Nice work biolabee, it's been a while; how have you been?

doubleDx: Nice work biolabee, it's been a while; how have you been?

Oga mii ive been around o.. one, the thing was becoming too complex for me you know say na night school i go and secondly it seemed some people were just bringing up variants of the same problem with no attempt to even think through and learn ..

Goodevening richiez and all other respected generals here, please i have a question, how can you calculate for square root without the use of calculator?

biolabee:

Oga mii ive been around o.. one, the thing was becoming too complex for me you know say na night school i go and secondly it seemed some people were just bringing up variants of the same problem with no attempt to even think through and learn ..

Right on point bruv! LMAO @ the bolded part

johnpaul1101: Goodevening richiez and all other respected generals here, please i have a question, how can you calculate for square root without the use of calculator?

^ Binomial expansion: If √(z) = √(a(x + 1/a) = √(a).[(x + 1/a)]^(1/2). Expanding [(x + 1/a)]^(1/2) using binomial theorem and multiplying the result by √(a) gives you the answer. It's quite easy if 'z' can be expressed in terms of 'a and x' such that a = perfect square!


Eg===>>

√10 can be rewritten as =>

= √[9(1 + 1/9)]
= 3√(1 + 1/9)
= 3 (1 + 1/9)^(1/2)
Expanding the bolded part yields =>
= 3[1 + (1/2)(1/9) + (1/2)(-1/2)(1/9)²/2! + (1/2)(-1/2)(-3/2)(1/9)³/3! + ....]
Simplifying further yields =>
= 3[ 1.0541 approx]
= 3.162 approx

Wooow! I love Mathematicians!!!

Becacia_Barbie: Wooow! I love Mathematicians!!!

welcome...

biolabee:

welcome...

thank you...

Wao! Been going thru this thread and I'm really impressed. Unfortunately, maths was my nightmare in secondary school. Had to leave science class in my SS 3 just cos of maths, even though I was doing well in Bio, Phy and Chem and every other subject. Anytime the maths teacher came in and started writing the numbers and symbols, I would begin to feel dizzy. After my Uni, I tried to go for math lessons and wrote WAEC GCE, but I still got a pass, not credit. I cried when I saw the result. Felt so ashamed of myself. Most annoying part is I got distinctions and credits in all the other 7 subjects that I didn't even study for.
Anyway, kudos to you guys.

@tearie
its ok, a lot of the people that struggle with maths are that way because of introduction methods
It then seems to be a chore instead of fun

no wahala
Welcome to the thread.....

If you have any need for help in any subject, im sure you can get help

@Generals Biolabee, doubledx and ositadama, you've all done a great job keeping the thread rolling.
@Admirers and new friends in the thread, your comments has fueled our courage. we are here to uplift eachother so feel free and let's relate!

Tuale to you Sir Richiez

I am greatly impressed with what you have done here... I am interested in this thread... I want to get a job as a maths/f.maths teacher as soon as I am done with NYSC in the Ministry..... I will try to answer a few questions here myself... Thanks
Chibuzor...

@chibuzor u'r highly welcomed, ur contributions wud be of great help.

Richiez: @chibuzor u'r highly welcomed, ur contributions wud be of great help.

I had huge problems with Real Analysis (Abstract Algebra) While in School, I had to do a lot of cramming to pass the exams. I studied later to catch up tho... I know a lot of people will have the same problem.

@chibuzor, wise man! well i'v answered some questions on pigeonhole principle. buh i think, groups, rings, field e.t.c are more used terms when we talk of abstract algebra.pls can u explain wot these terms are?

Hi guys,

I have some difficulty in critiquing a statistical report (ANOVA and Linear regression), can anyone be of help pls.
my email address is: mailay2day@yahoo.com

@Richiez... Yeah I ll do some explanation in the evening... I am at work at the moment...

echibuzor: @Richiez... Yeah I ll do some explanation in the evening... I am at work at the moment...

okay bro! wow here comes anoda general

Richiez: @chibuzor, wise man! well i'v answered some questions on pigeonhole principle. buh i think, groups, rings, field e.t.c are more used terms when we talk of abstract algebra.pls can u explain wot these terms are?

A group is a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms (Axioms are statements/facts that are undisputable (more or less)...). The Axioms are; (1) Closure, (2) Associativity (3) Identity, (4) Invertibility. Popular examples of Group is the INTEGER, NATURAL NUMBERS....
The above definition is from Google (Edited by me)

Illustration...
For a Group of Integers..
Two elements (3 and 4) operation +
3 + 4 = 7 and 7 is also a member of the group Integer (This fact is called Closure).

(3 + 4) + 5 = 3 + (4 + 5) = 12 (Associativity)

Identity element is that which when combined with another element in the group with an operation returns the latter element e.g 3 + 0 = 3 (0 is the identity element of addition). 3 * 1 = 3 (1 is the identity element for multiplication)

The illustration for Invetibility is simply too long to put here and i dont want to copy and paste.. please google it and ask question about it... Others are coming right up...

A Ring is an algebraic system consisting of a set, an identity element (see my previous post), two operations and the inverse of the first operation...
Example... ring R = {S, 01, 02, 1} where S is the set of Real numbers (You all know what Real Numbers are right?) , 01 is the opeartion of addition, the inverse of which is subtraction, 02 is the operation of multiplication, 1 is the identity element which for for addition (which is the first operation) is zero (0).

Still too abstract right? Lets get practical...

A ring is mostly called Commutative ring because Commutativity (Google) must be met before a Set of elements can be called a RING..

Illustration...

Let R (Real Numbers) be a set on which two binary operations (A binary operation is an opeation that needs exactly two inputs before it can return an output) are defined, Operations are Addition +, and Multiplication *.

Then R is a Commutative Ring if the following axioms hold...
(1) Closure - If a,b R, (Please ask quetion if you dont undastand notations) then the sum a+b and the product a*b are uniquely defined (returns an output) and belong to the set R (Closure)

(2) Associative Laws (Associativity) - For all a,b,c R, a+(b+c) = (a+b)+c and a*(b*c) = (a*b)*c. (See previous post)

(3) Commutativity - For all a,b R, a+b = b+a and a*b = b*a

(4) Distributivity - For all a,b,c R, a*(b+c) = a*b + a*c and (a+b)*c = a*c + b*c.

(5) Identity - The set R contains and an additive identity element, denoted by 0 (identity for addition which is the first operation in our example) such that for all a R, a+0 = a and 0+a = a.

(6) Inverse - For each a R, the equations a+x = 0 and x+a = 0 have a solution x R, (x R, is read as x is a member of the set R) called the additive ( our first operation) inverse of a and is denoted as -a.

You can read more on this and ask your questions but to explain in respect in its simplest form; a Ring is Group with two operations, identity of the first operation, inverse of the first operation, and it obeys the axioms of a group plus its commutative and distributive.. Thats all on Rings for now.... Next up is Fields....

A field is a ring with inverses and identity for the two operations... (Thats explanatory enuf right?)

Illustrations.....

A Field F = {S,01,02,11,12} where S is the set, 01 is the first operation (lets say addition), the inverse of which is subtraction, 02 is the second operation (lets say Multiplication), the inverse of which is division, 11 is the identity of the first operation (in this case (0) for addition) and 12 is the identity of the second operation (in this case (1) for multiplication)

Bear in mind that it must satisfy all the conditions which are required for a Ring (See my previous post)...
I think that wraps it for now.........



@Ayowumie... Its not possible to discuss/teach ANOVA from the scratch over the internet....... You read up and ask questions...
Thank you...
Chibuzor

@chibuzor i'm extremely impressed. 10ks

Richiez: @chibuzor i'm extremely impressed. 10ks

You are welcome chief... Its my pleasure to be of service....

If anyone has questions on Modelling and Simulation, Operations Research, Queue Theory, Markov Chain... They should post them. These are some of the areas of mathematics that cuts across several Fields... And of course Calculus.. We all can learn a thing or too.. No man is an island of knowledge.....

Chibuzor...

I have a trick Question coming up... Its on Modeling...

hmmm, this i getting more and more interesting!

First let someone derive a comprehensive Malthusian Growth model and then we can begin from there...

I havent tried solving this question, saw it on the internet. But, hey! lets see what you got...


The population of a country is 6 million in 2010 and growing at a rate of 1.4% each year. If the rate of population growth remains constant, the population will reach 24 million in...


Its an objective question but I did not include in my CTRL C.....

Chibuzor

And here comes another one....
This actually the trick Question...


(a) The population of the world was 5.28 billion in 1990 and 6.07 in 2000. Find an exponential model for these data and use the model to predict the world pop. in the year 2020?

According to the model in part (a), when will the world pop. exceed to 10 billion?

Using the data in part (a) to find a logistic model for the pop. Assume a carrying capacity of 100 billion. Then use the model to predict the pop. in 2020.

According to the logistic model, when will the world pop. exceed 10 billion?

I am having a go at the first question...
Malthusian Growth model also known as the Exponential Model...

Change in Population is directly proportional to Change in Time..

dP @ dt
dP = k dt
§dP = k§dt
Ln P = kt + c
P = e^[kt + c)
P = e^ (kt) * e^c [let e^c =A)
P = Ae^kt....... [i]
{at t = 0, P = P© [ read P© as P not [peanut]]
P© = Ae^k0
P© = A...
P<t> = P© e^kt........

For the calculation, I got 2109.something...