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A list of Free and Opensource Maths textbooks


#maths #mathematics #science #books
 

La solución a un meme matemático con trampa


Bild/Foto

#ciencia #curvas elípticas #ecuaciones diofánticas #matemáticas #mathematics #noticias #science #teoría de números
La solución a un meme matemático con trampa

La Ciencia de la Mula Francis: La solución a un meme matemático con trampa - La Ciencia de la Mula Francis

 

La solución a un meme matemático con trampa


Bild/Foto

#ciencia #curvas elípticas #ecuaciones diofánticas #matemáticas #mathematics #noticias #science #teoría de números
La solución a un meme matemático con trampa

La Ciencia de la Mula Francis: La solución a un meme matemático con trampa - La Ciencia de la Mula Francis

 

"Darwin is dead, and we have killed him!"

Mathematical challenges to Darwin’s Theory of Evolution, with #DavidBerlinski, #StephenMeyer, and #DavidGelernter





Based on new #evidence and #knowledge that functioning #proteins are extremely rare, should #Darwin’s theory of evolution be dismissed, dissected, developed or replaced with a theory of intelligent design?

Has #Darwinism really failed? #PeterRobinson discusses it with David #Berlinski, David #Gelernter, and Stephen #Meyer, who have raised #doubts about Darwin’s #theory in their two books and essay, respectively #TheDeniableDarwin, #DarwinsDoubt, and “Giving Up Darwin” (published in the Claremont Review of Books).

#Robinson asks them to convince him that the term “species” has not been defined by the authors to Darwin’s disadvantage. Gelernter replies to this and explains, as he expressed in his essay, that he sees Darwin’s theory as #beautiful (which made it difficult for him to give it up): “Beauty is often a telltale sign of #truth. Beauty is our guide to the intellectual #universe—walking beside us through the uncharted wilderness, pointing us in the right direction, keeping us on track—most of the time.” Gelernter notes that there’s no reason to doubt that Darwin successfully explained the small adjustments by which an #organism #adapts to local circumstances: changes to fur density or wing style or beak shape. Yet there are many reasons to doubt whether Darwin can answer the hard questions and explain the big picture—not the fine-tuning of #existing #species but the #emergence of new ones. Meyer explains Darwinism as a comprehensive #synthesis, which gained #popularity for its #appeal. Meyer also mentions that one cannot disregard that Darwin’s book was based on the facts present in the 19th century.

Robinson then asks the panel whether Darwin’s theory of gradual evolution is contradicted by the explosion of fossil records in the #Cambrian period, when there was a sudden occurrence of many species over the span of approximately seventy million years (Meyer’s noted that the date range for the Cambrian period is actually narrowing). Meyer replies that even #population #genetics, the mathematical branch of Darwinian theory, has not been able to support the explosion of fossil records during the Cambrian period, biologically or geologically.

Robinson than asks about Darwin’s main problem, #molecular #biology, to which Meyer explains, comparing it to digital world, that building a new biological function is similar to building a new #code, which Darwin could not understand in his era. Berlinski does not second this and states that the cell represents very complex machinery, with complexities increasing over time, which is difficult to explain by a theory. Gelernter throws light on this by giving an example of a necklace on which the positioning of different beads can lead to different #permutations and #combinations; it is really tough to choose the best possible combination, more difficult than finding a needle in a haystack. He seconds Meyer’s statement that it was impossible for Darwin to understand that in his era, since the math is…

#science #biology #mathematics #maths #bio #research #evidence #empiricism
 

"Darwin is dead, and we have killed him!"

Mathematical challenges to Darwin’s Theory of Evolution, with #DavidBerlinski, #StephenMeyer, and #DavidGelernter





Based on new #evidence and #knowledge that functioning #proteins are extremely rare, should #Darwin’s theory of evolution be dismissed, dissected, developed or replaced with a theory of intelligent design?

Has #Darwinism really failed? #PeterRobinson discusses it with David #Berlinski, David #Gelernter, and Stephen #Meyer, who have raised #doubts about Darwin’s #theory in their two books and essay, respectively #TheDeniableDarwin, #DarwinsDoubt, and “Giving Up Darwin” (published in the Claremont Review of Books).

#Robinson asks them to convince him that the term “species” has not been defined by the authors to Darwin’s disadvantage. Gelernter replies to this and explains, as he expressed in his essay, that he sees Darwin’s theory as #beautiful (which made it difficult for him to give it up): “Beauty is often a telltale sign of #truth. Beauty is our guide to the intellectual #universe—walking beside us through the uncharted wilderness, pointing us in the right direction, keeping us on track—most of the time.” Gelernter notes that there’s no reason to doubt that Darwin successfully explained the small adjustments by which an #organism #adapts to local circumstances: changes to fur density or wing style or beak shape. Yet there are many reasons to doubt whether Darwin can answer the hard questions and explain the big picture—not the fine-tuning of #existing #species but the #emergence of new ones. Meyer explains Darwinism as a comprehensive #synthesis, which gained #popularity for its #appeal. Meyer also mentions that one cannot disregard that Darwin’s book was based on the facts present in the 19th century.

Robinson then asks the panel whether Darwin’s theory of gradual evolution is contradicted by the explosion of fossil records in the #Cambrian period, when there was a sudden occurrence of many species over the span of approximately seventy million years (Meyer’s noted that the date range for the Cambrian period is actually narrowing). Meyer replies that even #population #genetics, the mathematical branch of Darwinian theory, has not been able to support the explosion of fossil records during the Cambrian period, biologically or geologically.

Robinson than asks about Darwin’s main problem, #molecular #biology, to which Meyer explains, comparing it to digital world, that building a new biological function is similar to building a new #code, which Darwin could not understand in his era. Berlinski does not second this and states that the cell represents very complex machinery, with complexities increasing over time, which is difficult to explain by a theory. Gelernter throws light on this by giving an example of a necklace on which the positioning of different beads can lead to different #permutations and #combinations; it is really tough to choose the best possible combination, more difficult than finding a needle in a haystack. He seconds Meyer’s statement that it was impossible for Darwin to understand that in his era, since the math is…

#science #biology #mathematics #maths #bio #research #evidence #empiricism
 
Interesting. A conjecture about Boolean functions has just been proven. Article also shows the real world relevance of the conjecture and other related measures of Boolean functions.
A paper posted online this month has settled a nearly 30-year-old conjecture about the structure of the fundamental building blocks of computer circuits. This “sensitivity” conjecture has stumped many of the most prominent computer scientists over the years, yet the new proof is so simple that one researcher summed it up in a single tweet.

“This conjecture has stood as one of the most frustrating and embarrassing open problems in all of combinatorics and theoretical computer science,” wrote Scott Aaronson of the University of Texas, Austin, in a blog post. “The list of people who tried to solve it and failed is like a who’s who of discrete math and theoretical computer science,” he added in an email.
[...]
Imagine, Mathieu said, that you are filling out a series of yes/no questions on a bank loan application. When you’re done, the banker will score your results and tell you whether you qualify for a loan. This process is a Boolean function: Your answers are the input bits, and the banker’s decision is the output bit.

If your application gets denied, you might wonder whether you could have changed the outcome by lying on a single question — perhaps, by claiming that you earn more than $50,000 when you really don’t. If that lie would have flipped the outcome, computer scientists say that the Boolean function is “sensitive” to the value of that particular bit. If, say, there are seven different lies you could have told that would have each separately flipped the outcome, then for your loan profile, the sensitivity of the Boolean function is seven.

Computer scientists define the overall sensitivity of the Boolean function as the biggest sensitivity value when looking at all the different possible loan profiles. In some sense, this measure calculates how many of the questions are truly important in the most borderline cases — the applications that could most easily have swung the other way if they’d been ever so slightly different.
[...]
Sensitivity is usually one of the easiest complexity measures to compute, but it’s far from the only illuminating measure. For instance, instead of handing you a paper application, the banker could have interviewed you, starting with a single question and then using your answer to determine what question to ask next. The largest number of questions the banker would ever need to ask before reaching a decision is the Boolean function’s query complexity.

This measure arises in a host of settings — for instance, a doctor might want to send a patient for as few tests as possible before reaching a diagnosis, or a machine learning expert might want an algorithm to examine as few features of an object as possible before classifying it. “In a lot of situations — diagnostic situations or learning situations — you’re really happy if the underlying rule … has low query complexity,” O’Donnell said.
#Mathematics #Proofs #Conjectures #ComputerScience
 
Interesting. A conjecture about Boolean functions has just been proven. Article also shows the real world relevance of the conjecture and other related measures of Boolean functions.
A paper posted online this month has settled a nearly 30-year-old conjecture about the structure of the fundamental building blocks of computer circuits. This “sensitivity” conjecture has stumped many of the most prominent computer scientists over the years, yet the new proof is so simple that one researcher summed it up in a single tweet.

“This conjecture has stood as one of the most frustrating and embarrassing open problems in all of combinatorics and theoretical computer science,” wrote Scott Aaronson of the University of Texas, Austin, in a blog post. “The list of people who tried to solve it and failed is like a who’s who of discrete math and theoretical computer science,” he added in an email.
[...]
Imagine, Mathieu said, that you are filling out a series of yes/no questions on a bank loan application. When you’re done, the banker will score your results and tell you whether you qualify for a loan. This process is a Boolean function: Your answers are the input bits, and the banker’s decision is the output bit.

If your application gets denied, you might wonder whether you could have changed the outcome by lying on a single question — perhaps, by claiming that you earn more than $50,000 when you really don’t. If that lie would have flipped the outcome, computer scientists say that the Boolean function is “sensitive” to the value of that particular bit. If, say, there are seven different lies you could have told that would have each separately flipped the outcome, then for your loan profile, the sensitivity of the Boolean function is seven.

Computer scientists define the overall sensitivity of the Boolean function as the biggest sensitivity value when looking at all the different possible loan profiles. In some sense, this measure calculates how many of the questions are truly important in the most borderline cases — the applications that could most easily have swung the other way if they’d been ever so slightly different.
[...]
Sensitivity is usually one of the easiest complexity measures to compute, but it’s far from the only illuminating measure. For instance, instead of handing you a paper application, the banker could have interviewed you, starting with a single question and then using your answer to determine what question to ask next. The largest number of questions the banker would ever need to ask before reaching a decision is the Boolean function’s query complexity.

This measure arises in a host of settings — for instance, a doctor might want to send a patient for as few tests as possible before reaching a diagnosis, or a machine learning expert might want an algorithm to examine as few features of an object as possible before classifying it. “In a lot of situations — diagnostic situations or learning situations — you’re really happy if the underlying rule … has low query complexity,” O’Donnell said.
#Mathematics #Proofs #Conjectures #ComputerScience
 
Hey everyone, I’m #newhere. I’m interested in #academia, #chinoiserie, #economics, #gametheory, #literature, #lowbrowart, #mathematicians, #mathematics, #philosophy, #physics, #poetry, #science and #talking (and listening...sometimes 😏). Wow, I feel like a snob just looking at those tags, so:

My musical tastes are broad and shallow. I'm basically, guiltily monolingual (though I'd be happy to get back into Hindi if I had someone to talk to... I'm not ready to inflict my French on anyone yet). I have the soul of a stamp-collector, or perhaps, to be kinder, a medieval scholastic. My guilty pleasures include reading shitty, self-indulgent fanfiction fix-its and running too far in dumb places/conditions. I love to travel, especially in moldy, old European cities, but rarely get to do so for pleasure. I also like the outdoors, provided that it doesn't go much above 25 C... Feynman was my first crush. (Actually, that's a lie, I think it was the guy with the turtlenecks from Earth Final Conflict, but I don't even remember his name. No, that's also a lie, I think it was 'Liam.') I may or may not still have a huge man-crush on Pascal.

I find Facebook deeply boring, and not a great way to find new people or ideas (also, everyone I know is on there). Twitter has its uses, but those are mostly: finding interesting thinkers, and then, well, twitting them 😏. I thought about trying Diaspora a few years ago, but now all the cool people I followed on Google+ are... not on Google+ anymore. This is, apparently, what happens to me: the mysterious operations of the free market manage to create something that I really love, and then there isn't enough of a consumer base to actually sustain it. It happens with make-up, books, TV series and ice cream flavors too. Economics is a bitch. (But I love her anyway.)
 
Hey everyone, I’m #newhere. I’m interested in #academia, #chinoiserie, #economics, #gametheory, #literature, #lowbrowart, #mathematicians, #mathematics, #philosophy, #physics, #poetry, #science and #talking (and listening...sometimes 😏). Wow, I feel like a snob just looking at those tags, so:

My musical tastes are broad and shallow. I'm basically, guiltily monolingual (though I'd be happy to get back into Hindi if I had someone to talk to... I'm not ready to inflict my French on anyone yet). I have the soul of a stamp-collector, or perhaps, to be kinder, a medieval scholastic. My guilty pleasures include reading shitty, self-indulgent fanfiction fix-its and running too far in dumb places/conditions. I love to travel, especially in moldy, old European cities, but rarely get to do so for pleasure. I also like the outdoors, provided that it doesn't go much above 25 C... Feynman was my first crush. (Actually, that's a lie, I think it was the guy with the turtlenecks from Earth Final Conflict, but I don't even remember his name. No, that's also a lie, I think it was 'Liam.') I may or may not still have a huge man-crush on Pascal.

I find Facebook deeply boring, and not a great way to find new people or ideas (also, everyone I know is on there). Twitter has its uses, but those are mostly: finding interesting thinkers, and then, well, twitting them 😏. I thought about trying Diaspora a few years ago, but now all the cool people I followed on Google+ are... not on Google+ anymore. This is, apparently, what happens to me: the mysterious operations of the free market manage to create something that I really love, and then there isn't enough of a consumer base to actually sustain it. It happens with make-up, books, TV series and ice cream flavors too. Economics is a bitch. (But I love her anyway.)
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
Apparently there is a eukaryotic phytoplankton called Braa­rudosphaera bigelowii which surrounds itself with twelve regular pentagonal CaCO3 scales (each of which in turn is constructed from five isosceles trapeziums - yes, they really are - look carefully). Each pentagon edge measures about 5μm. I am not a marine biologist so I have no idea why it does this but what a stunning piece of micro architecture it is!
Bild/Foto
#plankton #maths #dodecahedron #pentagon #mathematics #geometry #platonic #trapezium #microscopy #electronmicroscope #calcium #algae #cyanobacteria #math
 
Bild/Foto
#mathematics #animations And now an oldie from Google-plus (Oct 2014)
 
The problem is that spammer, click-baiters, all-round-troll-assholes will often tag their posts and replies with false #science, #mathematics, #news, etc. tags.
Thanks for using false tags.
 
You are correct about the #hashtags being insufficient in themselves. The problem is that spammer, click-baiters, all-round-troll-assholes will often tag their posts and replies with false #science, #mathematics, #news, etc. tags. Unfortunately, the system will add that disguised crap into your stream. :(
 
#maths #mathematics #mathsmanuelacasasoli
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.
 
#maths #mathematics #mathsmanuelacasasoli
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.
 
#maths #mathematics #mathsmanuelacasasoli
A number theorist with programming prowess has found a solution to 33 = x³ + y³ + z³, a much-studied equation that went unsolved for 64 years.
 
#science #biology #corals #mathematics #crochet

Whoa :-o awesome crochet stuff is awesome!

What happens when you mix math, coral and crochet? It’s mind-blowing

Gallery: What happens when you mix math, coral and crochet? It’s mind-blowing

How two Australian sisters channeled their love of STEM and coral reefs into the most glorious participatory art project.




https://ideas.ted.com/gallery-what-happens-when-you-mix-math-coral-and-crochet-its-mind-blowing/
 
#science #biology #corals #mathematics #crochet

Whoa :-o awesome crochet stuff is awesome!

What happens when you mix math, coral and crochet? It’s mind-blowing

Gallery: What happens when you mix math, coral and crochet? It’s mind-blowing

How two Australian sisters channeled their love of STEM and coral reefs into the most glorious participatory art project.




https://ideas.ted.com/gallery-what-happens-when-you-mix-math-coral-and-crochet-its-mind-blowing/
 

La primera solución entera de la ecuación x³+y³+z³=33


Bild/Foto

#ciencia #curiosidades #ecuaciones diofánticas #matemáticas #mathematics #noticias #science
La primera solución entera de la ecuación x³+y³+z³=33

La Ciencia de la Mula Francis: La primera solución entera de la ecuación x³+y³+z³=33 - La Ciencia de la Mula Francis

 

La primera solución entera de la ecuación x³+y³+z³=33


Bild/Foto

#ciencia #curiosidades #ecuaciones diofánticas #matemáticas #mathematics #noticias #science
La primera solución entera de la ecuación x³+y³+z³=33

La Ciencia de la Mula Francis: La primera solución entera de la ecuación x³+y³+z³=33 - La Ciencia de la Mula Francis

 
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