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#1 Dark Discussions at Cafe Infinity » How difficult is calculus by spivak supposed to be? » 2015-07-04 22:35:25

Replies: 1

When I was reading this book I thought this isn't so hard. Most of this seems straight forward since I'm familiar with maths. That was until I tried to do the problems. I have never done proofs before except for a few in serge lang's algebra book. It took me a very long time just to do the first 2 proofs in chapter one. I don't even know if they're right. In the 3rd chapter I don't even know how to approach the proofs. It wil take me over a year to finish this book at this rate because I'll have other responsibilities. Is it supposed to be this hard and do you know of any resources that give you practice with proof?

#3 Help Me ! » basic calculus question » 2015-04-29 09:18:00

Replies: 2

The acceleration of a body is given by the formula a = -(v^3/70) find the general equation for velocity. If the velocity was 7m/s when x = 0, dinf the position of the body when its velocity was 5m/s

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#4 Re: Help Me ! » Write partial fraction » 2015-03-21 08:12:51

Thanks all done. Actually the original method I was using works but is just long and tedious. Thanks for the help and information.

#5 Help Me ! » Write partial fraction » 2015-03-20 08:13:31

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.

#6 Re: Help Me ! » Basic rearranging formula » 2015-03-06 07:44:35

but zetafunc there are 3 unkown variables in this equation? Usually when you use the quadractic formula they only have an x unknown.

#7 Help Me ! » Basic rearranging formula » 2015-03-06 07:28:45

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?
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#8 Re: Help Me ! » basic differentiation » 2015-02-26 09:15:01

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

#9 Help Me ! » basic differentiation » 2015-02-21 01:46:46

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.

#10 Dark Discussions at Cafe Infinity » What distinguishes a rule from a theorem? » 2015-02-16 05:14:44

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?

#11 Re: Help Me ! » Complex number » 2015-02-15 09:11:30

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

#12 Help Me ! » Complex number » 2015-02-15 08:39:01

Replies: 3

= √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?

#13 Dark Discussions at Cafe Infinity » How do you develop a conceptual understanding of mathematics? » 2015-01-15 13:33:02

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?

#14 Re: Help Me ! » Logarithm Problem » 2014-12-19 07:09:41

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

Does this help you?

#15 Help Me ! » How to write the patterns mathematically? » 2014-12-19 05:46:31

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?

#16 Re: Help Me ! » Logarithm Problem » 2014-12-19 05:15:39

Take a picture of the question.

#17 Re: Dark Discussions at Cafe Infinity » Do you really want a solution? » 2014-12-17 09:21:44

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.

#18 Dark Discussions at Cafe Infinity » Do you really want a solution? » 2014-12-17 05:54:52

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?

#19 Euler Avenue » Where does PEDMAS/BIDMAS come from? » 2014-11-15 11:30:07

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?

#20 Maths Teaching Resources » Worksheets and stuff » 2014-11-08 09:53:41

Replies: 3

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?

#21 Dark Discussions at Cafe Infinity » When is your mathematical prime? » 2014-11-06 11:52:36

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+?

#22 Re: Introductions » Why I'm here » 2014-11-06 09:27:44

(Problem) At the end of the first chapter and beyond, the book is slightly over my head. I only cover a few pages a day at my current pace because I have to really think about the material and I have other responsibilities. Sometimes I need to look up other references to understand certain things. At my current pace it will take me 10-12 months to finish this book. Is the payoff from reading and understanding this book worth the effort or should I read other books?

#23 Re: Introductions » Why I'm here » 2014-11-06 04:31:25

lol yep I'm not good enough. Well at least Spivak is going to be too much of an uphill battle for me to keep progressing for now. I have not fully mastered elementary algebra since occasionally I run into a basic problem where I get stuck and routinely get bewildered on brilliant.orgs more difficult ones. Does anyone know any rigorous algebra books? Is gelfand's algebra good enough for this? I haven't read it. I would like the ones that use an axiomatic approach. You know the ones that give the definitions, theorems and then prove them. Then they have the corrolaries and all that good stuff. Also I think it's best that I go through an introductory proof book. Do you know any great introductory ones?

#24 Re: Introductions » Why I'm here » 2014-10-16 10:02:43

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....

That is the right book (by the way, it is available online and legally at 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

#25 Re: Introductions » Why I'm here » 2014-10-14 07:29:54

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....

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