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**PatternMan**- Replies: 4

How to write this as a partial fraction. I'm not sure how I would do this with more than two unknowns. Since I need to find a third numerator. I can't split it into three fractions with 3 variables as numerators and isolate them.

**PatternMan**- Replies: 4

When you rearrange for a it doesn't matter if there are two t's on the other side. However if I wanted to isolate t I would have to get them both on one side and factor right? In this case is there any way to isolate t?

Yes I didn't realize they were the same. I'm barely proficient with surds and indices.

**PatternMan**- Replies: 2

y=kx then dy/dx = k

if y= x^4 + 1/x -6x

then dy/dx = d/dx(x^4) + d/dx(x^-1) etc

so differentiation sqrt(x) + 1/sqrt(x) w.r.t.x

d/dx(sqrt(x)) = 1/2sqrt(x), d/x(1/sqrt(x)) = ? I get -1/2x^-3/2 but the book says -1/(2xsqrt(x))

I really should learn to use Latex.

**PatternMan**- Replies: 0

Rules like these are deduced from axioms of algebra. (-a)(-b) = ab People write proofs for them. However little facts like these are just called rules. People don't even mention them in mathematical notation when teaching. They just say two negatives next to each other make a plus and two positives make a plus. Why are these statements just called rules whereas something like the the binomial theorem is called a theorem?

Thanks. I was just confused because they simplified everything else.

**PatternMan**- Replies: 3

√-20

= √20 i

= √4 x √5 i

= 2 x √5 i

= 2√5i

The textbook said the answer to this is √20i. did I misunderstand something?

**PatternMan**- Replies: 12

The other day I was doing polynomial division and thought "I have no idea why this works." There are only a few parts of math that I just do without knowing how it works. I realized that lots of people probably feel this way about the other topics. FOIL, BIDMAS, plug and chug the formula are not good enough if I want to write a basic proof or solve a problem with no immediately obvious solution.

The other day I taught a girl that the equal sign means the left and right side are equivalent like scales. It doesn't matter what you have on each side. The total is the same. She told me she didn't know this and that she thought it was just where the answer went. I had to explain to a guy that a minus number squared is the same as its positive squared though I didn't understand why. I think it's important to know these things.

So is there a method to learn so you can understand the subject conceptually?

I'm a noob too so anyone correct me if I'm wrong.

Does this help you?

**PatternMan**- Replies: 1

I have been looking at sequences an series at the moment and their patterns don't always match mine. I'll describe the pattern in English and not know how to describe it mathematically. They will sometimes write a mathematical expression for the sequence and I wont know if it matches my word description. For example you could use

(x+1)^2 or x^2 +2x +1 as a formula for something. It's obvious to us that they will give the same result even though they look different. Also some methods may seem the same until you input values like 0 or -1/2 into the function so my word description may not work. Anyway does anyone know any resources where I can learn to write word descriptions of patterns in maths notation?

Take a picture of the question.

bobbym wrote:

Hi PatternMan;

It is hard to give specific advice without a specific example but you should always work in a manner that you have at least an approximately correct answer before even starting a problem. In other words before you bring the heavy machinery in you should know where, what type and how much you need.

And after all is done, check, check and check again.

I suppose what I'm asking is how do you develop the intuition of knowing whether you're answer is correct or at least approximately correct? With basic arithmetic I know that the answer will be within the 100s of 1000s unit. However when doing multi step problems at a higher level it becomes more difficult. The algebra ignores the specific values. Or for example when Even when physics where you have a feeling for the units, it is hard to conceptualize the scale of atomic particles and know that the answer will be 4*10^-16 or whatever instead of 4*10^-18

Basically I feel like I have to have fully mastered every piece of a topic knowing all the relationships to be confident I'm on the right track. So there is some way to cross reference what I have done to other methods of validation that I have. I am thinking that if I wanted to apply math or physics to the real world then I wouldn't be given a solution. At best my method would or wouldn't work in reality so I would know it's right, or wrong. But there has to be some way to reason with a high probability that you're right.

**PatternMan**- Replies: 4

When learning maths I'm used to looking at the rules, one or so examples of a method then going through some practice exercises and then checking the answer. With some problems With maths and physics some books do not give solutions. This may be because of space or to prevent cheating or something. However I noticed it forces you to check yourself and stick with a problem. I'm wondering are there is any way you could understand what you are doing so well that you would be pretty sure when your answer is right or wrong without looking at a solution?

**PatternMan**- Replies: 1

*what is it's origin?

*We are taught this in school but do we actually need to use it?

*Are there better ways to do algebra rather than remembering the acronym?

**PatternMan**- Replies: 1

Hi I'm going to try and teach a couple of people algebra. I was wondering if anyone knew any free programs (online or downloadable) that I could use to make worksheets. I just need something to help me put in explanations and examples. Then I need to put in some exercises and a few theoretical problems at the end. Anyway it's just basic stuff.

At the moment I have only daum equation editor and microsoft word to type in. Does anyone have any other suggestions?

**PatternMan**- Replies: 2

Someone told me that pretty much all the great mathematicians made their contributions before 30. The exception being Grigori Perelman. Do you agree or disagree with this and to what extent? Can you name any mathematicians that made decent contributions 30+?

ShivamS wrote:

PatternMan wrote:Hello guys it's been a while. I have been very busy crash coursing the basics of the sciences. I'm learning physics now(classical mechanics). Kinematics, dynamics, newtons laws etc... It's algebra based not calculus based. I'm looking to transition to calculus very soon. I'm just going over logarithms and trigonometry stuff.

Is this the book right book? I will try to devour it in 2 weeks next month. I don't care if I can't do the problems as long as I understand the definitions, rules, applications etc....

http://www.ebay.co.uk/itm/Calculus-by-Michael-Spivak-third-Edition-/121459248987?pt=LH_DefaultDomain_3&hash=item1c47890f5b

That is the right book (by the way, it is available online and legally at https://archive.org/details/Calculus_643). Although, I'm pretty surprised you're covered precalculus/algebra already. However, even if you have a few gaps, you can fill them up later.

As for the problems, they are basically a must if you want to gain a good level of understanding. They're half the reason why Spivak is such a good book. Also, even if you put in about 8 hours a day, Spivak in 2 weeks is pretty ambitious.

To be fair I already knew most of elementary algebra. I just didn't understand it and needed to fill in lots of gaps. lol I just scanned through the online book. It will probably take me till next summer to go through this properly. But it doesn't seem that intimidating after going through Serge Lang's books. It seems to follow from there quite easily. I just feel maybe I should go through trigonometry and proofs in more detail first. Oh well good luck to me. xD

Hello guys it's been a while. I have been very busy crash coursing the basics of the sciences. I'm learning physics now(classical mechanics). Kinematics, dynamics, newtons laws etc... It's algebra based not calculus based. I'm looking to transition to calculus very soon. I'm just going over logarithms and trigonometry stuff.

Is this the book right book? I will try to devour it in 2 weeks next month. I don't care if I can't do the problems as long as I understand the definitions, rules, applications etc....

http://www.ebay.co.uk/itm/Calculus-by-Michael-Spivak-third-Edition-/121459248987?pt=LH_DefaultDomain_3&hash=item1c47890f5b

anonimnystefy wrote:

91 does seem more appropriate.

Yep it's 91. My bad.

bobbym wrote:

Horrible definitions of math books.

For numbers it is always the positive value.

When you switch the subtraction of two numbers you change the sign.

a - b = - ( b - a )

I hope I understand it. I did skim over this stuff in one of the books Shivam suggested.

a + (-a) = 0

a = -(-a)

-b = -b,

a - b = -b - (- a) = -(b - a)

anonimnystefy wrote:

Hi PatternMan

Do you remember how the absolute value of a number is defined?

I just wrote

|9-5-3| = |5-9-3| = 6 I don't know why that works but it works for those values anyway. Also I just learnt that the absolute value was the displacement from the origin or 0.