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Nairaland Mathematics Clinic - Education (3) - Nairaland

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Re: Nairaland Mathematics Clinic by godstino(m): 10:18am On Jan 03, 2013
WebsiteDesigner: @Richiez, pls can u solve a Von Smoluchowski equation. Let me know if u can.
Re: Nairaland Mathematics Clinic by agog: 10:19am On Jan 03, 2013
Richiez:

Mathematical induction is a method of mathematically proving that a statement is true for all natural numbers i.e positive integers
it usually involves 2 basic steps;
1. showing that the statement is true when the lowest natural number is used e.g n=0 or n=1 (preferably)
2. showing that if the statement is true for any natural number n=k, then it is true for the next natural number n=k+1

let us do some examples;

1. prove by mathematical induction 1+2+3+4+.......+n+(n+1) = n(n+1)/2
SOLUTION
note that n represents the number of elements in the series
step 1---we have to show that the statement is true for n=1
1= 1(1+1)/2
1= 2/2
1=1 therefore since L.H.S = R.H.S the statement is true for n=1
we can even go ahead to show that the statement is true for any other small value of n, say n= 4
1+2+3+4 = 4(4+1)/2
10= 4(5)/2
10= 20/2
10= 10 therefore it is also true for n=4
next is step 2
here we shall consider an arbitrary value of n, say n=k and assume it is true
i.e 1+2+3+4+....+k = k(k+1)/2 ................(1)
if the above statement is true, then the final step is to show that it is also true for n= k+1
1+2+3+4+....+k+(k+1) = (k+1)(k+1+1)/2
1+2+3+4+....+k+(k+1) = (k+1)(k+2)/2 ...............(2)

to show that eqn 2 is true, let us add (k+1) to both sides of eqn 1
1+2+3+4+....+k+(k+1) = k(k+1)/2 + (k+1).............(3)
the job here is to make the R.H.S of eqn 3 look like that of eqn 2
taking l.c.m as 2
1+2+3+4+....+k+(k+1) = [k(k+1)+2(k+1)]/2
since (k+1) is a common factor in the R.H.S we factorize
1+2+3+4+....+k+(k+1) = (k+1)(k+2)/2

This is same as eqn 2 above, hence the statement 1+2+3+4+....n+(n+1) = n(n+1)/2 is true for all natural numbers.
grin
feel free to post more exercises.

I give it to you fair and square. You inspire me!
Re: Nairaland Mathematics Clinic by Ehinafe: 10:21am On Jan 03, 2013
Richiez:

nice try bro, although you made some some mistakes especially at the point where you took log of both sides. e.g it ought to be log(x+y)= log5 and not logx + logy = log5. but i must admit, you did a very good job.

here's another approach;

x + y = 5.......(1)
x^x + y^y =31.......(2)

from eqn(1), x=5-y, hence we substitute this value for x in eqn(2).
(5-y)^(5-y) + y^y = 31.......(3)
now, we have reduced the problem to what value of y that must be inserted in eqn (3) to obtain 31.

a thorough look at eqns (1) & (2) shows that the values of x & y must be positive integers within the range 0<x<5 and 0<y<5
clearly, y=3
i.e (5-3)^(5-3) + 3^3
2^2 + 27
4+27=31
now that we have established that y=3, we shall substitute the value of y in eqn(1) to get x
recall that x+y=5
therefore; x+3=5 or x=5-3=2
hence, x=2 when y=3

Richiez, how good are you in solving Dynamic Programming mathematical algorithm? I need to know because I have one here that I am not sure you can get the answer right.
Re: Nairaland Mathematics Clinic by yorke1: 10:21am On Jan 03, 2013
Mathematics is my favorite subject anytime anyday. And i had good grade in courses that has to do with mathematics in the university. Drop any question my way let me destroy it.

3 Likes

Re: Nairaland Mathematics Clinic by solomon111(m): 10:22am On Jan 03, 2013
olasesi:

Naaaaa its.the same

x+y=5. Is the same as (x+y)=5

Try the same value for x and y in both equations.....
What do u get.....try 2 and 3
the answer obeyed the equation.
X+y=5
2+3=5.
X^x+y^y=31
2^2+3^3=31
(equation proved)
Re: Nairaland Mathematics Clinic by Philipschasis(m): 10:22am On Jan 03, 2013
Richiez, I really must commend your effort, you are good..

I've got this questions on Metric Spaces and I will really appreciate if you give a thorough breakdown.

1. If d1 and d2 are metrics of X, is it true that d1 + d2, d1 - d2, d1 * d2 are metrics of X ? I just need to grasp the basic concept.

2. We say that two metrics d and d' are equivalent on X if a convergent sequence in (X,d) is a convergent in (X, d') and vice versa.. Given a metric d of X, prove that there exist a metric d' equivalent to d and bounded by 1.

3. Suppose dn is a sequence of metric of X. Show that there exists a metric bounded by 1, such that the convergence sequence in (X,d) is convergent in each (X,dn)

This is under topology, I will appreciate if you can attempt or give a clue to these questions.
Re: Nairaland Mathematics Clinic by fuke(m): 10:25am On Jan 03, 2013
Calebsworld: @ Richiez,my question,is how can I become a mathematician,as in having distinctions in the subject.God bless u.

Work 10 sums a day
Re: Nairaland Mathematics Clinic by Immortal1(m): 10:25am On Jan 03, 2013
I LUV MATHEMATICS! Itz not just about numbers... It really helps u 2 think & be creative!

4 Likes

Re: Nairaland Mathematics Clinic by solomon111(m): 10:25am On Jan 03, 2013
olasesi:

It is very essential to understand the meaning of "=" (equal to" ) in mathematics......
If AB=CD,
Then AB+F=CD+F

Therefore if (x+y)=5
only log (x+y) must be equal to log5

Log is another operation on its own
yes you are correct.
My bad.
I tried solving it by loging the x and y individually,and it was wrong.
Log(x+y)=correct.

1 Like

Re: Nairaland Mathematics Clinic by Ehinafe: 10:27am On Jan 03, 2013
I need to optimize my earnings from the sale of some products which depends on combining sale of certain optimum number from the different market available, in such a manner to optimise my profit, Can Richiez help me out analytically before presenting the problem algorithm?
Re: Nairaland Mathematics Clinic by calculusx(m): 10:28am On Jan 03, 2013
I will forever be stick to this thread as i'v lost touch with my best subject which gave me my nickname 'Calculusx' till today. Mathematics is the BEST Subject...Yes the BEST SUBJECT among all other subjects.

1 Like

Re: Nairaland Mathematics Clinic by olasesi(m): 10:28am On Jan 03, 2013
x+y=5..........(eqn 1)
.......means that .....the summation of x and y is equal to 5......


Bracket in mathematics is used to group expressions......giving it the idea of a single number

E.g (ABC)D=19.......this means that the product of A,B and C gives a number in that bracket whose product with D then gives 19
even though the product can be made in any other I.e product is associative....that is exactly what the example means.....


(x+y)=5.....(eqn 2) means that the summation of x and y gives a number in that bracket which is equal to 5........

Therefore equation 1 is the same as equation 2
The bracket is not just written as the summation is between two numbers and a bracket in this case would appear redundant......

2 Likes

Re: Nairaland Mathematics Clinic by solomon111(m): 10:30am On Jan 03, 2013
Ehinafe: Richiez:

nice try bro, although you made some some mistakes especially at the point where you took log of both sides. e.g it ought to be log(x+y)= log5 and not logx + logy = log5. but i must admit, you did a very good job.

here's another approach;

x + y = 5.......(1)
x^x + y^y =31.......(2)

from eqn(1), x=5-y, hence we substitute this value for x in eqn(2).
(5-y)^(5-y) + y^y = 31.......(3)
now, we have reduced the problem to what value of y that must be inserted in eqn (3) to obtain 31.

a thorough look at eqns (1) & (2) shows that the values of x & y must be positive integers within the range 0<x<5 and 0<y<5
clearly, y=3
i.e (5-3)^(5-3) + 3^3
2^2 + 27
4+27=31
now that we have established that y=3, we shall substitute the value of y in eqn(1) to get x
recall that x+y=5
therefore; x+3=5 or x=5-3=2
hence, x=2 when y=3

Richiez, how good are you in solving Dynamic Programming mathematical algorithm? I need to know because I have one here that I am not sure you can get the answer right.
dynamic and programming mathematical algorithm are for those studying mathematics as a course on it own.
Though,it's very intriguing,and looks superior to the logarithmic method.
Re: Nairaland Mathematics Clinic by moneyhungry(m): 10:31am On Jan 03, 2013
Jesus !.!.! na maths abi na jazz be this? diz thread fit illiterate to run mad o! *logs out*
Re: Nairaland Mathematics Clinic by ultranet(m): 10:31am On Jan 03, 2013
Richiez:

yep, but don't be scared, any level of maths is accepted here
pls can u solve dis question: 3^x=9x...(interested in d working)
Re: Nairaland Mathematics Clinic by olasesi(m): 10:31am On Jan 03, 2013
solomon111: the answer obeyed the equation.
X+y=5
2+3=5.
X^x+y^y=31
2^2+3^3=31
(equation proved)

Naaaaaa. 6.2 was approximated to 6...,...
Why didn't u use 6.2....or must u approximate.....

2 and 3 are the answers but it was dubiously gotten
Re: Nairaland Mathematics Clinic by hammedkola(m): 10:32am On Jan 03, 2013
Thank God this thread is created..So, which project is better to write relating to computer science
Re: Nairaland Mathematics Clinic by kaysy(m): 10:33am On Jan 03, 2013
Seriously am loving this thread... what a great idea from OP
Re: Nairaland Mathematics Clinic by EzePromoe: 10:36am On Jan 03, 2013
I LOVE THIS THREAD AND I'LL LOVE THE MATHS GURU TO SOLVE THIS EQUATION FOR ME!

A boy, X sleeped with my girlfriend, Y and produced 2 kids (2XY), using the onyonyo meter I saw that the pikins is not my own shildren. If Y is 22 years old and her name is Gracie
i)find X?
ii)find X's father, X^2
iii)can X beat me, Z if we fight?


Do that equation quick before i go gaga angry

3 Likes

Re: Nairaland Mathematics Clinic by igbeke: 10:36am On Jan 03, 2013
solomon111: I dread statistics.
That is one area of mathematics,i have not mastered.
As far as am concerned,statisticians are the real mathematicians.
maths is more challenging than stats.
although dey r both fun if u hav interest 4 dem.
dey used 2 be my favourites in my schl days. 12yrs after grad, d fun lingers.
so feel free, ask questions.
Re: Nairaland Mathematics Clinic by Nobody: 10:37am On Jan 03, 2013
Una say na "Mathematics" thread meanwhile all of una dey speak "English"

Some dey solve Indices, others dey solve Simultaneous equations...very soon another person go come solve Quadratic equations...abi na SS1 students dey here?

Wey the Engineers dem make we solve some First Order Differential Equations...and apply am to Fluid transfer and Thermodynamics

Meanwhile wey my Gala and La Casera?

2 Likes

Re: Nairaland Mathematics Clinic by Nobody: 10:37am On Jan 03, 2013
Lol. All I have seen here is some very pithy attempts at mathematics, in fact bordering on simple arithmetic. Let's have some hard-core simulation and pursuit theory.
Re: Nairaland Mathematics Clinic by harrisconsult1(m): 10:39am On Jan 03, 2013
With a Well Defined example, Explain what you understand by Galois Theory of Homeomorphism?
Re: Nairaland Mathematics Clinic by solomon111(m): 10:40am On Jan 03, 2013
olasesi:

Naaaaaa. 6.2 was approximated to 6...,...
Why didn't u use 6.2....or must u approximate.....

2 and 3 are the answers but it was dubiously gotten
well,that is the beauty of mathematics.
You try and find a way to suit the equation.
6~=6.2.
Besides,even if 6.2 is used the difference in the answer gotten is negligible.
Re: Nairaland Mathematics Clinic by paranorman(m): 10:40am On Jan 03, 2013
solomon111: I dread statistics.
That is one area of mathematics,i have not mastered.
As far as am concerned,statisticians are the real mathematicians.
u don't have ta dread it,jst fall in love.. Its applications are vast,esp in d busines world.. I luv maths too.
Re: Nairaland Mathematics Clinic by Ehinafe: 10:40am On Jan 03, 2013
Maths guru, can I proceed stating my problem?
Re: Nairaland Mathematics Clinic by tayejay(m): 10:41am On Jan 03, 2013
Richiez:

nice try bro, although you made some some mistakes especially at the point where you took log of both sides. e.g it ought to be log(x+y)= log5 and not logx + logy = log5. but i must admit, you did a very good job.

here's another approach;

x + y = 5.......(1)
x^x + y^y =31.......(2)

from eqn(1), x=5-y, hence we substitute this value for x in eqn(2).
(5-y)^(5-y) + y^y = 31.......(3)
now, we have reduced the problem to what value of y that must be inserted in eqn (3) to obtain 31.

a thorough look at eqns (1) & (2) shows that the values of x & y must be positive integers within the range 0<x<5 and 0<y<5
clearly, y=3
i.e (5-3)^(5-3) + 3^3
2^2 + 27
4+27=31
now that we have established that y=3, we shall substitute the value of y in eqn(1) to get x
recall that x+y=5
therefore; x+3=5 or x=5-3=2
hence, x=2 when y=3
[color=#990000][/color]

This solution is more appropriate. Log(x + y) nt = logx + logy, as earlier observed.
The first solution gave same answers with later but applying d approach in another question can b fatal

1 Like

Re: Nairaland Mathematics Clinic by solomon111(m): 10:42am On Jan 03, 2013
PortHarcourtBoy: Una say na "Mathematics" thread meanwhile all of una dey speak "English"

Some dey solve Indices, others dey solve Simultaneous equations...very soon another person go come solve Quadratic equations...abi na SS1 students dey here?

Wey the Engineers dem make we solve some First Order Differential Equations...and apply am to Fluid transfer and Thermodynamics

Meanwhile wey my Gala and La Casera?
we dey here o.
But it looks like this thread is for pure mathematians and statisticians.
Re: Nairaland Mathematics Clinic by Aafulenu(f): 10:43am On Jan 03, 2013
Eze Promoe: I LOVE THIS THREAD AND I'LL LOVE THE MATHS GURU TO SOLVE THIS EQUATION FOR ME!

A boy, X sleeped with my girlfriend, Y and produced 2 kids (2XY), using the onyonyo meter I saw that the pikins is not my own shildren. If Y is 22 years old and her name is Gracie
i)find X?
ii)find X's father, X^2
iii)can X beat me, Z if we fight?


Do that equation quick before i go gaga angry

lol, op u r really funny.
Re: Nairaland Mathematics Clinic by CohenJane: 10:44am On Jan 03, 2013
I hoe this tread can be sustained on the front page for long so that we can continue to help those who may have problem with their maths skill. You know, majority of the people are literate and not numerate.
Re: Nairaland Mathematics Clinic by Ehinafe: 10:45am On Jan 03, 2013
solomon111: dynamic and programming mathematical algorithm are for those studying mathematics as a course on it own.
Though,it's very intriguing,and looks superior to the logarithmic method.

Solomon111, you are quite correct, but you should realize that dynamic programming and Non-linear programme are better-suited to real-life situation than all other mathematical models
Re: Nairaland Mathematics Clinic by tellwisdom: 10:49am On Jan 03, 2013
Op, this is for u: 10 fishes were divided btwn four people. A gurl came in and requested for a share of hers. Now, 3 raise to power of the balance of the fishes, is what??

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