Mathematics

[Einstein]

Mathematics is very Important subject in the world of science.. It plays a great role all over the field of science.. A good example for this is the use of mathematics in computers.. The arithmetic and logical micro-operations performed by the computer depends on mathematics.. In Physics all of the calculations depend on mathematics.. Just think of the formula for the energy required to launch a rocket into the space...

Computer programming on the other hand, it sucks when you are not familiar with mathematics. Just imagine the coding of programs on banking systems. How can you code while you don't know mathematics??? It is hard without mathematics..

It is very CRUCIAL in our daily life as it is accompanied with the advancement in technology..

To understand mathematics is easier as long as you know the concepts.. You need to know how formulas works, the logic behind the concepts and all of the theories governing the particular concept.. The problem with many students is to prefer to cram mathematics which it is in contrast with the principles of mathematics.. It needs to understand the theory governing a particular concept..

Let us take a small example..2 + 2 = 4.. and 2*2=4. If you understand the concept behind addition and multiplication, it will be very easy for you to perform all the "add" and "multiply" arithmetic operations. For a poor student he will implicate that, whenever you add or multiply the same number you will get the same result.. For him, 3 + 3 = 6, and 3*3=6 which is wrong.. The basic thing is to understand the theory behind that particular operation..

Let us take another example..1 + 1 = 2 in normal arthmetic operations.. In Boolean mathematics 1 + 1 = 1.. The question arises, why is 1 + 1 = 1 in Boolean mathematics ?? The answer is as simple as you understand the theory behind Boolean algebra..It needs not to cram.. It needs to understand..

One important part in mathematics is the Integration and Differentiation... These topics are very useful in Physics.. In integration for instance, there is problems which can take a number of pages, just to find the solution of a single problem.. Some lazy and poor students may wonder how their bright colleagues are going through a number of pages approaching a single question. They try to figure it out how are they going to perform such an operation on their own, and how are they going to cram all of those pages..

The only solution is to understand the theory behind that operation..

Mathematics is always easier, it is a matter of how you treat it..

The most important thing is to understand the theory behind each and every concept.. On that case, you will enjoy mathematics for the rest of your life..

By Gagah

 

[Makanyaga]

Einstein;
Concept nzuri mno; I mean topic ni nzuri sana, isipokuwa lugha ni hafifu mno. Usipoirekebisha, badilisha jina, otherwise utakuwa hulitendei haki jina hilo ni kubwa mno duniani! Ningekushauri uchague jingine, hata la aliyekuwa mwalimu wako wa hesabu primary au sekondari!

 

[SILENT WHISPER]

umenikumbusha Fourier series ( mambo ya univ. haya)

swali moja unapiga page kama 4 hivi..! kaaaaaaaaaaaa!! INDICIAL EQUATIONS.....:confused2::confused2:

 

[Ruge Opinion]

Language is our national problem. Not only English but even Kiswahili is being distorted on an amazing scale. You hear words like "haijarishi" which is a literal translation of "no matter" "it does not matter what". You hear words like "kiukweli" instead of "kwa kweli". Not to mention the inability to speak one language without mixing it with another - Kiswangish. In my opinion it is this phenomenon which makes Tanzanian youth look down on themselves in comparison with their Kenyan and Ugandan peers. That is why Tanzanian musicians (Bongo flavour) cannot make an impact outside East Africa.

 

[Einstein]

Einstein;
Concept nzuri mno; I mean topic ni nzuri sana, isipokuwa lugha ni hafifu mno. Usipoirekebisha, badilisha jina, otherwise utakuwa hulitendei haki jina hilo ni kubwa mno duniani! Ningekushauri uchague jingine, hata la aliyekuwa mwalimu wako wa hesabu primary au sekondari!

Thanks! It is a challenge to me, I will work on it perpendicularly.. But I will keep on using Einstein's name basing on three important facts

1. He is my driving model..
2. He failed at the beginning at last he became the winner (E=mc^2)
3. He is a great scientist..

 

[Einstein]

umenikumbusha Fourier series ( mambo ya univ. haya)

swali moja unapiga page kama 4 hivi..! kaaaaaaaaaaaa!! INDICIAL EQUATIONS.....:confused2::confused2:

Heheeee, yap well said bro..

 

[Makanyaga]

umenikumbusha Fourier series ( mambo ya univ. haya)

swali moja unapiga page kama 4 hivi..! kaaaaaaaaaaaa!! INDICIAL EQUATIONS.....:confused2::confused2:

Au recurrency relations!

 

[Einstein]

Language is our national problem. Not only English but even Kiswahili is being distorted on an amazing scale. You hear words like "haijarishi" which is a literal translation of "no matter" "it does not matter what". You hear words like "kiukweli" instead of "kwa kweli". Not to mention the inability to speak one language without mixing it with another - Kiswangish. In my opinion it is this phenomenon which makes Tanzanian youth look down on themselves in comparison with their Kenyan and Ugandan peers. That is why Tanzanian musicians (Bongo flavour) cannot make an impact outside East Africa.

Yeah, we have to work on it..
Actually I think the problem starts with the foundation we got from primary schools.. In most of government schools, students are not fluent in English..

When they join secondary schools (In government schools), they don't get motivated to understand English.. Sometimes, they take it for granted especially science students.. Some science students, dare to bunk the English class for the reason that, they are not concerned with it..

We need to come up with the solution on this..

 

[Makanyaga]

Thanks! It is a challenge to me, I will work on it perpendicularly.. But I will keep on using Einstein's name basing on three important facts

1. He is my driving model..
2. He failed at the beginning at last he became the winner (E=mc^2)
3. He is a great scientist..

Einstein (JF);
I am not informed about his failures; when did he? I mean at what stage of his scholary work? Unless if you mean at the time he was a secondary school kid.Otherwise, I have not heard anything of the sort in his older age

 

[Einstein]

Einstein (JF);
I am not informed about his failures; when did he? I mean at what stage of his scholary work? Unless if you mean at the time he was a secondary school kid.Otherwise, I have not heard anything of the sort in his older age

Actually I meant he was not fluent in English at his early life, though he was becoming the best student ...

 

[Mtazamaji]

SWALI
Can we have mathematical history and /or historical mathematics?

 

[introvert]

yet, there's no nobel prize in mathematics, sad!!

 

[Matarese]

SWALI
Can we have mathematical history and /or historical mathematics?

There is a course at University evel called " History of Mathematics"

 

[Koba]

Einstein (JF);
I am not informed about his failures; when did he? I mean at what stage of his scholary work? Unless if you mean at the time he was a secondary school kid.Otherwise, I have not heard anything of the sort in his older age

..he was failure kuna wakati from marriage,works etc,na hata theory yake (general relativity) kukubaliwa was not a cake walk,hiyo E=MC" unayoiona was a failure at one point and was just out of many ambazo alikuwa anafanyia kazi lakini nyingi tuu hakufanikiwa ndio maana hata hujasikia,hata in his later days of his life was working in Theory of everything lakini was unsuccessful & never finished...kuna movie/documentary based on true story imeeleza life yake yote sio MC" tuu inaitwa Albert Einstein nafikiri if you search au HULU or Netflix unaweza kuipata

 

[Kiranga]

..he was failure kuna wakati from marriage,works etc,na hata theory yake (general relativity) kukubaliwa was not a cake walk,hiyo E=MC" unayoiona was a failure at one point and was just out of many ambazo alikuwa anafanyia kazi lakini nyingi tuu hakufanikiwa ndio maana hata hujasikia,hata in his later days of his life was working in Theory of everything lakini was unsuccessful & never finished...kuna movie/documentary based on true story imeeleza life yake yote sio MC" tuu inaitwa Albert Einstein nafikiri if you search au HULU or Netflix unaweza kuipata

Seldom is Einstein looked in the right light, he is mostly overrated as some demigod and mathematical genius .Mathematically he wasn't a Gauss, not even a Poincare, who was also on the verge of coming up with relativity, his forte was thought experiments. But this adds, rather than diminishes, his credit. One is not justified in belittling him unjustly as a fluke. He was neither a fluke nor a scientific demigod. He was a gifted human being who persisted unflinchingly where most would have given up. I don't know if I can call somebody who bested Newton's laws a failure, the guy contributed the special and general theories of relativity to humanity, and as to his failure on the theory of everything, it says so much about his ambition and curiosity than his inability to solve problems or his failure.

There were a great number of scientist during his time, but why isn't Rutherford a household name ? Why isn't Niels Bohr a household name ? The truth is, Einstein did not just discover relativity as a mere scientific discovery, this was a paradigm shift that gave us a new view on the cosmos, established the speed of light as the ultimate yardstick, revealed time as nothing but the fourth dimension of the space-time continuum and uprooted the clockwork and deterministic universe charted by Blaise Pascal and Isaac Newton, his was a revolution of Copernican proportions. Up to today when you are using GPS you are not using Newton's classical laws, but Einstein's relativistic equations, how can you say this man whose work hasn't been improved upon a hundred years now, is a failure ?

Einstein was such an original thinker to the extent that even when he thought he was wrong due to being far too advanced for his time, it turns out he was right (read about the cosmological constant). I wouldn't call this fellow a failure exactly, he was dealing with questions that havent been answered up to today, and some are even entertaining the thought that "The Theory of Everything" is really a blind alley (Read Dr. Steven Hawking's new book "The Grand Design" )

I could go on and on, but the bottom line is, like any paradigm shift pioneer, Einstein is probably deified in a fanatical fashion, but to say the man was a failure is a total misunderstanding of the level of challenges he was ambitious enough to grapple with.

 

[Misterdennis]

.... who persisted unflinchingly where most would have given up. I don't know if I can call somebody who bested Newton's laws a failure, ....... and as to his failure on the theory of everything, it says so much about his ambition and curiosity than his inability to solve problems or his failure.

............ whose work hasn't been improved upon a hundred years now, is a failure ?

Einstein was such an original thinker to the extent that even when he thought he was wrong due to being far too advanced for his time, it turns out he was right.
.

The above shows that he was a very succesful scientist.
Na kama a scientist / researcher, kutofanikiwa ktk experiment moja haimaanishi kwamba umefeli .... inakuwa imekupa uhakika kuwa njia au model ulizotumia hajikuwa relevant, and then u change your direction...

 

[Eric Cartman]

A million Dollar equation

Goldbach Conjecture

Goldbach's original conjecture (sometimes called the "ternary" Goldbach conjecture), written in a June 7, 1742 letter to Euler, states "at least it seems that every number that is greater than 2 is the sum of three primes" (Goldbach 1742; Dickson 2005, p. 421). Note that here Goldbach considered the number 1 to be a prime, a convention that is no longer followed. As re-expressed by Euler, an equivalent form of this conjecture (called the "strong" or "binary" Goldbach conjecture) asserts that all positive even integers

can be expressed as the sum of two primes. Two primes

such that

for

a positive integer are sometimes called a Goldbach partition (Oliveira e Silva).

According to Hardy (1999, p. 19), "It is comparatively easy to make clever guesses; indeed there are theorems, like 'Goldbach's Theorem,' which have never been proved and which any fool could have guessed." Faber and Faber offered a

prize to anyone who proved Goldbach's conjecture between March 20, 2000 and March 20, 2002, but the prize went unclaimed and the conjecture remains open.

Schnirelman (1939) proved that every even number can be written as the sum of not more than

primes (Dunham 1990), which seems a rather far cry from a proof for two primes! Pogorzelski (1977) claimed to have proven the Goldbach conjecture, but his proof is not generally accepted (Shanks 1985). The following table summarizes bounds

such that the strong Goldbach conjecture has been shown to be true for numbers

.
boundreference

Desboves 1885

Pipping 1938

Stein and Stein 1965ab

Granville et al. 1989

Sinisalo 1993

Deshouillers et al. 1998

Richstein 1999, 2001

Oliveira e Silva (Mar. 24, 2003)

Oliveira e Silva (Oct. 3, 2003)

Oliveira e Silva (Feb. 5, 2005)

Oliveira e Silva (Dec. 30, 2005)

Oliveira e Silva (Jul. 14, 2008)

The conjecture that all odd numbers

are the sum of three odd primes is called the "weak" Goldbach conjecture. Vinogradov (1937ab, 1954) proved that every sufficiently large odd number is the sum of three primes (Nagell 1951, p. 66; Guy 1994), and Estermann (1938) proved that almost all even numbers are the sums of two primes. Vinogradov's original "sufficiently large"

was subsequently reduced to

by Chen and Wang (1989). Chen (1973, 1978) also showed that all sufficiently large even numbers are the sum of a prime and the product of at most two primes (Guy 1994, Courant and Robbins 1996).

A stronger version of the weak conjecture, namely that every odd number

can be expressed as the sum of a prime plus twice a prime is known as Levy's conjecture.
An equivalent statement of the Goldbach conjecture is that for every positive integer

, there are primes

and

such that

where

is the totient function (e.g., Havil 2003, p. 115; Guy 2004, p. 160). (This follows immediately from

for

prime.) Erdős and Moser have considered dropping the restriction that

and

be prime in this equation as a possibly easier way of determining if such numbers always exist (Guy 1994, p. 105).

Other variants of the Goldbach conjecture include the statements that every even number

is the sum of two odd primes, and every integer

the sum of exactly three distinct primes.
Let

be the number of representations of an even number

as the sum of two primes. Then the "extended" Goldbach conjecture states that