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## Rattle my worldview - Has a book ever changed your life?

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drunken
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### Re: I need a book to rattle my worldview

Zen and the Art of Motorcycle Maintenance
Gödel, Escher, Bach (this is long and difficult but 100% worth it)
Catch 22

I would also like to ad this one that I am surprised is not present (perhaps it is too obvious and everyone has read it).

A Brave New World - Aldous Huxley
***This post is my own opinion and no claim is being made that it is in any way scientific nor intended to be construed as such by any reader***

Koboldskind
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### Re: I need a book to rattle my worldview

RedNifre wrote:"The Selfish Gene" by Richard Dawkins. is just one book that totally shattered my world view. The book is so intense and powerful, I literaly gasped at some parts of it. At some parts I put the book down, got out of my chair, walked around and stared at the wall for a few minutes to let it sink in. It is really the most mind-expanding book I ever read. It totally turned my brain inside out.

..snip..[/color]

I can not agree enough with this one. Even if you are certain that live on earth was created in an evolutionary process (something i assume about everyone reading xkcd), this book will make you realize you never really thought about it in detail. And in doing so, it will make you see the world in a very different light.

After that one, i suggest "The Meme Machine" by Susan Blackmore. She takes Dawkin's ideas and applies them to culture and the way we think. To be quite exact, Dawkins himself came up with the basic idea, but Blackmore takes it and fleshes it out in unexpected ways and forms a theory of culture that you may or may not agree with, but that will certainly give you lots to think about.

Ended
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### Re: I need a book to rattle my worldview

the_stabbage wrote:I would recommend the novel "Hunger", by Knut Hamsun. It's about a writer wandering through a city on the edge of starvation. Apparently it was based on 10 years of the author's live on the edge of starvation in deep poverty. It's fascinating for the mindset of its character, almost like he's happy being close to death.

I was also going to recommend this. I'm not sure that it will rattle your worldview, as such, but it's certainly one of the most profoundly disturbing novels I have read. (It's also worth reading as a classic of world literature).
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the_stabbage
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### Re: I need a book to rattle my worldview

Ended wrote:I was also going to recommend this. I'm not sure that it will rattle your worldview, as such, but it's certainly one of the most profoundly disturbing novels I have read. (It's also worth reading as a classic of world literature).

I'd say disturbing is a good way to describe the tone of the novel.. there aren't really any scenes of torture or bloodshed, but just the way the protagonist leads his life in complete emptiness really made me feel weird. Especially because I know a few people who live like that.

pullhard3r
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### Re: I need a book to rattle my worldview

Stranger in a Strange Land by Heinlein.

Antaeus
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### Re: I need a book to rattle my worldview

Guns, germs and steel, by Jared Diamond.

Diamond tries to answer the question why people on different continents and from different cultures show such dramatic differences in their scientific and social development. He makes a very convincing case for his central thesis that differences in development are largely a result of differing environmental factors, synthesising data from such diverse fields as biogeography, evolutionary biology, linguistics and archaeology.

Dori
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### Re: I need a book to rattle my worldview

V for Vendetta by David Lloyd and Alan Moore

ascendingPig
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### Re: I need a book to rattle my worldview

Another vote for GEB.

Also, I read Ender's Game at the age of nine and it changed me forever. I felt like an author had finally written about about kids without treating the reader like a child. It was so amazing, this feeling that a prepubescent girl like me was actually a real person, and actually meant something, and had the ability to achieve something awesome. That's why I always recommend Orson Scott Card to elementary schoolers who seem intelligent and like to read.
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Wildcard
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### Re: I need a book to rattle my worldview

ascendingPig wrote:Also, I read Ender's Game at the age of nine and it changed me forever. I felt like an author had finally written about about kids without treating the reader like a child. It was so amazing, this feeling that a prepubescent girl like me was actually a real person, and actually meant something, and had the ability to achieve something awesome. That's why I always recommend Orson Scott Card to elementary schoolers who seem intelligent and like to read.

Yes. Ender's Game, but I don't know that it would have the same effect if you first read it at an older age. Read it anyways, though.

1984 and Animal Farm, both by Eric Arthur Blair, had profound effects on my worldview. I find that Animal Farm gives a perfect illustration of the gradient scale from freedom to tyranny, which should have more attention put on it in our society.

I'm not done reading Dianetics yet, but even just the part I've read so far is beyond anything else I've read about the human mind and/or behavior. If you want to know why people do the things they do, read it. Definite shifts in perspective, and in a good way.
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ducknerd
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### Re: I need a book to rattle my worldview

Perhaps a little cheesy, and unusually religious for this audience, but Hugh Prather's "Notes On Love and Courage" is extremely personal and very, very powerful. As an atheist, it still affected me profoundly.

Rollo May's "Love and Will" is also excellent for changing one's worldview and is particularly powerful during existential crises (which is when I found it).

Allow me to second (or rather fourth) Fight Club, especially if you're approaching the whole "worldview-rocking" thing ironically, as it's a hard-hitting book about people trying to get hit hard metaphorically (and literally, I suppose ).

Illuminatus!, though? I read the first book of the trilogy and was amused for sure but by no means changed. I just read it as a really entertaining summary of 60s counterculture with a million hidden jokes (e.g. the yellow submarine and the KCUF) and a rehash of the whole paranoia vs. nihilism/Discordianism thing that happened in the early 70s. Please tell me if I missed something.
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Mother Nature's Son
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### Re: I need a book to rattle my worldview

Everyone likes Terry Pratchett for the humor found in his discworld books, but it seems that they often overlook the sterling sociopolitical commentaries hidden in plain sight. I love this series too, but I think his best work may be The Bromeliad Trilogy, which is both side-splittingly funny and slightly terrifying. Along a similar vein, The Science of Discworld books are probably the most entertaining, comprehensive and enlightening scientific texts I have ever read. They cover physics, biology, earth sciences, astronomy, history, and the nature of science itself, and that's just in the first few chapters. Reading any one of those three books you will learn more than in all four years of highschool science class, and you will probably learn that some of what they did teach you was wrong.

Sergei Lukyanenko's Watch books give an interesting perspective of the classic good/evil dichotomy, as well as being beautifully written and highly entertaining.

Read The Fountainhead, too. It's a sterling example of what's wrong with the world.
Cave et audi.

i_ll_winn
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### Re: I need a book to rattle my worldview

ducknerd wrote:
Illuminatus!, though? I read the first book of the trilogy and was amused for sure but by no means changed. I just read it as a really entertaining summary of 60s counterculture with a million hidden jokes (e.g. the yellow submarine and the KCUF) and a rehash of the whole paranoia vs. nihilism/Discordianism thing that happened in the early 70s. Please tell me if I missed something.

Read it, and then think about what it is really saying. Seriously, it paints a uplifting picture of death and destruction. Not only that, but it gives you a window into the warped minds of thousands of people, because the secret behind the book is that it was based off of the ramblings of multiple "crazy" people.
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icenine
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### Re: I need a book to rattle my worldview

Ender's Game and the Shadow series by Orson Scott Card: I tend to think of Ender's Game as a book for younger readers and the Shadow series as books that can last till you're older. Personal experience only, though.

Cat's Cradle by Kurt Vonnegut didn't change my view so much as reinforce my beliefs. Again, a personal thing.

Just In Case by Meg Rosoff was an interesting read which jolted me a little, but I felt like it was missing something.

poxic
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### Re: I need a book to rattle my worldview

Antaeus wrote:Guns, germs and steel, by Jared Diamond.

A whole lot of ^THIS.

GEB was wonderful, but you have to check out Hofstadter's latest: I Am a Strange Loop. It brings the notion of consciousness right into the open. It was tough reading, but once I was through it, I felt that I grokked what consciousness is. (It also pretty much convinced me that there is no "hereafter" -- does a computer keep processing "somewhere else" after you pull the plug?)
In everyone's life, at some time, our inner fire goes out. It is then burst into flame by an encounter with another human being. We should all be thankful for those people who rekindle the inner spirit.
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Hendecatope
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### Re: I need a book to rattle my worldview

The Picture of Dorian Gray, conveniently - legally - available for free. The characters in this book are engaging from the first chapter on and seem to say something relevant to themselves and you every other page. (Where a page is the amount of words you can fit on an ipod touch screen ) The idea is simple though, what if a picture soaked up your sins?

Noa
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### Has a book ever changed your life?

My Greek history professor casually mentioned in class the other day that reading the novel The Brothers Karamazov by Dostoevsky changed his life. I began to consider if anything I've ever read affected me so profoundly as to earn the status of "life-altering".

I eventually reached the conclusion that the graphic novel Persepolis by Marjane Satrapi more than meets this standard. I actually was required to read this for a cultural perspectives in literature class and I'm so glad I did. It is a memoir of the life of the author growing up in Iran in the 70's and 80's. I remember reading it and realizing I knew nothing of Iran's history or even current events. The novel was so emotional and shocking that I began researching more about Iran and the Middle East. Now I read the news constantly and am heavily involved in Amnesty International and other human rights activism and advocacy groups. I honestly think reading this graphic novel was the catalyst for my becoming the person I am now.

So has anything you've read ever deeply affected your beliefs or the way you think and act?
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Mzyxptlk
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### Re: Has a book ever changed your life?

No book has ever qualified as life-changing for me. A lot of books (films, too) have changed my feelings and emotions though. A recent example is Cryptonomicon, which has (logically) changed my opinion of the importance, usefulness and limitations of crypto.
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WBLambert
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### Re: Rattle my worldview - Has a book ever changed your life?

The Gospel According to Larry by Janet Tashjian. When I read it back in sixth grade, I decided to simplify my life. So, because of this book, I'm a minimalist (and a Buddhist, but that's indirect.)
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Chfan
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### Re: Rattle my worldview - Has a book ever changed your life?

It may not be worldview-rattling for many of you, but anything on newer physics is fucked up in so many ways- especially quantum mechanics. I'm reading Fabric of the Cosmos by Brian Greene right now and it's just really weird.
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lilyanne
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### Re: Rattle my worldview - Has a book ever changed your life?

The last four words of 1984 will shake the very foundations of your soul. The Magus, by John Fowles, will introduce to you the true meaning of humanity, both its searing beauty and its dark and animalistic core. Camus' The Stranger will make you fear to be a member of the human race, while Of Human Bondage gives us the human condiditon shorn of extraneous adornment.

To read a book, if it is well written and well meant, is to be affected by it. For everyone who has cried for Emma Bovary, made excuses for Alec D'Urberville, been drawn to Rodya Raskolnikov, loved to hate Scarlett O'Hara and hated to love Rhett Butler, who has wished Bridge to Terebithia didn't have to end the way it did, fallen in love with Mr Darcy, discovered that Hell is other people but so is heaven, or seen any aspect of themselves in a character on a page -- their life has been changed by a book. It doesn't need to be some mind blowing experience (though, for me, The Magus was,) the mere act of reading is enough.

No other medium has the purity of relationship between artist and audience that books enjoy. Save an editor or possibly a translator (who, if he is good, will keep his voice out of the text as far as possible) books are the only way to experience the vision of another human being with only a flimsy sheet of paper to separate your selves. So yes, a book has changed my life. I wouldn't think myself alive if not for the joy of words and the companionship of characters which will never fade.

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### Re: I need a book to rattle my worldview

Zen and the Art of Motorcycle Maintenance
Gödel, Escher, Bach (this is long and difficult but 100% worth it)
Catch 22

I would also like to ad this one that I am surprised is not present (perhaps it is too obvious and everyone has read it).

A Brave New World - Aldous Huxley

Not quite as epic as GEB, but a couple of books that have solidified and expanded a lot of my feelings and thoughts about many personal experiences with science, beauty, problem solving, bad science, assholes, and problem creation have been

Complexity
The Black Swan
Fooled By Randomness

Coincidentally, some of the topics covered in Taleb's books relate directly to the current economic crisis. But in general theyhave helped me gain a lot or perspective on problems I face in day to day life as well .
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### Re: Rattle my worldview - Has a book ever changed your life?

aion7 wrote:Also, 1984 by George Orwell

Wildcard wrote:1984 and Animal Farm, both by Eric Arthur Blair, had profound effects on my worldview.

1984 truly changed my life. I was brought up in a cult (though of course we didn't think of it that way at the time), and when I read it around the age of 18/19 I realised that the way the Party operates was exactly like the controlling religious system I'd been brought up in, right down to the thoughtcrime.

As a story it is good in itself, and indeed I cried at the sadness of some parts, but as an eye-opener and a warning against systems of thought, control, oppression, it severely shook the foundations of my walled-in mind and helped me free myself.
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Fledermen64
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### Re: Rattle my worldview - Has a book ever changed your life?

Hitchhikers guide to the galaxy
2001
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### Re: Rattle my worldview - Has a book ever changed your life?

alain de botton's two books i enjoyed were: how proust can change your life and kiss & tell. they're books mostly about perception in some of the most subtle hurmor out there as well as some blatantly laugh out loud moments. i'd give both a chance as they both have heavy references to proust.
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### Re: Rattle my worldview - Has a book ever changed your life?

The Tao Of Physics was a massive eye-opener for me. After pining after my ex-girlfriend, it showed me how one of the most fundamental things about life and the universe is change. Had I read a book about Buddhism itself, it would have helped, but to have it married with my chosen subject and something I've been interested in for as long as I can remember, and to show that the two are equivalent on a certain level, was absolutely amazing. It helped me cope enormously and really changed my life at the time. I will always remember it.
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Bluggo
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### Re: Rattle my worldview - Has a book ever changed your life?

When I was a kid, The Neverending Story. That book shaped very, very much of what I am.
Later, GEB and de Unamuno's "The Life of Don Quixote and Sancho" - an essay on Don Quixote that I actually enjoyed more than the book itself: I really cannot recommend it highly enough.

Also, Kafka and Rimbaud.
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urbazewski
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### Re: Rattle my worldview - Has a book ever changed your life?

Little Raccoon and the Outside World by Lilian Moore // The 100 Dresses by Eleanor Estes

Amelia Earhart // Elizabeth Blackwell // Florence Nightingale // a series of biographies of famous women that I read in elementary school

Let’s Go Europe

The Feminine Mystique Betty Friedan // Growing Up Free: Raising Your Child in the 80’s Letty Cottin Pogrebin

The Presentation of Self in Everyday Life Irving Goffman

World Hunger: Twelve Myths Frances Moore Lappe, Joseph Collins, Peter Rosse

Laurel’s Kitchen: A Handbook for Vegetarian Cookery and Nutrition
Laurel Robertson, Carol Flinders, Bronwen Godfrey

The Zero-Sum Society Lester Thurow

Feeling Good: The New Mood Therapy David D. Burns, Aaron T. Beck

The Revolutionary Ideas of Karl Marx Alex Callinicos

Writing Down the Bones
Natalie Goldberg

Complexity: The Emerging Science at the Edge of Order and Chaos M. Mitchell Waldrop // Artificial Life: A Report from the Frontier Where Computers Meet Biology Steven Levy

Open Heart, Clear Mind Thubten Chodron
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### Re: Rattle my worldview - Has a book ever changed your life?

Definitely the Ender and Shadow series, they may not change your life if you read them as an adult, but they certainly changed mine when I found them in high school, and no matter your age are definitely worth a read.

Norwegian Wood (Haruki Murakami)
Notes from Underground (Dostoevsky)
The Elegant Universe (Brian Greene)
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GeorgeYoung
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### Re: Rattle my worldview - Has a book ever changed your life?

Hitchhikers I think is the first book to really change my life, for the simply reason that it got me into reading. I'd read books before and enjoyed them, but the Hitchhikers series (All five of them) made me actively seek out new books to read, simply for the pleasure of reading a good story. I can still remember the week when I was 14 when every day, Monday to Friday, I would bring home one of the Hitchhikers books from the school library, get home and, stopping only to eat, I would read non-stop until 11, 12 even 1 o'clock. That Friday evening as I finished Mostly Harmless is one of the defining moments in my life, I think.

tommorris
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### Re: Rattle my worldview - Has a book ever changed your life?

Kripke's Naming and Necessity convinced me that necessary a posteriori truths exist.

David Armstrong's Universals: An Opinionated Introduction and Universals and Scientific Realism convinced me that there is a prima facie case for immanent universals that are compatible with physics.

Then in Belief, Truth and Knowledge, Armstrong convinced me to adopt externalism.

John Rawls' Theory of Justice convinced me that social contract theories aren't all doomed to failure.

Nozick's Anarchy, State and Utopia convinced me that not all libertarians are Glenn Beck or Ayn Rand style morons.

El Spark
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### Re: Rattle my worldview - Has a book ever changed your life?

I'm gonna go ahead and underline Ender's Game and the Shadow series.

Also (and once again, probably a bit religious for this crowd, but it's the only one I could think of that fit the topic as stated), Mere Christianity by CS Lewis. I'm intellectually a Christian myself (and that will be the end of my brand of Bible-thumping, don't worry), and I re-read this one every year or two. I always find something that makes me say, "Wow." Whether or not the reader agrees with his conclusions, dude was a thinker. He's rocked my world many times.
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Josephine
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### Re: Rattle my worldview - Has a book ever changed your life?

The Singularity is Near, by Ray Kurzweil
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### Re: Rattle my worldview - Has a book ever changed your life?

In terms of fiction (Although they are all based on true stories and events): Ellen Hopkins' books. They're aimed at people about my age, and have given me a very different view on a lot of people, particularly those who are troubled. I've been very closed off in the past, and so have been unable to sympathise or even begin to understand what some people have to go though, but these books have really opened my eyes.

Non-fiction? Any of them really. Mostly the physics ones, that made me realise my crackpot theories as a kid were embarrassingly wrong.
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### Re: Rattle my worldview - Has a book ever changed your life?

The Web of Life by Fritjof Capra, probably the first dandelion-seed, spark-on-the-powder-trail event in the long reinvention of my persona and memeset. Just perfectly intoduced me to the fractal nature of the universe, the complexities interacting on every scale, the amazing behaviour of replicating systems with simple rules, and just about everything I'm now interested in.
Read it when I was something like thirteen, in a life previously starved of a decent education in the sciences (thanks to my dyscalculia, many of my teachers automatically assumed I was just an idiot or some sort of savant for drawing and writing) and had lumped me in the lowest-set classes for anything that they even suspected might be 'too technical'. I'd been programmed-by-deficit into thinking of science as some dull, grey, tabulated catalogue of things we already know.
Then I saw a book on the shelf with an interesting pattern on the cover (a Mandelbrot Set, of course)... then glanced at the back. Then read the blurb properly. Then opened it.
What followed were three brilliant nights sitting in my chair by the light of a flickering, half-broken re-appropriated desk lamp when everyone else was asleep, filling up the empty processing space in my head with raw natural complexity and over and over again just thinking "fan-TAS-tic".

And so yeah, I'd put that down as a major one, having changed a bored, unhappy scribbler-with-pencils who had to look inward on a clichéd and underdeveloped fantasy world to perceive any great deal of beauty at all into a burning-eyed, information-eating, not-quite-an-architect-yet-but-working-on-it sort of being.

A more recent one would be so cite most of Buckminster Fuller's written work, just because it's pretty fantastic
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Jexas
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### Re: Rattle my worldview - Has a book ever changed your life?

When I read Fountainhead last winter it solidified my agnosticism and made me seriously consider atheism. Before I was just kind of doubting the reasoning of religion and the influence of God. After I finished reading Fountainhead though, I realized that man is the supreme being and not the other way around.

I read Atlas Shrugged in the summer following that winter and turned into a huge jerk. It took me about a year to recover to quasi-normalcy in terms of valuing other people. But yeah, Atlas Shrugged and Fountainhead are great books that should be required reading. Read Fountainhead first too. It deals more with the individual and less with the role of government/organizations. Also doesn't feel like Ayn Rand is reading you her beliefs through a novel quite as much like Atlas did.

Aiwendil42
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### Re: Rattle my worldview - Has a book ever changed your life?

The Fountainhead is strange - it's probably my second least favorite book I've ever read, yet I have a friend whose literary tastes otherwise agree quite closely with mine who loves it.

I don't think any book has really fundamentally changed my life, though the Tractatus Logico-Philosophicus by Wittgenstein and the collection Logical Positivism edited by Ayer did rather change my view of the fundamental nature of things.

Nullifidian
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### Re: Rattle my worldview - Has a book ever changed your life?

In terms of changing what I choose to study, it's The Eighth Day of Creation by Horace Freeland Judson, father of biologist Olivia Judson, of Dr. Tatiana's Sex Advice fame. That book, which is a mammoth study of how the science of molecular biology began, made me want to study biology in earnest. But I had a long love affair with the natural world before that. My five year-old self's childhood dream was to be a nature documentarian because my parents would take me to IMAX documentaries and I'd look at the "making of" portions and see these guys hanging out of ultralights way up in the air and I thought, That is so cool! In regards to the natural world, Aldo Leopold's A Sand County Almanac and E.O. Wilson's The Future of Life changed how I relate to and think about it.

I was also drawn into sociology by Michel Foucault's Discipline and Punish: The Birth of the Prison and then Surveillance and Security: Technological Power and Politics in Everyday Life by Torin Monahan (ed.). Foucault blew my mind on the subjects of prisons, schools, and other forms of government-mandated group dynamics, and then Surveillance and Security took his insights and turned them into serious and insightful analyses of how these dynamics play out for people in real life. That's sociology at its best, and I was very impressed with it.

Pyotr Kropotkin's The Conquest of Bread changed my political views entirely by asking questions that I was only just coming around to — and asking them a hundred years before me. I started out a moderate conservative in the Burkean mold, then I grew disenchanted with the whole conservative thing, once I saw it turning into a form of far-right demagoguery than a sober political movement. I place the blame on Reagan, who got the ball rolling by turning the fundagelical right into a voting bloc, and Gingrich, who perfected this brand of power-hungry, amoral demagoguery. It was Gingrich's accession to the role of House Speaker that got me reconsidering. I only went as far as a Blairite "third way" social democracy until I left the country for Germany, where I spent a year as an exchange student and found that social democracy was just another form of capitalist domination. Then I fell over Kropotkin's "Die Eroberung des Brotes" in a German bookstore and started reading it. It helped me get over the ingrained fear and prejudice I had against anarchism.

Much of what was best in conservatism has kept with me throughout these changes so that I now half-jokingly describe myself as "what happens when a conservative loses his faith in capitalism and government".

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### Re: Rattle my worldview - Has a book ever changed your life?

1984, Brave New World, Makers, Little Brother, and The Perks of Being a Wallflower.
Marbas wrote:I'll usually jump from one strange thought to the next, such gems as: "I wonder if bears get depressed", "I think the sun is unnecessarily smug" and so on.

Redjack443
Posts: 7
Joined: Thu Mar 04, 2010 6:14 pm UTC
Location: The Netherlands

### Re: Rattle my worldview - Has a book ever changed your life?

I haven't read any books that changed my life in a meaningful way, but some do make me look at the world in a different way.
Off the top of my head:
Gödel, Escher, Bach by Douglas Hofstadter
Brave New World by Aldous Huxly

RabbitWho
Posts: 284
Joined: Sat May 01, 2010 10:16 pm UTC
Contact:

### Re: Rattle my worldview - Has a book ever changed your life?

The Plague by Albert Camus completely changed my way of looking at life.
The Unbearable Lightness of Being by Milan Kundera completely changed my way of looking at books.


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Posted by4 years ago
Archived

## Looking for a book that is full of real world applications for Calculus.

I'm currently in Calculus II and I'm really tired of working problems without seeing what I can do with it outside of the classroom.

11 comments
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level 1
Theory of Computing7 points · 4 years ago

Maybe take a look at a physics book.

level 1
Comment deleted4 years ago
level 2
Original Poster1 point · 4 years ago

James Stewart's Calculus

level 1
-1 points · 4 years ago

I don't know of any such book, but I will definitely keep an eye on this thread in case someone else does. I am an engineering student who is also taking calc II and I can relate. I'm perfectly willing to admit that I may not be the best to give input, but I've come to the tentative conclusion that there are relatively few real world applications that are absolutely demanding of calculus. most day-to-day problems can be solved to an appreciable degree with good old fashioned algebra (engineers can usually take the liberty of saying "close enough"). In real world application, calculus isn't typically as precise as a textbook would have us believe either, any reasonably simple model will neglect certain factors anyway. I'm content in my impression that calculus is most valuable as a springboard for other topics--just about any upper division math class it would seem.

I absolutely love what I'm learning and what I'm going to learn in the years to come, but it seems unavoidable. There's a reason why calculus and most related subjects are so new in the scheme of mathematics. They were developed to tackle very specific problems that came as a consequence of what couldn't be done by older, more rudimentary methods. This set of problems is astonishingly small all things considered and lends itself to just how powerful the 'rudimentary' methods are.

This post may come off as me hating on calculus and other forms of advanced math, but I did not mean to invalidate them. They serve their purpose and are damned interesting in the process. All I'm trying to say is that is that if OP is looking for real world problems that are accessible to him/her, the topics he/she has learned in previous courses might be more useful than calculus in receiving a satisfactory answer for most real life problems. The reason I am saying this is that while calculus allows for a much more precise way of determining values, an every-day problem isn't typically demanding of an exact value. It is demanding of a value close enough to tell the mathematician what sort of beast he/she is dealing with.

All this being said, that doesn't stop me personally from trying to figure out models that will tell me far more than I need to know. What's the matter with driving a Ferrari to work when all you really need is four wheels and an engine? you still get there, you just have a little more fun in the process.

This post probably makes no sense because I went on a tirade that was likely a bit discouraging to OP and immediately tried to rectify myself by saying I do the same thing. The topic sparked a train of thought that I wanted to share even if I was contradicting myself.

level 2
2 points · 4 years ago

Well, that was a rant. And I don't agree at all. What are these rudimentary / algebraic methods which give good-enough answers for real-world problems? Mathos are not interested in precision? Why wouldn't they want the best possible answer? The thing is, the development of calculus was essential to allow equations describing rates of change to be formulated. There would be very few natural phenomena not described by such equations. So the OP should consult almost any book on physics or applied maths.

level 3
Original Poster1 point · 4 years ago

Would you happen to have a recommendation for a good physics or applied math book?

level 4
1 point · 4 years ago

To clarify, calculus is foundational in analysing the real world, and provides indispensable tools, but you will rarely see theorems being referenced as part of the argument. The sort of books I had in mind would cover a single topic only, eg classical mechanics, and would contain a lot of physics as well. It's a very long time since I was a student, so I will gladly defer to the suggestions made by u/david_wxy above.

level 3
-2 points · 4 years ago

It certainly was a rant haha. The point that I was trying to get across is that for most problems you encounter on the norm, some creative high school level algebra will do the job just fine. need to figure out how much work it would take to empty a pool? make some simplifying approximations to find the volume and assume the distance the water is displaced is from the very bottom of the pool. Not only is this method requiring less formal schooling, but it will probably yield a closer answer. who would put a pump hose anywhere but the very bottom of the pool at any point in this process? I suppose it's also worth mentioning that even this problem is not one a person is likely to encounter, and even if they do, it's really just a matter of how powerful the pump is.

I didn't say these things with the average mathematician in mind, as they will value precision much more than the average person. I had someone in mind who's trying to find a practical solution with a minimal amount of knowledge and work. I suppose I neglected to mention that calculus has helped us determine a lot of equations and useful values, but what I meant was that through these developments he/she doesn't have to formally use calculus (taking derivatives or integrals) to answer questions.

level 4
2 points · 4 years ago

What do you mean by 'most problems you encounter on the norm'? Who? Sure, maybe the average person doesn't need calculus to solve problems they encounter but it's no surprise that the physical sciences really took off once calculus was developed in the 17th century.

Calculus is the foundation of many areas of mathematics that are applied in the physical sciences and engineering. There is no way that, for example, we would have quantum mechanics were it not for calculus and its derivatives (no pun intended).

level 5
0 points · 4 years ago

like I said, I'm not trying to talk down about calculus. OP was looking for real world problems and I don't typically see many chances to break out calculus because some clever intuition paired with basic algrebra will do the job just fine.

level 2
Original Poster1 point · 4 years ago

I really enjoyed your response, I'm glad I'm not the only one who feels this way. I do thoroughly enjoy the subject to the point where I haven't yet decided a major and I'm taking Calculus for fun. It would be nice to see where it is used to give me an idea of what I'd want to major in.

level 2
Comment deleted4 years ago
level 3
0 points · 4 years ago · edited 4 years ago

yes, but OP isn't talking about fourier analysis or PDE. He's talking about everyday applications of calculus by itself. To which I tend to believe there are few cases in which a knowledge in calculus can yield a reasonable answer where algebra cannot (if, admittedly, notably less accurate)

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# Cylinder and Möbius strip as fiber bundles: trivializations and cocycles

I have to show that the cylinder and the Möbius strip are fiber bundles over $S^1$ with fiber an open interval and I have to write down explicitly the transition functions and the cocycles.

Cylinder.

The cylinder is $E:=I\times S^1$ where $I$ is our open interval.

Let's consider $$\pi : I \times S^1 \to S^1$$ the projection on the second factor (by definition it's continuous and surjective).

Let's take $S^1$ as basis of the fiber bundle and let $\{U_\alpha\}_\alpha$ be an open covering of $S^1$.

$\pi_1:U_\alpha\times I\to U_\alpha$ is the projection on the first factor.

The trivialization is $$\phi_\alpha:\pi^{-1}(U_\alpha)\to U_\alpha\times I\\ \phi_\alpha:=id|_{U_\alpha\times I}$$ In this case the transition functions are such that for all $\alpha,\beta$ $$\phi_{\alpha\beta}=\phi_\alpha\circ\phi_\beta^{-1}=id|_{(U_\alpha\cap U_\beta)\times I}.$$ Hence the cocycles are just $$g_{\alpha\beta}:U_\alpha\cap U_\beta\to Aut(I)\\ p\mapsto id|_I$$

Möbius band Let's start with the closed interval $[0,1]$ and the map $$p:[0,1]\to S^1\\ x\mapsto e^{i2\pi x}$$ which identifies the point $0$ with the point $1$.

Let's consider $[0,1]\times I$, where $I$ is an open interval, let's say $(0,1)$. Let's define an equivalence relation on $[0,1]\times I$: $$(0,y)\sim (1,1-y)$$ and we obtain the Möbius band $E$.

Let's consider an open covering $\{U_\alpha\}_\alpha$ of sphere $S^1$ and let $$\pi:E\to S^1\\ [(x,y)]\mapsto p(x)$$ be continuous and surjective and $$\pi_1:U_\alpha\times I\to U_\alpha$$ be continuous and surjective.

I can't find a trivialization. I just know that I have to choose a proper open covering of $S^1$ like two open interval overlapped.

• Can you find the trivialization in the case that $U_\alpha \subset p(0,1)$? – Lee Mosher Jul 29 '15 at 13:52
• Yes! Let's define $U_1:=S^1-\{0\}=p((0,1))$. Then I want to construct a homeomorphism $\phi_1:\pi^{-1}(U_1)\to U_1\times I$. Let's see what $\pi^{-1}(U_1)$ is. $\pi^{-1}(U_1)=\{[(x,y)]\in E: p(x)\in p((0,1))\}=(0,1)\times I$. Hence $\phi_1:\pi^{-1}(U_1)\to U_1\times I$ maps $[(x,y)]$ to $(p(x),y)$. Right? – avati91 Jul 29 '15 at 14:16
• Yup. That knocks off one big case. Now all you have to do is figure out the complementary case $U_\alpha \not\subset p(0,1)$. – Lee Mosher Jul 29 '15 at 17:15
• I think I solved my doubts :) Thanks – avati91 Jul 29 '15 at 17:20
• The example of gluing a Mobius strip from a cocycle is covered in Jeffrey Lee's book in Example 6.16 in case you want a textbook source. – ಠ_ಠ Oct 29 '15 at 4:16


text:
# Question about thevenin circuit analysis with voltage across voltage source

I have a certain circuit in mind and I want to find its Thevenin equivalent resistor:

I see that there is an dependent voltage source so I add a voltage source of 1V between a and b and make the other voltage source equal to 0 (the independent 9v). when I use nodal analysis on the new circuit, I am not sure how to calculate the current i3. I thought about using Kirchhoff voltage law on the middle loop but for now I am confused. If I have three voltage sources, do I just take a wild guess about which way the current goes when I apply KVL on the middle loop? because if they didn't note the direction of the current on the Vx resistor, I would have said that Vx+2i3-2Vx+1=0, or would that be wrong because I assumed i3's direction to go to the right?

tl;dr

• how would I do a KVL equation on the middle loop
• is there an easier way to solve it using nodal analysis (specifically, to find i3)?

Sorry if the question seems a bit confused, because I'm confused.

• Well it seems to me that it is a reasonable question. He discussed what he tried to do and what is still confusing to him. – WalyKu Jun 1 '14 at 12:34

This is how i think i would solve the problem:

I don't see it necessary to add a 1V excitation source since there already a 9v in the circuit. The trick when analyzing circuit with dependent sources is to avoid the Short circuiting you would normally do when having a circuit with independent sources alone:

_Things to note that may help

Focus on node A:

define a current from the 9v source direction to node A and also define a current from 6ohm to A

_not Vx =Va

9 - Vx = I1

Vx/6 = I2

and i reckon Vab = 2Vx..

Hope this helps you!

If your objective is to find the Thevenin resistance, then I'm not sure why you're approaching it this way.

If you can find the Thevenin resistance $R'_{th}$ of the circuit to the left of the $1\Omega$ resistor, the total equivalent resistance is just

$$R_{th} = R'_{th}|| 1\Omega$$

And, I recommend using a current test source which will make finding $R'_{th}$ almost trivial.

For this particular question, i think the source conversion technique would be the best.

You convert the independent voltage source and 3 ohm resistor to a current source of 3A with 3 ohm res in parallel.

Next, this 3 ohm res is in parallel with 6 ohm res. Reduce it to a single res of 2 ohm. So now you have a current source of 3A in parallel with 2 ohm res.

At this point again use source conversion. You get a voltage source of 6V in series with a 2 ohm res, combined in series with 2 ohm res and dependent source. The remainder of the network can be easily solved.

A major benefit of this technique is that you have reduced one loop completely.

Hope i am correct.


text:
Unit root tests and ARIMA models

March 12, 2014
By

(This article was first published on Hyndsight » R, and kindly contributed to R-bloggers)

I have a small problem. I have a time series called x :

- If I use the default values of auto.arima(x), the best model is an ARIMA(1,0,0)

- However, I tried the function ndiffs(x, test=“adf”) and ndiffs(x, test=“kpss”) as the KPSS test seems to be the default value, and the number of difference is 0 for the kpss test (consistent with the results of auto.arima() ) but 2 for the ADF test.
I then tried auto.arima(x, test=“adf”) and now I have another model ARIMA(1,2,1). I am unsure which order of integration I should use as tests give fairly different results.

Is there a test that prevails ?

The KPSS test will often select fewer differences than the ADF test or a PP test. A KPSS test has a null hypothesis of stationarity, whereas the ADF and PP tests assume that the data have I(1) non-stationarity. Consequently, the KPSS test will only select one or more differences if there is enough evidence to overturn the stationarity assumption, while the other tests will select at least one difference unless there is enough evidence to overturn the non-stationarity assumption. A nice discussion to the tests and the models behind them is given on Eric Zivot’s website.

I have compared the forecast accuracy of the ARIMA models obtained using all three tests applied to the M3 data, and found that the KPSS tests led to models with better forecasts. That is why the default value in auto.arima() is test="kpss". In general, all the defaults are set to the values that give the best forecasts on average. It is better to leave them alone unless you know what you are doing and have a good reason to change them.


text:
User:
• Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

 Find the slope from two points Determine the slope of a line from two points You can determine the slope of a line finding two points P(x 1,y1) and Q(x2,y2) on the line and using the following equation: $m=\frac{y_2-y_1}{x_2-x_1}$ Look at the picture and determine the slope: $m=\frac{1-2}{4-(-3)}=\frac{-1}{7}$


text:
1. Dec 1, 2007

### idiotblue

integrate this

$$\int$$$$\frac{1}{U\sqrt{1-U^2}}dU$$

2. Dec 1, 2007

### rock.freak667

..Try using integration by parts and see if you can solve

u=$\frac{1}{U}$ find du/dx
$\frac{dv}{dx}=\frac{1}{\sqrt{1-U^2}}$ so get v=

and

$$\int u\frac{dv}{dx}dx=uv-\int v\frac{du}{dx}dx$$

3. Dec 1, 2007

### Dick

It can be done straightforwardly with a trig substitution, like u=sin(t).

4. Dec 1, 2007

### idiotblue

Sorry but...

the original question wasintegration from $$\epsilon$$to$$\pi-\epsilon$$
$$\int$$$$\frac{1}{sinx}dx$$

I tried to integrate it straight but i don't know how calculate cosec and cot...

Last edited: Dec 1, 2007
5. Dec 2, 2007

### Avodyne

Try the substitution u = tan(x/2).

6. Dec 2, 2007

### idiotblue

:)thanks guys. I got it~

7. Dec 13, 2007

### cummins

What is the term for the slope on an x axis that runs parallel but never actually touches the x axis?

8. Dec 13, 2007

### Dick

Get your own thread. But until you do 'horizontal asymptote with y value 0'.


text:
### How Risky is the Random-Oracle Model?

Gaetan Leurent and Phong Q. Nguyen

##### Abstract

RSA-FDH and many other schemes secure in the Random-Oracle Model (ROM) require a hash function with output size larger than standard sizes. We show that the random-oracle instantiations proposed in the literature for such cases are weaker than a random oracle, including the proposals by Bellare and Rogaway from 1993 and 1996, and the ones implicit in IEEE P1363 and PKCS standards: for instance, there is a practical $2^{30}$ preimage attack on BR93 for 1024-bit digests. Next, we study the security impact of hash function defects for ROM signatures. As an extreme case, we note that any hash collision would suffice to disclose the master key in the ID-based cryptosystem by Boneh et al. from FOCS '07, and the secret key in the Rabin-Williams signature for which Bernstein proved tight security at EUROCRYPT '08. Interestingly, for both of these schemes, a slight modification can prevent these attacks, while preserving the ROM security result. We give evidence that in the case of RSA and Rabin/Rabin-Williams, an appropriate PSS padding is more robust than all other paddings known.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. Full version of the CRYPTO 2009 article.
Keywords
hash functionscryptanalysispublic-key cryptography
Contact author(s)
pnguyen @ di ens fr
History
2009-07-23: last of 2 revisions
See all versions
Short URL
https://ia.cr/2008/441

CC BY

BibTeX

@misc{cryptoeprint:2008/441,
author = {Gaetan Leurent and Phong Q.  Nguyen},
title = {How Risky is the Random-Oracle Model?},
howpublished = {Cryptology ePrint Archive, Paper 2008/441},
year = {2008},
note = {\url{https://eprint.iacr.org/2008/441}},
url = {https://eprint.iacr.org/2008/441}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.


text:
# 6.8.1 Trigonometric Functions Long Questions (Question 1 & 2)

Question 1:
(a) Sketch the graph of y = cos 2x for 0°  x  180°.
(b) Hence, by drawing a suitable straight line on the same axes, find the number of solutions satisfying the equation for 0°  x  180°.

Solution:

(a)(b)

Question 2:
(a) Prove that $\frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=\mathrm{tan}2x.$
(b)(i) Sketch the graph of y = – tan 2x for 0  x ≤ π .
(b)(ii) Hence, by drawing a suitable straight line on the same axes, find the number of solutions satisfying the equation $\frac{3x}{\pi }+\frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=0$  for 0  x π .
State the number of solutions.

Solution:
(a)
$\begin{array}{l}\frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=\mathrm{tan}2x\\ \\ LHS:\\ \frac{2\mathrm{tan}x}{2-{\mathrm{sec}}^{2}x}=\frac{2\mathrm{tan}x}{2-\left(1+{\mathrm{tan}}^{2}x\right)}\\ \text{}=\frac{2\mathrm{tan}x}{2-{\mathrm{tan}}^{2}x}\\ \text{}=\mathrm{tan}2x\text{(RHS)}\end{array}$

(b)(i)

(b)(ii)

When x = 0, y = 0.
When x = π, = 3.
Number of solutions = 3


text:
# 1.3: Introduction to Functions

One of the core concepts in College Algebra is the function. There are many ways to describe a function and we begin by defining a function as a special kind of relation.

Definition 1.6

A relation in which each $$x$$-coordinate is matched with only one $$y$$-coordinate is said to describe $$y$$ as a $$\textbf{function}$$ of $$x$$.

Example $$\PageIndex{1}$$:

Which of the following relations describe $$y$$ as a function of $$x$$?

1. $$R_1 = \{ (-2,1), (1,3), (1,4), (3,-1) \}$$
2. $$R_2 = \{ (-2,1), (1,3), (2,3), (3,-1) \}$$

Solution

A quick scan of the points in $$R_1$$ reveals that the $$x$$-coordinate $$1$$ is matched with two different $$y$$-coordinates: namely $$3$$ and $$4$$. Hence in $$R_1$$ , $$y$$ is not a function of $$x$$. On the other hand, every $$x$$-coordinate in $$R_2$$ occurs only once which means each $$x$$-coordinate has only one corresponding $$y$$-coordinate. So, $$R_2$$ does represent $$y$$ as a function of $$x$$. $$\Box$$

Note that in the previous example, the relation $$R_2$$ contained two different points with the same $$y$$-coordinates, namely $$(1,3)$$ and $$(2,3)$$. Remember, in order to say $$y$$ is a function of $$x$$, we just need to ensure the same $$x$$-coordinate isn't used in more than one point.\footnote{We will have occasion later in the text to concern ourselves with the concept of $$x$$ being a function of $$y$$. In this case, $$R_1$$ represents $$x$$ as a function of $$y$$; $$R_2$$ does not.}

To see what the function concept means geometrically, we graph $$R_1$$ and $$R_2$$ in the plane.

The fact that the $$x$$-coordinate $$1$$ is matched with two different $$y$$-coordinates in $$R_1$$ presents itself graphically as the points $$(1,3)$$ and $$(1,4)$$ lying on the same vertical line, $$x=1$$. If we turn our attention to the graph of $$R_2$$ , we see that no two points of the relation lie on the same vertical line. We can generalize this idea as follows

Theorem 1.1

The Vertical Line Test: A set of points in the plane represents $$y$$ as a function of $$x$$ if and only if no two points lie on the same vertical line.

It is worth taking some time to meditate on the Vertical Line Test; it will check to see how well you understand the concept of function' as well as the concept of graph'.

Example $$\PageIndex{2}$$:

Use the Vertical Line Test to determine which of the following relations describes $$y$$ as a function of $$x$$.

$${\bf Solution.}$$ Looking at the graph of $$R$$, we can easily imagine a vertical line crossing the graph more than once. Hence, $$R$$ does not represent $$y$$ as a function of $$x$$. However, in the graph of $$S$$, every vertical line crosses the graph at most once, so $$S$$ does represent $$y$$ as a function of $$x$$. $$\Box$$

Example $$\PageIndex{3}$$:

Use the Vertical Line Test to determine which of the following relations describes $$y$$ as a function of $$x$$.

$${\bf Solution.}$$ Both $$S_1$$ and $$S_2$$ are slight modifications to the relation $$S$$ in the previous example whose graph we determined passed the Vertical Line Test. In both $$S_1$$ and $$S_2$$, it is the addition of the point $$1,2$$ which threatens to cause trouble. In $$S_1$$, there is a point on the curve with $$x$$-coordinate 1 just below $$1,2$$, which means that both $$1,2$$ and this point on the curve lie on the vertical line $$x=1$$. (See the picture below and the left.) Hence, the graph of $$S_1$$ fails the Vertical Line Test, so $$y$$ is not a function of $$x$$ here. However, in $$S_2$$ notice that the point with $$x$$-coordinate 1 on the curve has been omitted, leaving an open circle' there. Hence, the vertical line $$x=1$$ crosses the graph of $$S_2$$ only at the point $$(1,2)$$. Indeed, any vertical line will cross the graph at most once, so we have that the graph of $$S_2$$ passes the Vertical Line Test. Thus it describes $$y$$ as a function of $$x$$. $$\Box$$

Suppose a relation $$F$$ describes $$y$$ as a function of $$x$$. The sets of $$x$$- and $$y$$-coordinates are given special names which we define below.

Definition 1.7

• The set of the $$x$$-coordinates of the points in $$F$$ is called the $$\textbf{domain}$$ of $$F$$.
• The set of the $$y$$-coordinates of the points in $$F$$ is called the $$\textbf{range}$$ of $$F$$.

We demonstrate finding the domain and range of functions given to us either graphically or via the roster method in the following example.

Example $$\PageIndex{4}$$:

Find the domain and range of the function $$F = \{ (-3, 2), (0, 1), (4, 2), (5, 2) \}$$ and of the function $$G$$ whose graph is given above on the right.

$${\bf Solution.}$$ The domain of $$F$$ is the set of the $$x$$-coordinates of the points in $$F$$, namely $$\{ -3, 0, 4, 5 \}$$ and the range of $$F$$ is the set of the $$y$$-coordinates, namely $$\{ 1,2 \}.$$

To determine the domain and range of $$G$$, we need to determine which $$x$$ and $$y$$ values occur as coordinates of points on the given graph. To find the domain, it may be helpful to imagine collapsing the curve to the $$x$$-axis and determining the portion of the $$x$$-axis that gets covered. This is called $$\textbf{projecting}$$ the curve to the $$x$$-axis. Before we start projecting, we need to pay attention to two subtle notations on the graph: the arrowhead on the lower left corner of the graph indicates that the graph continues to curve downwards to the left forever more; and the open circle at $$1,3$$ indicates that the point $$1,3$$ isn't on the graph, but all points on the curve leading up to that point are.

We see from the figure that if we project the graph of $$G$$to the $$x$$-axis, we get all real numbers less than $$1$$. Using interval notation, we write the domain of $$G$$ as $$(-\infty, 1)$$. To determine the range of $$G$$, we project the curve to the $$y$$-axis as follows:

Note that even though there is an open circle at $$1,3$$, we still include the $$y$$ value of $$3$$ in our range, since the point $$(-1,3)$$ is on the graph of $$G$$. We see that the range of $$G$$is all real numbers less than or equal to $$4$$, or, in interval notation, $$(-\infty, 4]$$. $$\Box$$

All functions are relations, but not all relations are functions. Thus the equations which described the relations in Section 1.2 may or may not describe $$y$$ as a function of $$x$$. The algebraic representation of functions is possibly the most important way to view them so we need a process for determining whether or not an equation of a relation represents a function. (We delay the discussion of finding the domain of a function given algebraically until Section 1.4 .)

Example $$\PageIndex{5}$$:

Determine which equations represent $$y$$ as a function of $$x$$.

1. $$x^3 + y^2 = 1$$ 2. $$x^2 + y^3 = 1$$ 3. $$x^2y = 1 - 3y$$

$${\bf Solution.}$$ For each of these equations, we solve for $$y$$ and determine whether each choice of $$x$$ will determine only one corresponding value of $$y$$.

1. $\begin{array}{rclr} x^3 + y^2 & = & 1 & \\ y^2 & = & 1 - x^3 & \\ \sqrt{y^2} & = & \sqrt{1 - x^3} & \mbox{extract square roots} \\ y & = & \pm \sqrt{1 - x^3} & \\ \end{array}$

If we substitute $$x=0$$ into our equation for $$y$$, we get $$y = \pm \sqrt{1 - 0^3} = \pm 1$$, so that $$(0,1)$$ and $$(0,-1)$$ are on the graph of this equation. Hence, this equation does not represent $$y$$ as a function of $$x$$.

2. \item $\begin{array}{rclr} x^2 + y^3 & = & 1 & \\ y^3 & = & 1 - x^2 & \\ \sqrt[3]{y^3} & = & \sqrt[3]{1 - x^2} & \\ y & = & \sqrt[3]{1 - x^2} & \\ \end{array}$

For every choice of $$x$$, the equation $$y = \sqrt[3]{1 - x^2}$$ returns only $$\textbf{one}$$ value of $$y$$. Hence, this equation describes $$y$$ as a function of $$x$$.

3. \item $\begin{array}{rclr} x^2y & = & 1 - 3y & \\ x^2y + 3y & = & 1 & \\ y \left(x^2 + 3\right) & = & 1 & \mbox{factor} \\ y & = & \dfrac{1}{x^2 + 3} & \\ \end{array}$

For each choice of $$x$$, there is only one value for $$y$$, so this equation describes $$y$$ as a function of~$$x$$. $$\Box$$

We could try to use our graphing calculator to verify our responses to the previous example, but we immediately run into trouble. The calculator's Y='' menu requires that the equation be of the form $$y$$ = some expression of $$x$$'. If we wanted to verify that the first equation in Example \refeq{1.3.5} does not represent $$y$$ as a function of $$x$$, we would need to enter two separate expressions into the calculator: one for the positive square root and one for the negative square root we found when solving the equation for $$y$$. As predicted, the resulting graph shown below clearly fails the Vertical Line Test, so the equation does not represent $$y$$ as a function of $$x$$.

Thus in order to use the calculator to show that $$x^3 + y^2 = 1$$ does not represent $$y$$ as a function of $$x$$ we needed to know analytically that $$y$$ was not a function of $$x$$ so that we could use the calculator properly. There are more advanced graphing utilities out there which can do implicit function plots, but you need to know even more Algebra to make them work properly. Do you get the point we're trying to make here? We believe it is in your best interest to learn the analytic way of doing things so that you are always smarter than your calculator.

## Contributors

• Carl Stitz, Ph.D. (Lakeland Community College) and Jeff Zeager, Ph.D. (Lorain County Community College)


text:
# S Duality and Effective Couplings

I am brand new to this subject, so this will probably be a very stupid question, but I would appreciate any patient explanations.

S-duality is typically described as a relationship between two QFTs (I am ignoring string theory here) where one theory describing objects interacting with some characteristic strength or coupling constant $g$ is equivalent to a different theory containing different objects (which might be solitonic objects in the dual description, like monopoles) with characteristic interaction strength $1/g$. We can then use the $g \to 0$ limit in one theory to infer information about the strong-coupling dynamics of the dual.

However, according to the renormalization group ideas, any garden-variety QFT will undergo dimensional transmutation and the perturbation theory really ends up being in an effective coupling $g(\mu)$ which flows according to the RG. Even the most simplistic loop calculations in dimensional regularization reflect this, and from a more highbrow point of view, the theory is defined by its UV fixed point. From this point of view, when we look at asymptotically free theories like QCD or gauge theories, the correct question to ask is not "What happens when $g \to \infty$?" but "What does the theory flow to in the infrared?". While it is evident that the IR theory will have some kind of strong-coupling dynamics, how does S duality incorporate this idea?

I know that some examples like Seiberg duality are phrased in terms of the infrared behavior according to the RG, but it seems that the general paradigm is still weak/strong coupling. But even then, exactly what coupling are we referring to? In the classical theory there is just "the coupling", but as soon as you go to the quantum theory dimensional transmutation destroys this, right? Any help would be appreciated.

In QFT, the notion of couplings is only reliable in the perturbation setting. So it doesn't make much sense to have a strong/weak duality, unless the theory is actually free or integrable. For example, in N=4 SYM, you have S duality which sends the coupling $\tau$ to $-1/\tau$.


text:
# VertexID¶

class pygamer.surfacemesh.VertexID

Wrapper around gamer::SurfaceMesh::SimplexID<1> object.

This is a token to represent a 1-simplex object. It serves as a reference to the actual object.

Methods

 VertexID.cover(self) Get the coboundary relations of this simplex. VertexID.data(self) Access the data stored on the 1-simplex. Get the indices of this simplex. Checks if VertexID refers to a valid simplex.


text:
# How do you solve 5+sqrt(g-3)=6 and check your solution?

Jul 6, 2017

$g = 4$

#### Explanation:

$5 + \sqrt{g - 3} = 6$

Subtract $5$ from each side.

$5 - 5 + \sqrt{g - 3} = 6 - 5$

$\sqrt{g - 3} = 1$

Square both sides.

$g - 3 = {1}^{2}$

Since the square of $1$ is $1$:

$g - 3 = 1$

Add $3$ to each side.

$g - 3 + 3 = 1 + 3$

$g = 4$

To check substitute $g$ with $4$ in the original equation:

$5 + \sqrt{g - 3} = 6$

$5 + \sqrt{4 - 3} = 6$

$5 + \sqrt{1} = 6$

The square root of $1$ is either $+ 1$ or $- 1$. Taking it to be $+ 1$:

$5 + 1 = 6$

We can use slightly different steps for the last two steps to confirm the solution:

$5 + \sqrt{1} = 6$

Subtract $5$ from each side.

$5 - 5 + \sqrt{1} = 6 - 5$

$\sqrt{1} = 1$

Square both sides. The square of $1$ is $1$.

$1 = 1$


text:
SIST ISO 12830

SIST EN 12839 standard obravnava:

• določevanje v kislini topnega magnezija, kalcija, mangana, železa, bakra, natrija in kalija

This document specifies the procedure for the determination of acid-soluble magnesium, calcium, manganese, iron, copper, sodium and potassium by atomic absorption spectrometry (AAS) or by inductively coupled plasma emission spectrometry (ICP/ES). The acid-soluble element comprises the acid-soluble part of the incineration residue, i.e. that part of the ignition residue obtained after incineration which is soluble in hydrochloric acid or nitric acid. In cases where the residue is completely soluble, the result obtained by the procedure specified in this document is a measure of the total amount of each element in the sample. This document is applicable to all types of paper, board, pulps and cellulose nanomaterials. The limit of determination depends on the element and on the instrument used.

Vir: Slovenski inštitut za standardizacijo, povzeto s spletne strani junij 2022.

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Prikaz vseh 12 rezultatov


text:
Opened 10 years ago

Closed 10 years ago

# Calculus constructions mix explicit calls to maxima

Reported by: Owned by: robertwb mvngu major sage-4.4.2 documentation sage-4.4.2.rc0 Karl-Dieter Crisman David Joyner N/A

### comment:1 Changed 10 years ago by wdj

From an email [sage-support] error in documentation "Construction" on 2010-01-15:

Hi everyone,

I just checked out one of  first page in the "Constructions" page:

http://www.sagemath.org.nyud.net/doc/constructions/calculus.html

Just after the first example "Differentiation"

sage: var('x k w')
(x, k, w)
sage: f = x^3 * e^(k*x) * sin(w*x); f
x^3*e^(k*x)*sin(w*x)
sage: f.diff(x)
k*x^3*e^(k*x)*sin(w*x) + w*x^3*e^(k*x)*cos(w*x) + 3*x^2*e^(k*x)*sin
(w*x)
sage: latex(f.diff(x))
k x^{3} e^{\left(k x\right)} \sin\left(w x\right) + w x^{3} e^{\left(k
x\right)} \cos\left(w x\right) + 3 \, x^{2} e^{\left(k x\right)} \sin
\left(w x\right)

there is

"If you type view(f.diff('x')) another... "

When I do that, I get a long error message, which could frighten off
(it is the first example...). With "view(f.diff(x))" it works.
However, if the function is defined via

f = maxima(....)

then both ways work:   view(f.diff('x')),  view(f.diff(x))

I don't know if this is intended, but at least on the website it
should be changed, not to get the error.

Greets,
Stefan

### Changed 10 years ago by mvngu

apply to sage-main; based on Sage 4.3.1.alpha2

### Changed 10 years ago by mvngu

apply to examples/ repository; based on Sage 4.3.1.alpha2

### comment:2 Changed 10 years ago by mvngu

• Authors set to Minh Van Nguyen
• Status changed from new to needs_review

Here are two patches, which should fix errors in the calculus chapter of the Constructions document. Apply the patch trac_7936-constructions.patch to the repository sage-main. The second patch applies to the examples/ directory, which is separate from sage-main. But before applying the second patch, the release manager needs to remove a junk file:

[mvngu@boxen examples]$pwd /dev/shm/mvngu/sage-4.3.1.alpha2-7936-maxima/examples [mvngu@boxen examples]$ hg st
? .hgtags.orig
[mvngu@boxen examples]$rm .hgtags.orig [mvngu@boxen examples]$ hg st

### comment:3 Changed 10 years ago by robertwb

It would be really nice if that whole constructions page could be written without any explicit calls to maxima at all--not sure how much of that is possible, but for derivatives, integrals, and power series it certainly is.

Also, nearly every example involves Piecewise, which doesn't play nicely with all the symbolic stuff (nor does it make for concise examples).

### comment:4 Changed 10 years ago by kcrisman

The constructions document is quasi-deprecated in any case, as it dates from over two years ago, I believe. wdj wanted to make a new 'cookbook' document which replaced it, but no one has had time to do so. Of course, if the whole constructions document were updated, that would be great! I agree that if one is serious about that, though, one would have to remove Piecewise stuff, as at the time that was one of the better-implemented function types but now is waiting on someone to add them to Pynac.

### comment:5 follow-up: ↓ 6 Changed 10 years ago by was

The constructions document is quasi-deprecated in any case, as it dates from over two years ago,

Two years? It from at least *four* years ago! It was mostly written around the time of Sage 1.0, or earlier. It needs a total rewrite. When it was written, explicit calls to maxima were the only way to do any calculus.

### comment:6 in reply to: ↑ 5 Changed 10 years ago by kcrisman

• Status changed from needs_review to needs_work

The constructions document is quasi-deprecated in any case, as it dates from over two years ago,

Two years? It from at least *four* years ago! It was mostly written around the time of Sage 1.0, or earlier. It needs a total rewrite. When it was written, explicit calls to maxima were the only way to do any calculus.

Like I said, over two years ago :)

### comment:7 follow-up: ↓ 8 Changed 10 years ago by mvngu

Is this fixed by #8132?

### comment:8 in reply to: ↑ 7 ; follow-up: ↓ 9 Changed 10 years ago by wdj

• Status changed from needs_work to needs_info

Is this fixed by #8132?

No, unfortunately, I don't think so.

I give a positive review to the first patch. I don't understand the second patch. I'm giving the first a positive review though. Fell free to reverse my vote back to needs review, but I'm marking it for now as needs info. The instructions for patch 2 are just completely unclear to me.

### comment:9 in reply to: ↑ 8 Changed 10 years ago by mvngu

I give a positive review to the first patch.

I think the attachment trac_7936-constructions.patch is now superseded by #8132. No need to use that patch anymore.

I don't understand the second patch. The instructions for patch 2 are just completely unclear to me.

Without the attachment trac_7936-desolvers.patch applied to the repository examples/calculus, I get an error when loading the file desolvers.sage:

[mvngu@mod calculus]$pwd /dev/shm/mvngu/sage-4.3.2.alpha1-sage.math/examples/calculus [mvngu@mod calculus]$ ls
desolvers.py    eulers_method.sage  newton_raphson.sage
[mvngu@mod calculus]$../../sage ---------------------------------------------------------------------- | Sage Version 4.3.2.alpha1, Release Date: 2010-01-31 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- ********************************************************************** * * * Warning: this is a prerelease version, and it may be unstable. * * * ********************************************************************** sage: load "desolvers.sage" ------------------------------------------------------------ File "<string>", line 147 #maxima.eval(cmd) ^ SyntaxError: invalid syntax  Now apply the patch trac_7936-desolvers.patch to the repository examples/calculus to resolve this syntax error: [mvngu@mod calculus]$ hg qimport http://trac.sagemath.org/sage_trac/raw-attachment/ticket/7936/trac_7936-desolvers.patch && hg qpush
applying trac_7936-desolvers.patch
now at: trac_7936-desolvers.patch
[mvngu@mod calculus]\$ ../../sage
----------------------------------------------------------------------
| Sage Version 4.3.2.alpha1, Release Date: 2010-01-31                |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
**********************************************************************
*                                                                    *
* Warning: this is a prerelease version, and it may be unstable.     *
*                                                                    *
**********************************************************************
sage: des=["'diff(x(t),t)=-4*y(t)","'diff(y(t),t)=-x(t)"]
sage: vars = ["t","x","y"]
sage: desolve_system(des,vars)
[x(t)=(2*y(0)+x(0))*%e^-(2*t)/2-(2*y(0)-x(0))*%e^(2*t)/2,y(t)=(2*y(0)-x(0))*%e^(2*t)/4+(2*y(0)+x(0))*%e^-(2*t)/4]

### comment:10 follow-up: ↓ 11 Changed 10 years ago by wdj

Thanks for explaining that about the second patch.

desolvers.sage can be removed now since Robert Marik has kindly implemented everything in it in sage already.

Can you just delete the file, Minh?

### comment:11 in reply to: ↑ 10 Changed 10 years ago by kcrisman

Thanks for explaining that about the second patch.

desolvers.sage can be removed now since Robert Marik has kindly implemented everything in it in sage already.

Can you just delete the file, Minh?

I just want to point out also that William is probably going to get rid of the examples directory in the near future - as usual, I do not have the URL for that discussion :) so the sooner we explicitly know it's not necessary, the better.

### comment:12 follow-up: ↓ 13 Changed 10 years ago by kcrisman

I can verify that desolvers.sage and euler_method.sage from this directory are completely taken care of by the changes of Robert, and some of field_plot2d.sage is also now in the plot/plot_field.py file (maybe not all of it, but maybe not all is needed?). I think the stuff in newton_raphson.sage probably should be jettisoned or somehow put in one of the sage/calculus files.

wdj, what do you think? Probably we can just about delete that whole directory. What do you think is worth putting into the main Sage library?

### comment:13 in reply to: ↑ 12 Changed 10 years ago by wdj

I can verify that desolvers.sage and euler_method.sage from this directory are completely taken care of by the changes of Robert, and some of field_plot2d.sage is also now in the plot/plot_field.py file (maybe not all of it, but maybe not all is needed?). I think the stuff in newton_raphson.sage probably should be jettisoned or somehow put in one of the sage/calculus files.

wdj, what do you think? Probably we can just about delete that whole directory. What do you think is worth putting into the main Sage library?

Agreed. delete it. newton_raphson is so simple, it is easy to just post to the wiki or something anyway. Thanks for looking at this!

### comment:14 follow-up: ↓ 17 Changed 10 years ago by kcrisman

• Authors changed from Minh Van Nguyen to Minh Van Nguyen, Karl-Dieter Crisman
• Reviewers set to David Joyner
• Status changed from needs_info to needs_review

Okay, this patch, applied to the examples/ repository, should take of this. Needs review. wdj, why don't you go ahead and look at the newton-raphson examples on the interact part of the Wiki and see if that essentially has that, otherwise can you think of an appropriate place to store it?

Also see #7494 on removing all of this examples/ directory.

### comment:15 follow-up: ↓ 16 Changed 10 years ago by mvngu

Do I only need to apply trac_7936-no-calc-examples.patch?

### comment:16 in reply to: ↑ 15 ; follow-up: ↓ 18 Changed 10 years ago by kcrisman

Do I only need to apply trac_7936-no-calc-examples.patch?

I think so. Someone should check the interact wiki and make sure that the essence of the Newton-Raphson example is captured in the interacts already there which are about that. Recall that this needs review, though, so you (or someone) would need to formally give this positive review at least.

### comment:17 in reply to: ↑ 14 Changed 10 years ago by wdj

Okay, this patch, applied to the examples/ repository, should take of this. Needs review. wdj, why don't you go ahead and look at the newton-raphson examples on the interact part of the Wiki and see if that essentially has that, otherwise can you think of an appropriate place to store it?

Looks good to me. I also copied the file to http://boxen.math.washington.edu/home/wdj/sagefiles/

Also see #7494 on removing all of this examples/ directory.

### comment:18 in reply to: ↑ 16 Changed 10 years ago by wdj

• Status changed from needs_review to needs_info

Do I only need to apply trac_7936-no-calc-examples.patch?

I think so. Someone should check the interact wiki and make sure that the essence of the Newton-Raphson example is captured in the interacts already there which are about that. Recall that this needs review, though, so you (or someone) would need to formally give this positive review at least.

This patch does not apply to 4.4.2.a0 for me. Does anyone else have this problem?

### comment:19 follow-up: ↓ 20 Changed 10 years ago by kcrisman

• Status changed from needs_info to needs_review

You have to apply it "manually" (using ./sage -hg, unfortunately) to the examples/ directory. There is no hg_examples :(

### comment:20 in reply to: ↑ 19 Changed 10 years ago by wdj

You have to apply it "manually" (using ./sage -hg, unfortunately) to the examples/ directory. There is no hg_examples :(

Can you tell me exactly the command to use to apply the patch Please?

sage -hg ????

### comment:21 follow-up: ↓ 22 Changed 10 years ago by kcrisman

I'll use ... to indicate the rest of the path until the Sage folder.

cd .../sage-4.4.1/examples/
~/.../sage-4.4.1/sage -hg log | less  # gives you the log, which is very boring :)
~/.../sage-4.4.1/sage -hg import http://trac.sagemath.org/sage_trac/raw-attachment/ticket/7936/trac_7936-no-calc-examples.patch
~/.../sage-4.4.1/sage -hg log | less  # gives you the log, which should now indicate the patch was applied.

And if you go in ./sage/examples/calculus/ now, it should be empty. The release manager would have to remove the empty folder by hand, I think.

I agree that it is very annoying that one has to do this without hg_sage - it took me a long time to figure out how to do it - but eventually the examples directory will cease to exist and so that won't be a problem. This is just a first step.

### comment:22 in reply to: ↑ 21 Changed 10 years ago by wdj

• Status changed from needs_review to positive_review

I'll use ... to indicate the rest of the path until the Sage folder.

cd .../sage-4.4.1/examples/
~/.../sage-4.4.1/sage -hg log | less  # gives you the log, which is very boring :)
~/.../sage-4.4.1/sage -hg import http://trac.sagemath.org/sage_trac/raw-attachment/ticket/7936/trac_7936-no-calc-examples.patch
~/.../sage-4.4.1/sage -hg log | less  # gives you the log, which should now indicate the patch was applied.

And if you go in ./sage/examples/calculus/ now, it should be empty. The release manager would have to remove the empty folder by hand, I think.

I agree that it is very annoying that one has to do this without hg_sage - it took me a long time to figure out how to do it - but eventually the examples directory will cease to exist and so that won't be a problem. This is just a first step.

Thanks very much!

This applies fine to 4.4.2.a0 and sage -testall passes (except for unrelated failures in interfaces/r.py and misc/sagedoc.py).

### comment:23 Changed 10 years ago by mvngu

• Authors changed from Minh Van Nguyen, Karl-Dieter Crisman to Karl-Dieter Crisman

### comment:24 Changed 10 years ago by mvngu

• Merged in set to sage-4.4.2.rc0
• Resolution set to fixed
• Status changed from positive_review to closed

Merged trac_7936-no-calc-examples.patch in examples repository.

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