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please solve my math problem by Edwin Sorryfield - Fri, 24 Jul 2015 09:31:58 EST ID:C4sQWBeJ No.14825 Ignore Report Reply Quick Reply
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Im trying to figure out how much paper I have to pick up at work...
A roll of paper weighing in at 4200 pounds and a diameter of 50". If I have to cut off let's say an inch of paper, how much would that inch weigh?
To tired for math
Simon Pommerhat - Fri, 24 Jul 2015 15:17:28 EST ID:i84x+n57 No.14826 Ignore Report Quick Reply
You'd need to know the length of the roll - knowing the diameter does you no good without knowing the density.
Simon Pommerhat - Fri, 24 Jul 2015 15:37:13 EST ID:i84x+n57 No.14827 Ignore Report Quick Reply
Unless you mean spool off and cut the paper so the diameter of the roll you're cutting from decreases by an inch (this is almost certainly what you mean, so disregard my previous post). In that case, the paper you spool off will weigh [R^2 - (R - r)^2]/R^2×4200 lbs = 329.28 lbs. Here r is the inch and R is 25''.
Simon Pommerhat - Fri, 24 Jul 2015 15:42:18 EST ID:i84x+n57 No.14828 Ignore Report Quick Reply
>diameter of the roll
Meant radius of the roll. FML, apparently forgot my thinking cap today.
Frederick Naddlebet - Sat, 25 Jul 2015 10:35:38 EST ID:Va1A/b0+ No.14829 Ignore Report Quick Reply
Thank you so much for that. Now I can tell my boss how ridiculous it is to pick that up twenty times a day.
Clara Claywell - Sat, 25 Jul 2015 14:55:57 EST ID:i84x+n57 No.14830 Ignore Report Quick Reply
No prob. How were you supposed to lift that much weight? I don't know how giant rolls of paper are usually transported.

dot dot dot by Barnaby Babbleshaw - Sat, 13 Jun 2015 01:58:32 EST ID:F9AJX/Os No.14795 Ignore Report Reply Quick Reply
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So the symbol of ... in mathematics is kind've confusing I've realized. Or an ellipsis. or just "that dot dot dot thing". whatever the hell you wanna call it.


both use the ... symbol, and in very different ways. In the first example, I think most people would say that it means a decimal point followed by an infinite amount of 9s. I would agree.

But it would be wrong to assume the same in the second case, as the number I was obviously stating is pi, and as such is irrational therefore doesn't have infinite repeating digits.
Archie Brickleman - Sat, 13 Jun 2015 05:53:14 EST ID:i84x+n57 No.14796 Ignore Report Quick Reply
What's your point? That it's bad notation for certain cases? All it means is that the decimal expansion of a number is nonterminating. To emphasize a repeating decimal, a vinculum (a line) is marked above the string of digits that repeat.

Nakura !xMsGPnYjBI - Tue, 14 Jul 2015 15:37:37 EST ID:NAU1L+Of No.14819 Ignore Report Quick Reply
The (...) in the decimal form of pi represents the decimal sequence continuing in an infinite series of numerals with the complexity state holding at that expected for pi.
Does that make sense?
Martha Nimmledock - Thu, 30 Jul 2015 00:18:21 EST ID:AopNL+nM No.14833 Ignore Report Quick Reply
Only a nerd would complain about something like that.

Math Anxiety (Know the material) by Frederick Megglechere - Thu, 09 Jul 2015 04:44:52 EST ID:oIF65CiW No.14812 Ignore Report Reply Quick Reply
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I have horrible math test anxiety.

Originally, I thought it had to do with failing to practice enough. I never had math anxiety or problems with tests in school up to ~algebra 2 (I never took AP classes, I had to start working.) I will admit, I tried to slack off at first but I knocked it off. You can even find a panic post of mine on this board if you look hard enough. I did alright on that test, but not what I could have done.

That was my wake up call.

I realized, going into college and having not used math, it made sense that I'd have to work harder than others to understand the material at first.

I started doing an insane amount of problems - the homework and then more on top of it. I re-took the class.

No. I get into a Calc test and am fine at first. I browse the whole test and smile because I covered all of the material. I did problems upon problems - I have a stack of printer full of shit (not an entire ream... but a lot), and yet, as I go through, I fall apart. I am slow and the clock ticks, and I can't remember simple concepts. I bomb. I do worse than before I prepared well!

I end up start switching endlessly from problem to problem because I'm missing little factoring issues or I used f'' instead of f'. I mean, for fuck's sake, I couldn't formally derive d/dx(x^1/2) using a limit... it's not difficult in the slightest. It's like I forget how to use LCDs and the simplest crap when I am tested.

I'm almost paranoid that there will just be algebraic tricks I'm not accustomed to and so sometimes I go down the wrong path solving a problem I could have done easily with a method I knew.
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Nathaniel Niggerfuck - Mon, 13 Jul 2015 05:34:55 EST ID:Dk8yywxc No.14813 Ignore Report Quick Reply

Everyone goes through this to a certain extent, some much more so than others. Sadly this is the limitation of the grading system, that someone like you with good understanding will slip through.

My advice is:

1) Slow down with your problems. You might be burning through stacks of problems without taking the time to think about what's going on, memorizing methods without developing any intuition. If you're going too fast or writing illegibly, you could be doing work that the grader can't make sense of, or worse you can't make sense of when you come back to the problem if you need to.

2) Don't be afraid to make mistakes. It's ok to have a shit ton of scratch paper to try again, if you've gone down a fruitless path try something different. I'm not saying half ass a bunch of different approaches, but if something just isn't working move on and come back to it.

3) Read the test, think about how you'll do each problem, then start doing the grunt work. The way math often works is that your brain is confused by a problem at first, but when you come back to it, it may be crystal clear. This is what's happening when you get back to your car, you've primed yourself for the problem on the test and it's then crystal clear when you take the second look at it. There's something subconscious going on, but if you read something and come back to it later you'll find that you have been processing it without noticing.

4) Calm down. It's easy to get worked up about things, it's just a test that you're prepared for and you can do it. Try doing something that calms you down before a test, such as drinking a coffee, reading a favorite short story, sitting under a tree with a cigarette, whatever it is you like.

5) After you do a practice problems, don't just do an entirely different set the next time you study. Try looking back over your work, think about why you did something and whether it could have been better, reflect not only on the method itself but why you chose that particular method for the problem at hand.
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Jack Peddlewill - Wed, 09 Sep 2015 10:44:18 EST ID:BG0DExq5 No.14886 Ignore Report Quick Reply
Fucking quality advice. The only advice I have is based on my personal experience. My friends and I were in calculus (I never imagined in a million years I'd be in calculus but I was a high school stoner and the hard classes were the trippiest. I'm doing my 4th year of a physics degree now. Crazy how drugs can affect your life.), and we realized that our math ability was extremely lacking, so we had to take over our own math education in order to be comfortable with ourselves. The thing that changed me forever was taking over mathematics, because it's something that belongs to me. I think crazy and natural thoughts in private, I listen to Terence Mckenna and random psychedelic nonsense and I just own math. It's mine now. So when I sit in front of an exam, I'm totally shocked; because somehow my private hobby is showing up at school. Also, if you're someone who cares about math, nothing is more amazing than an exam. Think about it, you MUST sit there for 3 hours and do math with no distractions. There's no way out. That's the fastest 3 hours of your life, and if you identify math as being home, it's funny. That's the only way I can describe it. How dare you challenge me in my home turf. (Not very modest but if you're dealing with math anxiety, fuck all modesty). I'm not even very mathematically talented, but if you want to get rid of math anxiety, you need to make it a part of your world that you're fond of.

Helpful Youtube channels by Cyril Gebblecocke - Thu, 04 Jun 2015 09:55:27 EST ID:jNXUmpxk No.14775 Ignore Report Reply Quick Reply
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Hey /math/,

I'm taking a satistics course this summer to fulfill my last credit for community college, and I was wondering if you guys know of any good Youtube channels to help me out through. We're currently going over probability, and it flew right over my head.

Cyril Gebblecocke - Thu, 04 Jun 2015 09:57:20 EST ID:jNXUmpxk No.14776 Ignore Report Quick Reply
help me through this*

tired, sorry
Nicholas Bundlekire - Thu, 04 Jun 2015 21:08:37 EST ID:7QJ+5Rkj No.14777 Ignore Report Quick Reply
khan academy
Nicholas Ducklock - Thu, 02 Jul 2015 09:35:59 EST ID:kOuj74f1 No.14810 Ignore Report Quick Reply
this guy help me a lot last summer when i was studing statistics.

Good Ideas Thread by Nakura !xMsGPnYjBI - Sun, 28 Jun 2015 17:45:04 EST ID:NAU1L+Of No.14808 Ignore Report Reply Quick Reply
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Fourier analysis applied to violent events and plotted on a complex plane could assist in finding the root cause of violent events and prevent their occurence in the future. Wave dispersion field devices, in the future, could prevent violent behavior, by taking advantage of wavelengths determined by psychodynamical theory and data, and influencing neuronal firing patterns in the brain. It would work similarly to how radios already work, but calibrated much more carefully.
Frederick Nullyman - Mon, 29 Jun 2015 23:19:30 EST ID:rS9AJec8 No.14809 Ignore Report Quick Reply

>the root cause of violent events


>prevent their occurence in the future

Remove watermelon.

Passed test slayer by Martha Pullerkitch - Sun, 17 May 2015 12:48:46 EST ID:muTtSqY/ No.14736 Ignore Report Reply Quick Reply
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What's up /math/, I just got 84% on a test I was really worried about fuck yeah. But one question I couldn't answer, it seems like it's insoluble, can you help me out?

A rocket is traveling through space at a speed of 7500 m/s. If in one second it burns 710 kg of fuel, what is the change in momentum during this time interval in kg m/s.

Don't you need the exhaust velocity of the rocket to solve this? Thanks
Nathaniel Fuckingwell - Fri, 29 May 2015 15:50:41 EST ID:i84x+n57 No.14762 Ignore Report Quick Reply
Maybe because of an opposing pull of gravity, the velocity of the rocket doesn't change at all. The deceleration from gravity could exactly cancel the acceleration due to thrust. Whatever the case, whoever made the question wants you to assume the change in velocity is negligible and that the change in mass is all that contributes to the change in momentum. So (delta p) = (delta m)*v.
Matilda Pockcocke - Wed, 17 Jun 2015 00:15:37 EST ID:sPd/0oB/ No.14799 Ignore Report Quick Reply
This doesn't mean much without the exhaust velocity, really.
In fact I'm not sure the speed of the rocket is relevant to calculate the momentum change. Speed related to what? In which direction?

Looks like a trick question at best.
Jarvis Bardson - Wed, 17 Jun 2015 18:05:29 EST ID:x6xydNWl No.14800 Ignore Report Quick Reply
Guys, look at the units. Momentum is Mass x velocity. Velocity is fixed, change in mass is given. Find change in momentum.

Unless I'm missing something, this seems like a straightforward elementary physics problem.
Jarvis Bardson - Wed, 17 Jun 2015 18:08:54 EST ID:x6xydNWl No.14801 Ignore Report Quick Reply
Nathaniel has the right of it. Sorry I didn't see that sooner.

NB for double post.
Cedric Dubbersare - Thu, 18 Jun 2015 12:28:42 EST ID:nyIjuDfA No.14802 Ignore Report Quick Reply
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It's a "restate the momentum equation" kind of problem. You're calculating the change in Momentum"dM" over a given time period "dt". Naturally, we all remember that momentum"M" is given by mass"m" times velocity aka: M=m*v. We're given both the velocity"v" and the change in mass"dm" over a period of time"dt" so the equation looks like "dMomentum/dt = dmass/dt * v" fortunately for us, the "dt"s on both sides of the equation have a value of 1 second and can be ignored because anything/1=anything. this problem is now a simple multiplication problem: "dM = -710kg * 7500m/s" which anyone may plug into a calculater at their leasure.

Good night, sweet prince. by Barnaby Drapperstat - Sun, 24 May 2015 14:29:23 EST ID:z/dIPyff No.14746 Ignore Report Reply Quick Reply
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John F. Nash Jr., a mathematician who shared a Nobel Prize in 1994 for work that greatly extended the reach and power of modern economic theory and whose decades-long descent into severe mental illness and eventual recovery were the subject of a book and a 2001 film, both titled “A Beautiful Mind,” was killed, along with his wife, in a car crash on Saturday in New Jersey. He was 86.
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Nakura !xMsGPnYjBI - Tue, 02 Jun 2015 20:07:20 EST ID:NAU1L+Of No.14770 Ignore Report Quick Reply
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stfu kid
Chaos strikes at the strangest of times. You really are disrespecting a great mathematician, and though I forgive you, just, idk, watch your mouth around the greats of mathematics. Their life force is a squared gamma function of an iteration of the trancendental # e anyway, so, he's probably chill.
Phineas Peblingshaw - Wed, 10 Jun 2015 23:42:43 EST ID:rp0UlP7W No.14788 Ignore Report Quick Reply
Was there even a thread for Grothendieck?
Nicholas Chingerperk - Thu, 11 Jun 2015 13:14:16 EST ID:QIXSgr8C No.14790 Ignore Report Quick Reply
media didnt make as much of an event of it
Basil Sasslehut - Fri, 12 Jun 2015 23:48:17 EST ID:rp0UlP7W No.14794 Ignore Report Quick Reply
It's just weird, even my friends who are mathematicians didn't say anything about it but posted something about John Nash. I guess it's amazing what a movie can do to public perception. No disrespect to Nash I'm just kinda bummed that Grothendieck wasn't appreciated when he was one of the greatest mathematicians of the 20th century.
Fanny Soddlestut - Sat, 13 Jun 2015 21:37:56 EST ID:QBhQLlLE No.14798 Ignore Report Quick Reply

No one can deny that Nash was more well known than Grothendieck. Not to disparage Grothendieck, but I think Nash focused on much more practical and "relevant" areas of mathematics such as game theory and computer science, which is interesting to everyone, while Grothendieck was more of a specialist in the field of Algebraic Geometry and Topos theory, which is niche. Nash also did excellent Algebraic Geometry.

Basically, Nash achieved more and had a more interesting story and received more attention as a result. They were both great mathematicians and their death is a huge loss, but Nash was a bigger deal for many reasons.

Drinking your wallet by Whitey Bomblefodge - Fri, 12 Jun 2015 02:09:00 EST ID:vX6Harxq No.14791 Ignore Report Reply Quick Reply
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I thought this was a question for hooch, but I have a second thought here.

Say you pour a $8.00 bottle of vodka into a glass. You suddenly envision coins dripping out of the bottle. My question for you, what coin were you seeing?
Whitey Criffingbanks - Fri, 12 Jun 2015 05:32:17 EST ID:i84x+n57 No.14792 Ignore Report Quick Reply
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$8 for a 750 ml bottle? I'd imagine diarrhea dripping out, not coins.

Assuming we're talking about US currency and 750 ml bottles, using the penny - the coin with the greatest volume to value - you'd only fill the bottle up close to 2/5 of the way. This is assuming that the pennies sorta melt like the watches in pic related, which is a fair assumption considerring your wording. This way we don't have to worry about space between the pennies.
Whitey Criffingbanks - Fri, 12 Jun 2015 05:50:14 EST ID:i84x+n57 No.14793 Ignore Report Quick Reply
Clara Wennerfock - Sat, 13 Jun 2015 06:22:58 EST ID:YsOAl7K9 No.14797 Ignore Report Quick Reply
I'm assuming it's half that size. That sounds about right. It's cheap but might not make you go blind.

Anyway it's 2.13(recurring) cents per ml at that quality/quantity. Vodka is about 37% alcohol and a smidge of glycerine if it's that cheap. Glycerol is about 1.2g/ml water is 1 and alcohol is .789. Vodka can be up to 40% but by assuming it's cheap shit. Glycerine is like 5% and the rest water so 1 ml is .05*1.2g + .37*.789g + .58g

a cent has a displacement of about .0433ml while the current rate is about .46ml per cent so US cents are probably pretty appropriate actually.

If ti's a 350ml bottle it's probably dead on.

If you're that desperate to get drunk buy some cheap cider though. White lightning actually does taste like it's been through someone's kidneys already but it's got the same alcohol content in a 3 litre bottle as a quart of vodka and when I was young enough to be desperate it was about 1/3 of the price of the absolute worst vodka I could get that wasn't toxic and illegal.

fertilizer question by Isabella Blackforth - Fri, 22 May 2015 19:43:11 EST ID:YCs1tF7z No.14741 Ignore Report Reply Quick Reply
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Hello /MATH/ I have a quick question for you to help me out with if that's cool.
Basically I just need to know how much fertilizer 20-4-8 would be in a 100lb bag
Betsy Pongerlock - Fri, 22 May 2015 21:34:36 EST ID:rw1aY/ny No.14742 Ignore Report Quick Reply
about 100lb
Phineas Hepperdock - Wed, 27 May 2015 23:45:30 EST ID:Jz+dW0dw No.14755 Ignore Report Quick Reply
Those are percentages.

Surely you know what a percent is.

<3 <3 by Jack Benninghat - Wed, 18 Jun 2014 06:38:10 EST ID:Fj/YvlCk No.14096 Ignore Report Reply Quick Reply
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I love maths and I love you <3

Share whatever proof, trick, theorem, mathematical tool, number, or other maths-related stuff you like in this thread.

I like e. It's always felt a bit "blue" for me, you know 2.7182818284590452353... A nice deep blue.
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Emma Dibblelidge - Sun, 03 May 2015 01:57:34 EST ID:K8qJv5EF No.14717 Ignore Report Quick Reply
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I'm a bigger fan of the spectral theorem (orthogonality is the bee's knees), but functional analysis is ballin' no matter how you do it.

Integration by parts is sneakily one of the most powerful tools in calculus. Seemingly just a technique for calculating integrals in a second semester course, the IBP formula is actually the backbone of Sobolev Spaces, and thus the backbone of the theory of Partial Differential Equations.
Martin Dribberdark - Sat, 09 May 2015 02:05:15 EST ID:YlDX0MWs No.14728 Ignore Report Quick Reply
I have been meaning to learn what spectral theory is all about, but fuck wikipedia for learning, why do I ever bother with it. Got a free reading recommendation and/or care to write a bit about what it is, essentially? (audience: math BS)

That IBP bit is really interesting and I want to know more. I remember a similar feeling when learning Variation of Parameters in diff eq, like it was a specific case of something more fundamental but I can't recall the line of thought now. Seeing it again, but applied, in physics was neat.

I have looked at and hatefully closed the wiki for Sobolev spaces before, I think, and definitely Hilbert spaces (which came up in spectral theorem wiki). Fucking wikipedia, I just can't learn from it and need to accept that.
Caroline Brebbermag - Fri, 15 May 2015 20:25:48 EST ID:K8qJv5EF No.14733 Ignore Report Quick Reply
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Hmm, to really understand the gravity of the spectral theorem, you'd need to have a pretty firm understanding of functional analysis, which in turn requires a firm understanding of linear algebra *and* measure theory.

For measure theory, probably the best beginner's book would be Royden's "Real Analysis", 3rd edition. Very clear language, motivates the study, etc. Be ready for some abstraction, though: measurable sets and functions are ill-behaved to say the least.

Once you understand the Lebesgue Integral, you'll be ready for functional analysis. There are many fantastic texts on the topic, but if you're *only* interested in learning spectral theory, you might want to try "Theory of Linear Operators in Hilbert Space," by Akhiezer and Glazman. This is a Dover book, and therefore very cheap. It covers everything from the basics of functional analysis (on inner product spaces) to the full spectral theorem for self-adjoint operators.

If you want a basic rundown of the spectral theorem, it basically says that very symmetric operations of certain kinds (like multiplication by a real number [boring] or the second derivative operator [interesting]) can be used to decompose certain vector spaces via an orthonormal basis, i.e. into a coordinate system where each axis is at "a right angle" with each other axis. This allows one to decompose your symmetric operation into a sum of very simple transformations on individual components. Like any other "decomposition" theorem, this is *extremely* advantageous when solving tough problems where these operators play a big role.

As for IBP, when combined with Sobolev spaces, it allows you to transform a second order partial differential equation into an integral equation of sorts. If your original PDE was linear, your integral equation gets alllll sorts of special properties (bilinear forms are what they become). This allows for really interesting theorems from functional analysis, like the Lax-Milgram theorem or the spectral theorem, to become immediately applicable to solving, or at least guaranteeing a solution to, your PDE. You *must* have Sobolev spaces for this approach to be sou…
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Ian Noffingdock - Tue, 19 May 2015 15:35:08 EST ID:NCaB2rkH No.14738 Ignore Report Quick Reply
You've provided some great resources to look into here and a clear path forward Brebbermag, I thank you for it.
Caroline Murdbury - Wed, 27 May 2015 04:01:40 EST ID:96SVbDTc No.14753 Ignore Report Quick Reply
This is along the same lines as my little trick for squaring, will use the same number. I don't even remember where I got it from, I think my calc 3 teacher squared some big number with it and I thought it was really elegant.


As for my favorite thing, the bisection method of root finding is up there. Just a really really beautiful and simple way of looking at the problem. The idea of "just split an interval in half and figure out which half has the root in it, repeat" is just really neat to me.

Helpless dumbfuck calling for help by Sidney Passlenotch - Mon, 04 May 2015 16:43:13 EST ID:3dz0uQ7J No.14724 Ignore Report Reply Quick Reply
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Is a horizontal or vertical line that expands to infinity it's own asymptote? Or is this in this case not applicable and a really dumb question?
Phineas Hecklesot - Tue, 05 May 2015 10:18:46 EST ID:xOOOxXVr No.14725 Ignore Report Quick Reply
An asymptote is defined as a value that is approached but never reached. Y=3 reaches Y = 3, so it's not its own asymptote

nice question though
Reuben Chacklefield - Sun, 17 May 2015 06:24:17 EST ID:WtAxPZi7 No.14734 Ignore Report Quick Reply
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tl;dr not really but I can prove otherwise

So consider the horizontal line y (x) = 3 i.e. y is independent of x, so for all values of x, y is always 3.
If x/x = 1,
then y (x) = 3 = 3*1 = 3x/x
It would still give you a horizontal line, but at x = 0 shit fucks ass.
You can then repeat this idea with other values like (x-1)/(x-1) = 1 so you get a "hole" at x=1, so on and so forth. Repeat this for all values of x and insert it into the equation then your line will be asymptotic to itself.
Shit Bottingbire - Sun, 17 May 2015 13:24:26 EST ID:xOOOxXVr No.14737 Ignore Report Quick Reply

An asymptote is a discontinuity, but not all discontinuities are asymptotes. What you just described is a function that is not continuous at all integer values of x, but not one with an asymptote.

I would also tend to argue that y = 3(x/x) is a different function from y = 3 simply because it returns different results

How can I relearn math? by Nicholas Cluzzleshaw - Sun, 26 Apr 2015 16:13:04 EST ID:L+X0k1Ap No.14703 Ignore Report Reply Quick Reply
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Hello /math/. I have retrograde amnesia.
I've forgotten math essentially, so much so that my abilities have regressed to that of a high school freshman.
Where and how do I relearn what I've forgotten? I've lost my job because of this.
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Hamilton Siddlenare - Wed, 29 Apr 2015 14:00:24 EST ID:L/U2K+oV No.14712 Ignore Report Quick Reply
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This reason is why i was so pissed about school. I was in honors during middle and high school. About a year ago I realized it had been years since i did any math. I found that i couldnt remember how to do SIMPLE SUBTRACTION. Fuck grade school.
Henry Murdbury - Fri, 01 May 2015 06:40:52 EST ID:gp8hje0w No.14715 Ignore Report Quick Reply
I would say to check out your local community college and do a college mathmatics placement test to see where you are at. I would say you should be able to enroll in pre calculus if you have some memory of simple algebra and geometry
Barnaby Fizzletetch - Sat, 02 May 2015 19:18:23 EST ID:Hj/F401x No.14716 Ignore Report Quick Reply
I've been in the exact same situation. Didn't like math in HS, didn't do it for years afterward. When I started taking classes again, I got owned hard.
Fast forward to the day before yesterday and I feel like I did pretty good on the back-to-back midterms I took on Fourier analysis + linear ODEs and algorithms (which is proof-heavy).

The same boiling water that softens the potato hardens the egg.
Martin Dribberdark - Sat, 09 May 2015 01:52:04 EST ID:YlDX0MWs No.14727 Ignore Report Quick Reply
My memory has always been shit, but it turned out to work in my favor for maths because I couldn't just memorize everything, I ended up having to derive everything, and re-derive it and re-derive it sometimes, until it made sense in an I guess "intuitive" level. Turns out this is a pretty good way of learning math, if a bit "slow".

My advice is to start MORE basic than you think. If I say "learn about fractions" and your reaction is "no that's too easy I want to start higher", I would suggest not to skip it. Spend a little bit actually working problems so you definitely have a very solid foundation. When I tutored calculus, there were students who got all frazzled at when where and how (not to mention why) they could "cancel out" a numerator and denominator, so their learning got held up because somewhere along the way they were like "yeah yeah ok whatever got it"
Basil Giffingford - Mon, 11 May 2015 10:33:10 EST ID:bG7/Mgyv No.14731 Ignore Report Quick Reply
Buy/torrent the book "Basic Mathematics" by Serge Lang. It's highschool and precalc but written from the perspective of a mathematician so you get a rigorous logic and analysis course out of highschool math instead of just being a calculator.

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