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Cryptography where to start by Nigger Ganningfoot - Tue, 24 Mar 2015 06:01:37 EST ID:ZkV6uFpl No.14663 Ignore Report Reply Quick Reply
File: 1427191297762.jpg -(6693B / 6.54KB, 550x275) Thumbnail displayed, click image for full size. 6693
I need recommendations for books that teach a solid theoretical base of cryptography, and also what previous knowledge i need?
>>
Reuben Bardfield - Mon, 30 Mar 2015 03:06:15 EST ID:UqThtfYr No.14676 Ignore Report Quick Reply
Lot's of linear algebra and number theory. Here's a sample paper this cryptographer uses Lattice reduction to do analysis https://www1.lip6.fr/~joux/pages/papers/ToolBox.pdf

You need "mathematical maturity" which means you can read and write proofs, and you can figure out mathematical notation if given a key for what the symbols mean. Spivak's Calclulus is a good book to get said maturity, so is "How to Solve it" or "How to prove it" (look them up on Amazon).

There's some intro cryptography courses around http://bryanpendleton.blogspot.ca/2012/05/comparing-coursera-and-udacity.html
they usually use this book: https://books.google.ca/books?id=1YwIcpDtQPEC (Schneier's first book is too outdated, this version with Ferguson is good).

Or just go through various university calendars and see what kind of information you can find, like lecture notes, recommended reading to look up yourself, ect http://cseweb.ucsd.edu/classes/wi10/cse206a/

Universities consider advanced crypto courses their specialist shit so almost always make them expensive and not open to the public. You should look up whoever was a finalist at the SHA-3 competition and read through the papers (or public comments to NIST) of their analysis http://www.groestl.info/analysis.html where you'll learn how modern cryptographers break each other's shit and thus learn a solid theoretical base.
>>
Doris Clupperstock - Thu, 16 Apr 2015 05:22:05 EST ID:TG1mst7r No.14696 Ignore Report Quick Reply
>>14663
>I need recommendations for books that teach a solid theoretical base of cryptography

What do you mean by theoretical base? Provable security or the mathematical basis of underlying operations (elliptic curves, algebra, etc)...

"Introduction to Modern Cryptography" by Katz and Lindell for the former
"An Introduction to Mathematical Cryptography" by Hoffstein, Pipher, and Silverman for the latter


Mathematical induction by Mr.TickleDicks - Sat, 28 Mar 2015 19:11:07 EST ID:fghQwkMe No.14672 Ignore Report Reply Quick Reply
File: 1427584267069.png -(3736B / 3.65KB, 303x333) Thumbnail displayed, click image for full size. 3736
Hello /math/ can you guys help me?
I need to prove that these propositions are true for every whole positive N.
does any one know how to solve it ? pls explain how did he arrive at the solution.

A) 2 + 4+ 6 + ...+(4n-2)=2n^2

C)1 + 3 + 6 + .... ( n(n+1) )/2 = ( n(n+1)(n+2) )/6

D) 1/1.2 + 1/2.3 + 1/3,4+ . . . + 1/n(n+1) = n/(n+1)
>>
Beatrice Claywater - Sat, 28 Mar 2015 19:28:32 EST ID:uBbxSpMx No.14673 Ignore Report Quick Reply
>>14672
A) Test the case where n =1: LHS: 2, RHS 2*(1)^2=2
It works!
Assume it works for k.
Want: works for k+1.
sum to k+1: 2 + 4 +6 + ... + (4k-2) + (4(k+1)-2)
Write the sum up to k as 2k^2. (we're assuming it works)
we get: 2k^2 +4k-2
what does 2(k+1)^2 equal?
...
It works for k+1!
Now by principle of induction ... ... ...V-allz n in the o'naturelle we just proved blah blah blah

I'm not sure what the homework rules are on this bored. If it says "no homework threads" please delete this thread and take it to http://mathoverflow.net/, I'm sure they'll be more than happy to help
>>
Caroline Hubblechetch - Sun, 29 Mar 2015 02:27:13 EST ID:qz3c7Bt+ No.14675 Ignore Report Quick Reply
1427610433362.gif -(11312B / 11.05KB, 654x366) Thumbnail displayed, click image for full size.
I like these


Quadratic Reciprocity by Wesley Middlewudging - Fri, 13 Feb 2015 08:52:14 EST ID:iRDOjfyp No.14607 Ignore Report Reply Quick Reply
File: 1423835534426.jpg -(42733B / 41.73KB, 301x431) Thumbnail displayed, click image for full size. 42733
Hey /math/, I've been reading a lot of maths in the last year because I always enjoyed it at school. I'm comfortable with all the maths one might do in high school and bits and pieces of other areas.
I'm told that some proofs for quadratic reciprocity are very beautiful, although I just can't get my head around what it actually IS
Can anyone enlighten me?
Thanks
>>
Fanny Sacklested - Sun, 08 Mar 2015 07:56:03 EST ID:nxCnniYW No.14631 Ignore Report Quick Reply
I haven't come across it until just now, and I hate learning things from wikipedia. I hope someone comes along and enlightens us, Wes.

https://www.youtube.com/watch?v=HhWqQQI5HJU
This guy talks about Legendre symbols which I guess helps (introduced by Legendre while trying to prove quadratic reciprocity). I'm at about 4min, it's okay so far, a bit stumbly but still better than trying to learn from wikipedia imo.
>>
Phineas Dreshwell - Tue, 24 Mar 2015 17:59:19 EST ID:PeQJ0tWt No.14665 Ignore Report Quick Reply
>>14607
I've just finish a Number theory course which covered it.

First you should be pretty comfortable with modular arithmetic. If you're not then I'm kinda wasting my time here but I'll try and give a summary:
If we have a 12 hour clock, then the hour 1 is thought of as the same as the hour 13. We want a way of relating any integer to one of the numbers 1 to 12. We do this by saying that two numbers, x and y represent the same hour if (x-y) is divisible by 12 which is the same as saying x=y+12n for some integer n, this is kind of obvious as we deal with clocks on a day to day basis.

Now we can obviously generalize this to a "clock" of any size, where each hour is represented by a number from 0 to m. Then we say that x is "congruent to" y "modulo m" if (x-y) is divisible by m. So, 0 and m represent the same "class" as does 1 and m+1, -1 and 241m-1 etc.

If you're familiar with that, then we can also set up a quadratic congruence: so recall how we'd normally want to find an x such that ax^2+bx+c=0, well now we want to find a solution x (not a number but a class of numbers) such that ax^2+bx+c is /congruent/ to 0 modulo p, where p is an odd prime. We can complete the square to get y=2ax+b and the problem becomes: find a class, y such that y^2 is congruent to d (modulo p).

Now to skim over some details, refer to the video Fanny posted to go over Legendre Symbols, but basically if we stick to the notation from before then we just define (d/p) to be 1 if p doesn't divide a and there's a solution, y to " find a class, y such that y^2 is congruent to d (modulo p)", -1 if it doesn't have a solution and 0 if p divides a.

Now it turns out that there are a bunch of algorithms which make (d/p) easy to calculate and so we can easily tell if the quadratic congruence has a solution or not. For example:

Euler's criterion: (d/p) is congruent to d^((p-1)/2) (modulo p)
Comment too long. Click here to view the full text.
>>
Phoebe Bonnerbetch - Wed, 25 Mar 2015 10:22:53 EST ID:HZ1lfOQk No.14666 Ignore Report Quick Reply
>>14665
(a/b) is real bad notation, if I'm wrong I'd love to hear an argument in favor of it.

Fucking sloppy shit imo.

Way too much gets forgiven by "I'm familiar with it so it's okay"
>>
Whitey Mangerbare - Wed, 25 Mar 2015 16:10:23 EST ID:RzF3HHjt No.14667 Ignore Report Quick Reply
>>14666
I'm sorry, I was pretty tired last night when I typed it up.

Replace the (d/p) with [d/p], (p/q) with [p/q] and anything else involving (x/p) where x is anything by [x/p].

If you're talking about just in general then I personally don't see it as that much of a problem.
>>
Oliver Sobberchetch - Wed, 25 Mar 2015 21:10:05 EST ID:IaC61I0h No.14668 Ignore Report Quick Reply
>>14666
i wrote this in another thread on /math/ like a year ago but yeah (a/b) sucks ass and i prefer to do L_b (a) for legendre symbol


1/0 = ∞ by Archie Claybanks - Thu, 29 Jan 2015 21:34:01 EST ID:iL1ckGCn No.14588 Ignore Report Reply Quick Reply
File: 1422585241954.jpg -(68549B / 66.94KB, 590x750) Thumbnail displayed, click image for full size. 68549
1/ ∞ = 1 - .9(repeating) = 0

If 1/ ∞= 0 then 1/0 = ∞
7 posts omitted. Click Reply to view.
>>
Fuck Chundlechod - Thu, 12 Feb 2015 20:15:22 EST ID:lx6v5XWF No.14603 Ignore Report Quick Reply
U n00bz.

Recall the definition of divides:
If a divides b, there exists some number c such that a * c = b.

By the fundamental theorem of arithmetic, c is unique.

So let a = 0 and see what happens. If a = 0, then b = 0, which means c is free to be anything it wants. But this is impossible in the system of math we us because the fundamental theorem demands unique factorization.

Also, Fanny, no you didn't.
>>
Cyril Geddlegold - Thu, 19 Mar 2015 15:05:45 EST ID:YZXygvod No.14653 Ignore Report Quick Reply
>>14601
This is a mathematics board, not an engineering board…
>>
Cuntfuck - Thu, 19 Mar 2015 16:04:33 EST ID:xgdLZpNp No.14655 Ignore Report Quick Reply
>>14601

That's not math.
>>
Matilda Crillerwotch - Sat, 21 Mar 2015 11:07:23 EST ID:Jz+dW0dw No.14660 Ignore Report Quick Reply
>>14655
>related rates aren't math

Wait till you start taking calculus?
>>
Samuel Gebblestet - Tue, 24 Mar 2015 12:00:25 EST ID:Dk8yywxc No.14664 Ignore Report Quick Reply
>>14588

This is not true in the real line. In the hyperreals, where arbitrarily large and small quantities are included unlike the "standard" reals, 1/0.000...1 with infinitely many zeroes is indeed infinity. However 1/0 is just undefined and there is nothing more to it than that.

In short, the formal system you're taught in calculus can't handle it but there are systems that can.


hmmmm by G Man - Tue, 24 Mar 2015 05:18:08 EST ID:nIRThw+j No.14662 Ignore Report Reply Quick Reply
File: 1427188688076.jpg -(42148B / 41.16KB, 721x303) Thumbnail displayed, click image for full size. 42148
Express 89.84 Mbps and 2.49 Mbps in bits per second (bps) using scientific notation.


probability by Phoebe Cliddlesure - Wed, 18 Mar 2015 01:56:40 EST ID:DYY7KYkl No.14645 Ignore Report Reply Quick Reply
File: 1426658200314.jpg -(132478B / 129.37KB, 698x332) Thumbnail displayed, click image for full size. 132478
If there is a function that returns a random number from 1-7, why can't I add the result of this function 5 times to get a uniform distribution of 5 to 35?

rand5() + rand5() + rand5() + rand5() + rand5() != uniform [5,35]

wtf I can't wrap my mind around why this doesn't work!! I've been told you can't sample a random uniform distribution to create a new random distribution and something about the central limit theorem. Can I get an intuitive answer?
5 posts and 2 images omitted. Click Reply to view.
>>
Lillian Smallfoot - Wed, 18 Mar 2015 06:23:21 EST ID:Qzq4CNd5 No.14651 Ignore Report Quick Reply
>>14650
whoops. sorta assumed this was prog and forgot which board I was on when I saw rand(). Glad to help. nb
>>
Esther Crishston - Wed, 18 Mar 2015 23:15:38 EST ID:JDIWTmrz No.14652 Ignore Report Quick Reply
>>14645

Because it's the 5 fold convolution of the uniform distribution. The result will be a quartic distribution
>>
Cuntfuck - Thu, 19 Mar 2015 16:07:14 EST ID:xgdLZpNp No.14656 Ignore Report Quick Reply
Because that's not how random works?
>>
Priscilla Hezzlemore - Sat, 21 Mar 2015 06:14:50 EST ID:qz3c7Bt+ No.14658 Ignore Report Quick Reply
1426932890860.gif -(4378B / 4.28KB, 629x115) Thumbnail displayed, click image for full size.
You must use combinatorics.
>>
Priscilla Hezzlemore - Sat, 21 Mar 2015 06:20:27 EST ID:qz3c7Bt+ No.14659 Ignore Report Quick Reply
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oops that last part was not up to /math/ standards


Beginnings by Nemywa - Thu, 19 Mar 2015 15:26:51 EST ID:lxw6acDK No.14654 Ignore Report Reply Quick Reply
File: 1426793211813.jpg -(205881B / 201.06KB, 1024x768) Thumbnail displayed, click image for full size. 205881
>3rd yr Winter Semester
Currently taking :
>Calc 3
>Abstract Algebra
>Cryptography

I want to understand and design electronics but end goal is I Entrepreneurship

Course suggestions for my senior yr before I'm out in the wild?


Ability of other species to conduct mathematics by StellarCir - Sun, 15 Mar 2015 04:05:09 EST ID:M7BdweVS No.14637 Ignore Report Reply Quick Reply
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I would like to postulate the question of which if any animals are capable of math besides Homo sapiens?

Some notable contestants:

African Grey Parrot, estimated to have the cognition/IQ of a 4 year old child.
Octopus, possibly the smartest creatures without a bone structure
Chimpanzees, our 'closest' cousins known to fashion tools
Crows, with a surprising brain-body ratio in proportion to Chimpanzees
Elephants, demonstrating self-awareness
Gorillas, historically taught to learn and speak sign language
Dolphins, our marine-mammal navigation crew on /1701/

Do you believe any of these animals could learn to use math? To what degree? Do you believe another creature could be a serious contender?
>>
Lillian Fannerdale - Mon, 16 Mar 2015 08:56:29 EST ID:4/hffjyH No.14639 Ignore Report Quick Reply
>>14637
Depends how you define 'maths'. The fist step would be understanding that 5 apples and 5 bricks have some quality in common, or perhaps showing them 2 quantities of the same object and giving them treats if they add them. Chimps have a better working memory than us in tests which use numbers, but they use them as arbitrary symbols. There's a lot of conciusness involved in treating maths as an end in and of itself
>>
Lillian Fannerdale - Mon, 16 Mar 2015 08:58:54 EST ID:4/hffjyH No.14640 Ignore Report Quick Reply
>>14637
The thing about chimp sign language is that it's all repetition, any claims of them making new words always turn out to be overhyped. It's language without linguistics, in general the most animals can do in this realm is relate an actual object with some kind of symbolic representation of it, impressive but very far from any abstract logic
>>
Fanny Wittinghut - Mon, 16 Mar 2015 15:53:08 EST ID:SpD/fp2u No.14641 Ignore Report Quick Reply
>Crows, with a surprising brain-body ratio in proportion to Chimpanzees
That's your description? Come on, crows have demonstrated some mind-blowing cognitive abilities.

But yeah, like Lillian says, so far it's all repetition and parroting from my understanding. Wouldn't it be cool to make it your life legacy to be the one who successfully teaches a non-human to math?
>>
Fanny Wittinghut - Mon, 16 Mar 2015 15:54:04 EST ID:SpD/fp2u No.14642 Ignore Report Quick Reply
>>14641
And you left out octopus, wtf.
https://www.youtube.com/watch?v=x5DyBkYKqnM
>>
Fanny Wittinghut - Mon, 16 Mar 2015 15:57:41 EST ID:SpD/fp2u No.14643 Ignore Report Quick Reply
>>14642
Actually you didn't leave out octopus, apparently I am drunk


Help learning gcse maths by Shitting Lightridge - Sat, 03 Jan 2015 10:45:28 EST ID:NxPbw8hD No.14549 Ignore Report Reply Quick Reply
File: 1420299928533.jpg -(111066B / 108.46KB, 603x376) Thumbnail displayed, click image for full size. 111066
Im 25 and im back in college learning maths.The lesson is only one 2 hour lessons a week and to be honest I feel like ive learnt nothing there at all.Its hard and I just seem t learn better by my self.

My problem I have though is where the fuck should I start of,there is so much shit I dont know like I barely even know what a fuckin prime number is.

I only want a c but I need that so I can go onto an access course.

SO what should I do to learn maths (I dont like khan academy found a few other sites though)

Like when I say what should I do what subjects should I Start of learning first ?
IM going to take the whole of next week while im still of work to learn as much so I need a plan on what to start of learning first.
>>
Alice Snodshit - Fri, 09 Jan 2015 07:33:19 EST ID:ev+cRfEi No.14555 Ignore Report Quick Reply
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So at the moment Im trying to learn fractions but I keep on fucking up with baisc things like simplifying and converting ratios and the rest of it.

Im thinking I may need to go back a few steps as im not perfect with my time tables dont know all my prime numbers ect.
Wherre would you say I should start of with wht subjects ?

>btw Ive got to learn as muh as I can of thse by tuesday for a mock test im going to be doing

fractions
decimals
percentages

>algebra
simplify
expand brackets
factonise
Comment too long. Click here to view the full text.
>>
Hugh Collerfoot - Thu, 05 Feb 2015 22:24:09 EST ID:Gj+82UIb No.14595 Ignore Report Quick Reply
All you need is Basic Mathematics by Serge Lang. It covers everything, from the view of a professional mathematician explaining how the magic works. Torrents for it everywhere also can buy it used for cheap. Covers all of highschool and is a good precalc book.

After Basic Math get these short books:
How to Prove It: A Structured Approach
How to Solve it by Polya.

Now you are ready for any rigorous university level classes
>>
Rebecca Cushforth - Sun, 15 Mar 2015 04:25:46 EST ID:JDIWTmrz No.14638 Ignore Report Quick Reply
>>14549

Work through the following:

Algebra by Gelfand and Shen
Functions and Graphs by Gelfand, Glagoleva, and Shnol
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Trigonometry by Gelfand and Saul
Kiselev's Geometry


Analysis by William Gissleville - Thu, 26 Feb 2015 17:18:10 EST ID:Yi4ytYm1 No.14616 Ignore Report Reply Quick Reply
File: 1424989090559.jpg -(25012B / 24.43KB, 344x475) Thumbnail displayed, click image for full size. 25012
Due to circumstances I was unable to participate in my first analysis course. Now I have to take the next one (individually both take half a semester). I want to go through the important parts of the previous course, but while there is practice material, there is no material with solutions. I asked my professor about solutions to the homework excersizes, but he isn't giving them. Does anyone know of any, preferably free, practice material? The topics coverd is basically this book, plus some extra stuff on sets (boundaries/compactness) and integration.

I did find this:
http://scholarstock.com/p/solution-manual-for-friendly-introduction-to-analysis-a-2e-2nd-edition-130457965/
But I'm not sure how trustworthy the site is.
4 posts omitted. Click Reply to view.
>>
Charles Blathergold - Sat, 28 Feb 2015 15:32:06 EST ID:Gj+82UIb No.14623 Ignore Report Quick Reply
>>14622

Also, you may be interested in these short(ish) books to help you write proofs.
http://www.amazon.ca/How-Solve-Aspect-Mathematical-Method/dp/069111966X/
http://www.amazon.ca/How-Prove-It-Structured-Approach/dp/0521675995
>>
William Crucklemeck - Sun, 01 Mar 2015 22:15:42 EST ID:e+7yrnP7 No.14624 Ignore Report Quick Reply
>>14622
Unless you are talented and bright, Rudin's book is a very rough intro to analysis. You have to treat the entire book like an exercise, rather than just expecting the author to help you learn the material.

I would go only go through it after going through a BS level text first, so then you have some familiarity with what's going on.

But if you are devoted/intelligent enough it will certainly benefit you most
>>
Nigel Figgleputch - Wed, 04 Mar 2015 07:17:41 EST ID:weDVNH8d No.14627 Ignore Report Quick Reply
>>14624
I did not merge with the math community and neither had i very splendid start. So i need to be very self-reliant for now.
The professor who teaches analysis uses Tao's book. I like it except the fact it doesn't have solutions. Rudin's book has them, so good reason to train my devotion haha.

But there is also group theory and syllabus we got doesn't have solutions either. Anyone a good introductory book they're fond of?
>>
Nell Ceblingfoot - Mon, 09 Mar 2015 20:29:01 EST ID:JDIWTmrz No.14632 Ignore Report Quick Reply
>>14616
Read Baby Rudin. All the exercises are online.
>>
Hedda Niggerford - Mon, 09 Mar 2015 22:44:02 EST ID:Gj+82UIb No.14633 Ignore Report Quick Reply
>>14627
>group theory
http://store.doverpublications.com/0486477231.html

You can also pirate the Princeton Companion to Mathematics, which covers literally everything. There's plenty of recommended texts in it to dive further into material


just sayin by Nigger Drunkinstock - Thu, 05 Mar 2015 23:48:50 EST ID:PmLosP1P No.14628 Ignore Report Reply Quick Reply
File: 1425617330260.gif -(195877B / 191.29KB, 360x235) Thumbnail displayed, click image for full size. 195877
I like the idea of q-analogs but I think they're a little too advanced for selfstudy and that's all I've got at the moment.

I also like the idea of fractional calculus (same kind of realm in a way?) but that seems like something I could study on my own.
>>
Eliza Seggledet - Sun, 08 Mar 2015 01:45:50 EST ID:F9AJX/Os No.14629 Ignore Report Quick Reply
i like your picture.

although i dont get why they used (x^2)/2 instead of just x^2.
>>
Fanny Sacklested - Sun, 08 Mar 2015 06:04:20 EST ID:nxCnniYW No.14630 Ignore Report Quick Reply
>>14629
because (x^2)/2 is the antiderivative of x, and 1 is the derivative. its from the wiki page on fractional calculus.


always messing up the basics by Edwin Pimmleman - Mon, 23 Feb 2015 22:03:13 EST ID:zBSUDYOt No.14612 Ignore Report Reply Quick Reply
File: 1424746993952.png -(4013B / 3.92KB, 540x358) Thumbnail displayed, click image for full size. 4013
so anytime I see a problem like im about to write I always shit the bed and forget the basics with out further ado my nemesis so instead of simply giving me the answer Id rather like to have people interact with me as I try to preform this.
(2u^-5 * v^2
---------------
8w)^-2
so for starts I need to distribute ^-2

(1/4u^10 * v^-4)
---------------------
1/64w^-2
So if Im understanding this fraction within a fraction everything is going to switch between the numerator and the denominator except for 1/4u^10 because its not raised to a negative power thus.

64w^2 * 1/4u^10
-----------------------
v^4
then multiply the numerator
Comment too long. Click here to view the full text.
>>
Phoebe Blillerridge - Tue, 24 Feb 2015 22:30:13 EST ID:N0lLaAL+ No.14613 Ignore Report Quick Reply
>>14612
It would be helpful if you just typed out in paint what the equation is rather than using free draw. Right now i can hardly read the left side of the equation and have to trust your post to tell me exactly what it is we are doing
>>
Basil Donderwell - Wed, 25 Feb 2015 00:16:01 EST ID:zBSUDYOt No.14614 Ignore Report Quick Reply
1424841361224.png -(2779B / 2.71KB, 444x245) Thumbnail displayed, click image for full size.
>>14613
Well I solved but this problem is also hard for me here it is in paint also I'm practicing for a placement test and im using a guide online can't remember if links are allowed here but its number 17 in this link https://www.barton.edu/pdf/math/practice-math-placement-test.pdf

also its not for this school
>>
Basil Donderwell - Wed, 25 Feb 2015 00:18:51 EST ID:zBSUDYOt No.14615 Ignore Report Quick Reply
>>14614
Fuck meant 16 but yeah can't do 17 either =\
>>
Jack Hammerfoot - Sat, 28 Feb 2015 03:01:48 EST ID:e+7yrnP7 No.14619 Ignore Report Quick Reply
>>14615
The key to the top part of 17 is knowing that
a^2 - b^2 = (a + b)*(a - b)
The bottom part is trickier, but one of the terms needs to have a 2x
>>
Jack Hammerfoot - Sat, 28 Feb 2015 03:02:52 EST ID:e+7yrnP7 No.14620 Ignore Report Quick Reply
>>14619
I guess i should say, it's not 'knowing' it's observing the algebra. Splitting these equations up is mainly a trial and error sort of deal where the more practice you get the faster/better you are


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