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As Math Grows More Complex, Will Computers Reign?

As Math Grows More Complex, Will Computers Reign? | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

Shalosh B. Ekhad, the co-author of several papers in respected mathematics journals, has been known to prove with a single, succinct utterance theorems and identities that previously required pages of mathematical reasoning. Last year, when asked to evaluate a formula for the number of integer triangles with a given perimeter, Ekhad performed 37 calculations in less than a second and delivered the verdict: “True.”

 

Shalosh B. Ekhad is a computer. Or, rather, it is any of a rotating cast of computers used by the mathematician Doron Zeilberger, from the Dell in his New Jersey office to a supercomputer whose services he occasionally enlists in Austria. The name — Hebrew for “three B one” — refers to the AT&T 3B1, Ekhad’s earliest incarnation.

 

“The soul is the software,” said Zeilberger, who writes his own code using a popular math programming tool called Maple.

 

A mustachioed, 62-year-old professor at Rutgers University, Zeilberger anchors one end of a spectrum of opinions about the role of computers in mathematics. He has been listing Ekhad as a co-author on papers since the late 1980s “to make a statement that computers should get credit where credit is due.” For decades, he has railed against “human-centric bigotry” by mathematicians: a preference for pencil-and-paper proofs that Zeilberger claims has stymied progress in the field. “For good reason,” he said. “People feel they will be out of business.”


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MATH WORLD

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MATHEMATICS UNDERSTANDING AND HISTORY
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The World is Robert: Eglash on African Fractals: Architecture ...

The World is Robert: Eglash on African Fractals: Architecture ... | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Sure, some of the binary math rooted in doubling in various African societies can be found elsehwere in the world, but what struck me the most about Eglash's work is his claim for an African origin of 'geomancy' or divination that reached medieval...
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Online Math Programs | Math Practice & Learning

Online Math Programs | Math Practice & Learning | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Online Math Programs with Interactive math worksheets, hints, video Lessons.

Via Ann Marie Davis Bishop, Harpal S.sandhu
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Convert Fractional value to an equivalent Percentage value

Learn to convert a fractional value to percentage. Also learn the concept and reason behind the steps followed. For more video on percentage and many more ot...
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GCSE Maths - Rules of Indices (3) (Negative and Fractional Powers) A Star Higher

All videos can be found at www.m4ths.com and www.astarmaths.com These videos were donated to the channel by Steve Blades of maths247 'fame'. Please share via...
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Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles

Dynamics and Structure in Cell Signaling Networks: Off-State Stability and Dynamically Positive Cycles | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

The signaling system is a fundamental part of the cell, as it regulates essential functions including growth, differentiation, protein synthesis, and apoptosis. A malfunction in this subsystem can disrupt the cell significantly, and is believed to be involved in certain diseases, with cancer being a very important example. While the information available about intracellular signaling networks is constantly growing, and the network topology is actively being analyzed, the modeling of the dynamics of such a system faces difficulties due to the vast number of parameters, which can prove hard to estimate correctly. As the functioning of the signaling system depends on the parameters in a complex way, being able to make general statements based solely on the network topology could be especially appealing. We study a general kinetic model of the signaling system, giving results for the asymptotic behavior of the system in the case of a network with only activatory interactions. We also investigate the possible generalization of our results for the case of a more general model including inhibitory interactions too. We find that feedback cycles made up entirely of activatory interactions (which we call dynamically positive) are especially important, as their properties determine whether the system has a stable signal-off state, which is desirable in many situations to avoid autoactivation due to a noisy environment. To test our results, we investigate the network topology in the Signalink database, and find that the human signaling network indeed has only significantly few dynamically positive cycles, which agrees well with our theoretical arguments.


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Yummy Math | We provide teachers and students with mathematics relevant to our world today …

Yummy Math | We provide teachers and students with mathematics relevant to our world today … | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
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Tying Knots with Light: Spontaneous knotting of self-trapped light waves

Tying Knots with Light: Spontaneous knotting of self-trapped light waves | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

A new theory and simulations have been developed that describe a spinning optical soliton whose propagation spontaneously excites knotted and linked optical vortices. The nonlinear phase of the self-trapped light beam breaks the wave front into a sequence of optical vortex loops around the soliton, which, through the soliton's orbital angular momentum and spatial twist, tangle on propagation to form links and knots. Similar spontaneous knot topology should be a universal feature of waves whose phase front is twisted and nonlinearly modulated, including superfluids and trapped matter waves.


Via Dr. Stefan Gruenwald, Harpal S.sandhu
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Functional modules, structural topology, and optimal activity in metabolic networks

Functional modules, structural topology, and optimal activity in metabolic networks | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

Modular organization in biological networks has been suggested as a natural mechanism by which a cell coordinates its metabolic strategies for evolving and responding to environmental perturbations. To understand how this occurs, there is a need for developing computational schemes that contribute to integration of genomic-scale information and assist investigators in formulating biological hypotheses in a quantitative and systematic fashion. In this work, we combined metabolome data and constraint-based modeling to elucidate the relationships among structural modules, functional organization, and the optimal metabolic phenotype of Rhizobium etli, a bacterium that fixes nitrogen in symbiosis with Phaseolus vulgaris. To experimentally characterize the metabolic phenotype of this microorganism, we obtained the metabolic profile of 220 metabolites at two physiological stages: under free-living conditions, and during nitrogen fixation with P. vulgaris. By integrating these data into a constraint-based model, we built a refined computational platform with the capability to survey the metabolic activity underlying nitrogen fixation in R. etli. Topological analysis of the metabolic reconstruction led us to identify modular structures with functional activities. Consistent with modular activity in metabolism, we found that most of the metabolites experimentally detected in each module simultaneously increased their relative abundances during nitrogen fixation. In this work, we explore the relationships among topology, biological function, and optimal activity in the metabolism of R. etli through an integrative analysis based on modeling and metabolome data. Our findings suggest that the metabolic activity during nitrogen fixation is supported by interacting structural modules that correlate with three functional classifications: nucleic acids, peptides, and lipids. More fundamentally, we supply evidence that such modular organization during functional nitrogen fixation is a robust property under different environmental conditions.

 

Resendis-Antonio O, Hernández M, Mora Y, Encarnación S. (2012).  PLoS Comput Biol. 2012 Oct;8(10):e1002720.


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Welcome to Mathszone < Mathszone

Welcome to Mathszone < Mathszone | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
interactive primary maths resources for education
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Videos 3-4

Videos 3-4 | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
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Maths Games

Maths Games | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Maths games for all ages to help you practise all those important mathematics skills including counting, adding, subtraction, times tables, measuring, shapes, fractions and decimals and much more.
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Catherine Philpot's curator insight, April 8, 2013 5:17 AM

Great general maths games - especially good for times tables

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Plane Math

Click here to edit the title

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Math Videos, Games, and Worksheets for the Common Core | Math Chimp

Math Videos, Games, and Worksheets for the Common Core | Math Chimp | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Check out our selection of free math videos, games, and worksheets. We collect the best math activities online for K-8 and organize them by the Common Core Standards.
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IEEE 2013 MATLAB FULL DOCUMENT Multi fractal Texture Estimation for Detection and Segmentation of Br

PG Embedded Systems #197 B, Surandai Road Pavoorchatram,Tenkasi Tirunelveli Tamil Nadu India 627 808 Tel:04633-251200 Mob:+91-98658-62045 General Information...
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British Library - Press and Policy Centre - The importance of data ...

British Library - Press and Policy Centre - The importance of data ... | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Winton was founded by David Harding in 1997 with an absolute commitment to employing advanced mathematical, statistical and computational techniques to develop systematic, quantitative, trading strategies for global futures and equity markets, a...
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Special numbers - In this maths show DVD extract Matt Parker reveals his favourite number

An extract from "Are you feeling lucky?", a maths show for students aged 13-16, now available as a DVD maths teaching resource at www.mathsonscreen.com.
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Mathematical Art Presented by the American Mathematical Society

Mathematical Art Presented by the American Mathematical Society | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

"The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.

 

"Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more."

 


Via Jim Lerman, Alessandro Rea, Harpal S.sandhu
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BookChook's curator insight, May 31, 2013 3:52 PM

Help kids connect Maths with Art 

Cameron Brotherton -Jennings's comment, May 31, 2013 7:40 PM
Music Mathematics Man
MsPedagogicalProwess's curator insight, April 12, 9:28 PM

Provides an insight into the cross integration between Maths and Arts. This is a great link, for a foray into higher order thinking, and visualisation. Could be a valuable resource for upper primary, in linking their mathematical learning to a more meaning context (in linking to their experiences of art in nature and in man-made objects around them) –


There are links to galleries & exhibitions – which could translate into a class excursion. 

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Dark Roasted Blend: Topological Marvel: The Klein Bottle in Art

Dark Roasted Blend: Topological Marvel: The Klein Bottle in Art | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it

A geometric enigma, a convoluted mind-bender dropped upon us from the wonderful extra-dimensional realm of topology, the Klein Bottle is perhaps even popular with artists and architects than the ubiquitous Moebius strip. In fact, the Klein Bottle is what happens when you merge two Moebius Strips together: the resulting shape will still have only one side - with its inside and outside merging into one!


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Spatial Topology | GISDoctor.com

The concept of topology isn’t something that every spatially enabled person fully understands. That is OK, because I too had to learn (and relearn) how spatial topology works over the years, especially early on back in the ArcView 3.X days. I think this experience is fairly typical of someone who uses GIS. If one is taking a GIS course or a course that uses GIS it is not very often that the concept of spatial topology is covered in-depth or at all. Spatial topology also may not be something that people are overly concerned about during their day-to-day workflow, meaning they may let their geospatial topology skills slide from time to time. As a public service here is a basic overview of geospatial topology.

 

First question: What is topology?

You have probably heard the term topology before, whether it was in a GIS course where the instruction lightly glazed over the topic, or in a geometry /mathematics course.

 

Technically speaking, topology is a field of mathematics/geometry/graph theory, that studies how the properties of a shape remain under a number of different transformations, like bending, stretching, or twisting. The field of topology is well established within mathematics and far more complicated than I wish to get in this post.


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InfoSec Institute Resources – Network Topology

InfoSec Institute Resources – Network Topology | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
IDS: An intrusion detection system can be software-based or hardware-based and is used to monitor network packets or systems for malicious activity and do a specific action if such activity is detected.

Via Daniel A. Libby, CFC, Harpal S.sandhu
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Profile of math-inspired 3D printing sculptor Bathsheba Grossman - Boing Boing

Profile of math-inspired 3D printing sculptor Bathsheba Grossman - Boing Boing | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Boing Boing Profile of math-inspired 3D printing sculptor Bathsheba Grossman Boing Boing I was originally a math major interested in geometry and topology, when as a college senior I met the remarkable sculptor Erwin Hauer, and suddenly it was...

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Math Interactives

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Ayad Altory's curator insight, February 10, 2013 6:57 AM

משחקים במתמטיקה

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Erich's Puzzle Palace

Erich's Puzzle Palace | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
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Yummy Math | We provide teachers and students with mathematics relevant to our world today …

Yummy Math | We provide teachers and students with mathematics relevant to our world today … | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
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Math File Folder Games

Math File Folder Games | MATHEMATICS-NETWORK=NATURE=BASICS | Scoop.it
Math File Folder Games are an inexpensive way to teach and review a wide selection of math skills! Printable math games & Math apps: Specializing in 5th grade math games to 8th grade math games.
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