While much of the evidence claiming speciation is an abrupt and rapid process comes from fossil data, recent molecular phylogenetics show that the background of gradual evolution is often broken by accelerated rates of molecular evolution during speciation. However, what kinds of genes affect or are affected by speciation remains unexplored. Our analysis of 4843 protein-coding genes in five species of the Drosophila melanogaster subgroup shows that while ~70% of genes follow clock-like evolution, between 17–19.67% of loci show signatures of accelerated rates of evolution in recently formed species. These genes show 2-3-fold higher rates of substitution in recently diverged species compared to older species. This fraction of loci affects a diverse range of functions. Only a small proportion of reproductive genes experience speciation-related accelerated changes but many sex-and -reproduction related genes show an interesting pattern of persistent rapid evolution suggesting that sex-and-reproduction related genes are under constant selective pressures. The identification of loci associated with accelerated evolution allows us to address the mechanisms of rapid evolution and speciation, which in our study appears to be a combination of both selection and rapid demographical changes
The story of maths : a brief review
If you want a whirlwind tour of the history of mathematics
in four hours, where you will be taken to marvellous sites
all around the globe, meet historians of mathematics,
mathematicians, curators of museums, descendants of famous
mathematicians and also learn some mathematics, then
you must see the four-part series called The Story of Maths
A review of the cartoon guide to algebra and the cartoon guide to calculus
I don’t know what your experience of learning
mathematics was—but for me, till I went to
graduate school and except for a few courses as an
undergraduate, it was a very heavy affair. First of all, there
was an overwhelming sense of being weighed down that was
associated with ‘knowledge’. There was so much to learn, so
much to remember and so much to be tested on! There was
no sense of lightness associated with learning, no sense of
play or joy in discovering and understanding. I remember
once, wandering around a huge library with this feeling, and
coming upon a lovely poem by Justin Richardson (Punch,
1952), which gave me immense relief. It goes like this
From regular pentagons to the icosahedron via the golden ratio - part I
This series of articles will explore an amazing connection between three different objects in mathematics: the regular pentagon, the Golden Ratio and the icosahedron. Obviously, if the Golden Ratio is involved then the Fibonacci sequence can’t be far behind and, if the icosahedron is, so is its dual the dodecahedron! In the first of these articles we will begin with the question of how to construct regular polygons, and restrict our attention to the regular pentagon and some of its properties. The regular pentagon serves as a doorway to a veritable treasure house of interconnected mathematical ideas and it never fails to astonish me. At the outset I would like to acknowledge that almost all the ideas discussed here can be found in [3]. In this series of articles we expand on some of the ideas and take a few digressions along the way
Review of "math! encounters with high school students" by serge lang.
The notion of dialogue and mathematics may at first seem
a strange combination, but if one thinks about it, often
in a lively interactive classroom this is exactly what is
transpiring. According to the late physicist David Bohm, the root of the word dialogue comes from the Greek dialogus. The word logos in turn can be interpreted as ‘meaning of the word’ and dia means ‘through’. So dialogue can then be seen as a process where there is a flow of meaning. All teachers would agree that this is what they would like in their classroom. The book under review, Math! Encounters with High School Students by Serge Lang, is an old one, published in 1985, but well worth bringing to the notice of students and teachers of mathematics. It is a series of seven dialogues on mathematics with school students and a postscript discussing mathematics teaching
From regular pentagons to the icosahedron and dodecahedron via the golden ratio – ii
In the previous article (At Right Angles, Issue 4, July 2019,
pages 5-9 ) we saw how we could construct a regular
pentagon using a ruler and compass, and discovered a nested
sequence of pentagons that can be built up by extending the
sides of a given regular pentago
A culture of enjoying mathematics
It appears that whether we like or not, Mathematics pervades all aspect of our life. Whether you are a farmer or a techie, a comfortable relationship with mathematics, and competency at the level at which one uses it,is a requisite in a equitable society
Introducing numberphile
Ever since we decided to reintroduce our readers to
Numberphile(https://www.numberphile.com/), I have been obsessively watching videos hosted via YouTube on the site! I have also listened to some podcasts. The content is both
mathematics and interviews with mathematicians about a range
of topics from “Why do people hate mathematics?” to “Fame and
Admiration.
Introducing Steven Strogatz
He is the author of several best-selling books like The Joy of X: A Guided Tour of Math, From One to Infinity. He writes frequently for the New York Times, and appears regularly on National Public Radio in the US.
The purpose of this short review is to alert readers to Steven Strogatz’s work (http://www.stevenstrogatz.com) in general, and to draw special attention to 15 pieces, under the broad heading of ‘Elements of Maths,' that he wrote for the New York Times from January 2010 to May 2010(http://www.stevenstrogatz.com/essays/tag=Elements+of+Math)
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