گراف جهتدار فوق را گراف تابعی f مینامند، که راسهای آن مجموعه 0 تا 999 و یال های آن مجموعه همه زوج مرتبهای (x,y) است بطوریکه f(x)=y.
هر مولفه همبندی در این نوع گرافها دارای یک دور و چندین درخت ریشهدار است که به این دور متصل هستند.
این نوع گرافها دارای کاربردهای فراوان در نظریه رمزنگاری، به خصوص روشهای شکستن رمز هستند.
هر مولفه همبندی در این نوع گرافها دارای یک دور و چندین درخت ریشهدار است که به این دور متصل هستند.
این نوع گرافها دارای کاربردهای فراوان در نظریه رمزنگاری، به خصوص روشهای شکستن رمز هستند.
مقاله زیر مبتنی بر سخنرانی ریچارد همینگ در یک اجلاس جامعه ریاضی امریکاست. همینگ از معروفترین ریاضیدانان کاربردی عصر حاضر محسوب میشود. اصطلاح کد همینگ را همه کسانی که با نظریه کدگذاری آشنایی دارند شنیدهاند. همینگ نظراتی تند و بعضا نامتعارف در مورد شاخههای گوناگون ریاضیات داشت که گهگاه آنها را با زبان گزندهای بیان میکرد. نوشته زیر نیز از این قاعده مستثنی نیست.
@infinitymath
نشر ریاضی، سال ۱۱، شماره ۱
@infinitymath
نشر ریاضی، سال ۱۱، شماره ۱
تعریف:n امین عدد تاکسی برابر است با کوچکترین عددی طبیعی که به n طریق می توان آن را به صورت جمع دو مکعب کامل نوشت. داریم:
Ta(1)=1
Ta(2)=1729
پیدایش: روزی هاردی به دیدن رامانوجان به بیمارستان می رود و به رامانوجان میگوید که با یک تاکسی اومدم که شمارش 1729 بود . به نظر می رسد عدد بیخودی باشد. بعد رامانوجان سریعا جواب می دهد که این عدد کوچکترین عددی است که به دو صورت جمع دو مکعب کامل نوشته می شود.
به این عدد ، عدد رامانوجان-هاردی می گویند. و از آن روز به این عددها نام خاصی اطلاق می شود که دارای خواص جالب دیگری نیز می باشند.
مطلب بالا رو گفتم تا جوک زیر همه بتونند درک کنند:
I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. "No" he replied, "it is a very interesting number. It's the smallest number expressible as the product of 7 and 2 in two different ways."
متن اصلی هاردی:
I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways."
@infinitymath
Ta(1)=1
Ta(2)=1729
پیدایش: روزی هاردی به دیدن رامانوجان به بیمارستان می رود و به رامانوجان میگوید که با یک تاکسی اومدم که شمارش 1729 بود . به نظر می رسد عدد بیخودی باشد. بعد رامانوجان سریعا جواب می دهد که این عدد کوچکترین عددی است که به دو صورت جمع دو مکعب کامل نوشته می شود.
به این عدد ، عدد رامانوجان-هاردی می گویند. و از آن روز به این عددها نام خاصی اطلاق می شود که دارای خواص جالب دیگری نیز می باشند.
مطلب بالا رو گفتم تا جوک زیر همه بتونند درک کنند:
I went to visit him while he was lying ill at the hospital. I had come in taxi cab number 14 and remarked that it was a rather dull number. "No" he replied, "it is a very interesting number. It's the smallest number expressible as the product of 7 and 2 in two different ways."
متن اصلی هاردی:
I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. "No", he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways."
@infinitymath
A biologist, a physicist and a mathematician were all drinking coffee and tea and observing a house across the street from them. They notice that two people walk into the house and then an hour later, three people walk out.
Physicist: An experimental error. Our first measurement was incorrect.
Biologist: No, they've obviously reproduced.
Mathematician: No, now when a one person enters the house, it'll be empty again.
@infinitymath
Physicist: An experimental error. Our first measurement was incorrect.
Biologist: No, they've obviously reproduced.
Mathematician: No, now when a one person enters the house, it'll be empty again.
@infinitymath
A poet, a priest, and a mathematician are discussing whether it's better to have a wife or a mistress.
The poet argues that it's better to have a mistress because love should be free and spontaneous.
The priest argues that it's better to have a wife because love should be sanctified by God.
The mathematician says, "I think it's better to have both. That way, when each of them thinks you're with the other, you can do some mathematics."
@infinitymath
The poet argues that it's better to have a mistress because love should be free and spontaneous.
The priest argues that it's better to have a wife because love should be sanctified by God.
The mathematician says, "I think it's better to have both. That way, when each of them thinks you're with the other, you can do some mathematics."
@infinitymath
ویدیو زیر توسط گروه کلاین در Northwestern University اجرا شده است. این دانشجویان آهنگی با مزمون "Finite Simple Group (of Order Two)" که ترانه متن هم در زیر قرار میدم که پر از اصطلاحات ریاضی می باشد.
The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true
But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two
I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way
Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two
Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified
When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense
I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two
I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")
I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q.E.D.
(lyrics by Matt Salomone)
@infinitymath
The path of love is never smooth
But mine's continuous for you
You're the upper bound in the chains of my heart
You're my Axiom of Choice, you know it's true
But lately our relation's not so well-defined
And I just can't function without you
I'll prove my proposition and I'm sure you'll find
We're a finite simple group of order two
I'm losing my identity
I'm getting tensor every day
And without loss of generality
I will assume that you feel the same way
Since every time I see you, you just quotient out
The faithful image that I map into
But when we're one-to-one you'll see what I'm about
'Cause we're a finite simple group of order two
Our equivalence was stable,
A principal love bundle sitting deep inside
But then you drove a wedge between our two-forms
Now everything is so complexified
When we first met, we simply connected
My heart was open but too dense
Our system was already directed
To have a finite limit, in some sense
I'm living in the kernel of a rank-one map
From my domain, its image looks so blue,
'Cause all I see are zeroes, it's a cruel trap
But we're a finite simple group of order two
I'm not the smoothest operator in my class,
But we're a mirror pair, me and you,
So let's apply forgetful functors to the past
And be a finite simple group, a finite simple group,
Let's be a finite simple group of order two
(Oughter: "Why not three?")
I've proved my proposition now, as you can see,
So let's both be associative and free
And by corollary, this shows you and I to be
Purely inseparable. Q.E.D.
(lyrics by Matt Salomone)
@infinitymath