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Thread: Help learning Math.

  1. #1 Help learning Math. 
    Forum Freshman Andrei's Avatar
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    Hello everybody, I am new here and to be honest I'm quite new in the science field. Up until now, I've been more active in the human field although I always had an inclination for science, especially for biology. However I always feared Math because I never quite understood it and as I saw it's a very important discipline in science.

    I was woundering if someone has any tips or stories about how they learned Math. I would really apreciate it because I really want to learn more.


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    Hi Andrei

    In my opinion, mathematics is the forefather of all sciences. It isn't truly considered to be like the other sciences (physics, biology, anthropological, etc.) but it is definitely a science. It is the study of the most basic abstract things, numbers. And equally important: their interrelationships (which you will soon see in Algebra).

    I am a mathematics-oriented person... though I have no degree nor am I an expert, I sincerely love it. I like to discover new insights and since mathematics is my *thing*, my mind is constantly on it.

    Here are the fundamental things you should get into: First you should master basic arithmetic. Familiarize yourself with double-digit addition, subtraction, multiplication, and division if you have not learned such already. Also learn basic exponents and square roots. And learn about number systems/families (integers, rationals, naturals, reals, etc.) Having knowledge of these different kinds of numbers will help you in higher arithmetic and algebra.

    This is just my opinion of how you should learn math. See what other forum members suggest and good luck.

    (P.S. Edit: If you already know the above, then tailor what you will learn to whatever specific science you are studying. E.g. If you are learning physics, then there's no doubt that you will have to know trigonometry and calculus and other things. If you are learing biology, algebra will surely help, like working with chemistrial equations in metabolic pathways. So the rest, for convinience, should relate to your area of study)


    Last edited by brody; March 9th, 2012 at 04:52 PM.
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    For me, I really didn't get into math until I started to learn proofs. The first time we did a legit construction of the real numbers I was hooked. I personally recommend starting with real analysis and a construction of the real numbers but I'm not really sure what stage of your education you are in, and I suppose what you intend to do with your math education. I imagine there are perfectly competent engineers who don't know how to do a proof, but for me personally, I never feel comfortable with anything unless I have proven/derived it myself.
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    If you're keen on biology, you have no option but to get maths skills adequate to master statistics.

    I strongly agree with getting the arithmetic basics straight if you're not already there. If you're a novice with algebra, you must be sure to get manipulating fractions down really well. Once you can multiply and divide fractions - and recognise the numerical reality of the process and the results - you're in a much better place to get to grips with algebra.

    And the most important 'basic' number skill. Get your head around powers and orders of magnitude. I see far too many students coming for tuition at first year undergraduate level who think they've done well in passing yr 11 or 12 maths. To me, all they seem to have done was to learn how to do certain procedures without much recognition of what the numbers mean.
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    I am an electrical engineering major. I have almost finished all of my mathematics courses. I still consider myself a novice at mathematics.

    I didn't really have much mathematical ability besides high school algebra up to five years ago. I wanted to go back to school and learn electrical engineering technology, but I was afraid of not having the mathematical ability. So I went to a college textbook store and purchased one of their older copies that they couldn't resell of a popular precalculus and trigonometry book. I sat down and in my spare time worked my way through it. When I finally enrolled, I had the confidence that I needed that I would succeed. I aced Trig and wandered my way through calculus, not really 'getting it' at first, but able to succeed at it untl it clicked. I've fought my way through linear algebra, ordinary differential equations, discrete math. multivariable calculus and now I'm finishing up probability and stochastics (which I kind of 'don't get again').

    I feel great for knowing what I do, but on the other hand, I feel myself on the cusp of another world that needs exploring. I am going to continue my studies of mathematics even when I'm not in school and hopefully one day, it will be a more familiar place.
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    I want to thanks everybody for the kind answers, I really apreciate it.
    Brody thanks for giving me a path to walk on, I'm familiar with addition, substraction, multiplication and division as well as with exponents, however the square roots are a total mistery to me.
    Why I find Mathematics so hard is that I cannot link it to anything material, like I do with biology or physics.
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    Quote Originally Posted by Andrei View Post
    I want to thanks everybody for the kind answers, I really apreciate it. Brody thanks for giving me a path to walk on
    No problem. I'm glad to help. And thank you as I often feel most of my contributions to this forum aren't very helpful at all :P

    I'm familiar with addition, subtraction, multiplication and division as well as with exponents, however the square roots are a total mistery to me.
    Don't worry. I used to have trouble grasping the system behind all that. All these are operations: addition, subtraction, multiplication, division, exponents, and roots. They're all part of the same basic process. If you're confused about operations, feel free to ask about them here or in a new thread.

    Why I find Mathematics so hard is that I cannot link it to anything material, like I do with biology or physics.
    In science, we constantly use models to help us understand how things work. Mathematics itself is pretty much a model to help describe how the universe works. If you throw a ball up in the air at an angle, it will make a parabola. If you have a culture of one bacterium that reproduces via binary fission, you can roughly calculate the population growth rate with geometric progression. If it doubles every hour, you'll see 1 to start with, 2 within an hour, 4 the next, 8, 16, etc...

    And even though math is very applicable to several sciences, you still have to respect its abstractness. It sort of works within its own little perfect world of numbers. So everyone has to learn it plain and simply as math, regardless of real-world application.

    If you ever feel embarrased, never be shy to ask. It's math, everyone gets confused with it at some point. I've had math instructors having trouble remembering the simplest concepts. Again, good luck.
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    Quote Originally Posted by Andrei View Post
    Brody thanks for giving me a path to walk on, I'm familiar with addition, substraction, multiplication and division as well as with exponents, however the square roots are a total mistery to me.
    You could probably grasp logarithms and trigonometry then, maybe inverse functions as well.

    Quote Originally Posted by Andrei View Post
    Why I find Mathematics so hard is that I cannot link it to anything material, like I do with biology or physics.
    I can't speak for biology but a lot of basic physics is built on calculus and geometry.
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    And remember, for those having problems with powers and square roots and the like ......

    The simpler numbers and powers relate directly to geometric concepts.
    The number one is a point, any number at all of any size or sign to the power of 0 always equals 1.
    A number to the power of 1 represents a line (in any direction in any space).
    A number to the power of 2, a square, represents an area covered.
    A number to the power of 3 represents a volume or a space.

    So a square root of a number is just the length of the side of a square with that number as its area. The numbers might be messy, but that's the picture you want.

    One thing a lot of people don't do when dealing with maths is draw a picture. You can draw either the problem as presented or the solution you're looking for. Even if you make a mess of it, it's worth a shot. Especially if you're already having trouble relating numbers to physical reality.

    Once you get these concepts straight for things that do link to ordinary physical reality, you'll be able to move on to more abstract concepts.
    "Courage is what it takes to stand up and speak; courage is also what it takes to sit down and listen." Winston Churchill
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    Heres some tips from some one, who cant understand advanced math. But I wish I could understand it. I see math as the connector of all sciences.


    My simple advice, I would make a list of every math, from addition to calculus (and beyond).


    I would then read about them for about 15 minutes each. Learn how they came into existance, and what they are used for. And take a look how the numbers are set up for each math. Its what comes to mind, and I dont see how it could hurt. Maybe you would find the math you are most intersted in, or something else.

    Chad.
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    Hello Andrei,In my opinion there's nothing to fear about mathematics,the thing it requires the most is practice some people tries to memorize it but maths can't be done without practice.
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    Quote Originally Posted by suresh123 View Post
    Hello Andrei,In my opinion there's nothing to fear about mathematics,the thing it requires the most is practice some people tries to memorize it but maths can't be done without practice.
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    Hello Suresh. My problem with mathematics is that during school I changed many classes. I'm in the 11th grade in high school, I still have 2 more years (this one included). As I said I changed many classes in these 11 years, I did my 7th grade in Italy where the mathematic (and everything else) were much lower and when I returned in Romania I went directly in the 8th grade thus totaly skipping some lessons including the squares roots.
    To make things even better, I don't have Math, Biology, Chemistry or Physics in school, my profile being Philology (focusing more on foreign languages).
    I would change my profile and go to Natural Sciences but I'm afraid that I won't be able to recover so much information in 2 years and then I would have Math in my final exam in high school.
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    Quote Originally Posted by Andrei View Post
    My problem with mathematics is that during school I changed many classes. I'm in the 11th grade in high school, I still have 2 more years (this one included). As I said I changed many classes in these 11 years, I did my 7th grade in Italy where the mathematic (and everything else) were much lower and when I returned in Romania I went directly in the 8th grade thus totaly skipping some lessons including the squares roots.
    To make things even better, I don't have Math, Biology, Chemistry or Physics in school, my profile being Philology (focusing more on foreign languages).
    I would change my profile and go to Natural Sciences but I'm afraid that I won't be able to recover so much information in 2 years and then I would have Math in my final exam in high school.
    Hey again, Andrei. That's very unfortunate. I've moved across-states before, and transitioning to an entirely different curriculum is not easy. But don't worry, this is a science forum! Feel free to ask any questions concerning math (or any other subject) that you're having trouble with. You can also Google any cloudy term you come across and get extensive easy-to-understand information on anything (just don't use Wikipedia or college websites, since their generally not in layman's terms).

    Here's a more specific path for you to learn... Number kinds/families, then operations, then working in algebra with operations. Are you familiar with number families?

    • Natural numbers: Just your ordinary counting numbers (0, 1, 2, 3, 4 ... ) Negative numbers, fractions, and numbers with decimals are not natural ( are not natural numbers)



    • Integers: Includes all the natural numbers and their negatives ( ... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ... ) But not anything that you write as a fraction or with a decimal point ( like , 1.7, and are not integers)



    • Rational: Here, you can have integers and fractions/decimals. If it is a decimal, then it must have a repeating part or ends (1.333333... repeats, -9.142142142142142... repeats, and 7.9148139299325 eventually stops). If it's a fraction, convert it to a decimal and see if it passes the same way ( is rational because its decimal form repeats, is rational because its decimal form stops )

    Remember that integers are part of the rational category. Every integer is a rational number, but that doesn't mean every rational number is an integer. The same goes between natural numbers and integers. Diagrams like these usually help visualize what's going on.



    See how rational numbers "include" integers, and integers "include" natural numbers? And notice how in the rational numbers bubble there's space outside of the integer's bubble? That shows that not all rational numbers are integers, but all integers are still rational.
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    What about square roots are you having trouble with? If a number times itself is 9, then that number is a square root of 9!
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    Quote Originally Posted by brody View Post
    If the white background extended out infinitely, that would be the real numbers.
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    Quote Originally Posted by TheObserver View Post
    What about square roots are you having trouble with? If a number times itself is 9, then that number is a square root of 9!
    The fact is that I don't understand anything of them because I totally skipped that lesson and never came back to it. However I found a website where mathematics is explained quite well.
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    Quote Originally Posted by brody View Post
    Quote Originally Posted by Andrei View Post
    My problem with mathematics is that during school I changed many classes. I'm in the 11th grade in high school, I still have 2 more years (this one included). As I said I changed many classes in these 11 years, I did my 7th grade in Italy where the mathematic (and everything else) were much lower and when I returned in Romania I went directly in the 8th grade thus totaly skipping some lessons including the squares roots.
    To make things even better, I don't have Math, Biology, Chemistry or Physics in school, my profile being Philology (focusing more on foreign languages).
    I would change my profile and go to Natural Sciences but I'm afraid that I won't be able to recover so much information in 2 years and then I would have Math in my final exam in high school.
    Hey again, Andrei. That's very unfortunate. I've moved across-states before, and transitioning to an entirely different curriculum is not easy. But don't worry, this is a science forum! Feel free to ask any questions concerning math (or any other subject) that you're having trouble with. You can also Google any cloudy term you come across and get extensive easy-to-understand information on anything (just don't use Wikipedia or college websites, since their generally not in layman's terms).

    Here's a more specific path for you to learn... Number kinds/families, then operations, then working in algebra with operations. Are you familiar with number families?

    • Natural numbers: Just your ordinary counting numbers (0, 1, 2, 3, 4 ... ) Negative numbers, fractions, and numbers with decimals are not natural ( are not natural numbers)



    • Integers: Includes all the natural numbers and their negatives ( ... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ... ) But not anything that you write as a fraction or with a decimal point ( like , 1.7, and are not integers)



    • Rational: Here, you can have integers and fractions/decimals. If it is a decimal, then it must have a repeating part or ends (1.333333... repeats, -9.142142142142142... repeats, and 7.9148139299325 eventually stops). If it's a fraction, convert it to a decimal and see if it passes the same way ( is rational because its decimal form repeats, is rational because its decimal form stops )

    Remember that integers are part of the rational category. Every integer is a rational number, but that doesn't mean every rational number is an integer. The same goes between natural numbers and integers. Diagrams like these usually help visualize what's going on.



    See how rational numbers "include" integers, and integers "include" natural numbers? And notice how in the rational numbers bubble there's space outside of the integer's bubble? That shows that not all rational numbers are integers, but all integers are still rational.
    The way you put it makes it really easy to understand. I don't have problems with the number families although I had some uncertainties with rational numbers. Thanks
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    Quote Originally Posted by TheObserver View Post
    Quote Originally Posted by brody View Post
    If the white background extended out infinitely, that would be the real numbers.
    For the sake of just introducing the concept, I left that out, but true. Thanks.
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    Quote Originally Posted by Andrei View Post

    The way you put it makes it really easy to understand. I don't have problems with the number families although I had some uncertainties with rational numbers. Thanks
    No problem That's good. Understanding integers and natural numbers are critical in basic Algebra.

    And just to help a little more, here's a summary of operations if you're interested...

    -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    There are 3 basic levels of operations you'll need to know: Addition (), Multiplication ()...

    And then there's the third one, Exponentiation (which is the one that involves powers, exponents, and square roots).

    Now, pretend is just some number...

    Exponentiation





    Multiplication





    Now those are exponentiation and multiplication.

    Notice how exponentiation is just repeated multiplication. And multiplication is based on addition. They act like different levels of operations.

    So if you're not sure what is, just remember it's repeated multiplication: which is a big number (16,384 to be exact :P).

    So if exponents are based on multiplication... And multiplication is based on addition... What is addition based on? Right now, you just need to know that addition is self-defined. It simply is addition itself, and you can't really describe any other way for now. So again, remember that exponents are repeated multiplication. And multiplication is repeated addition. Addition isn't really repeated anything.

    Now, I'll present the inverse operations. These are subtraction, division, and roots.

    They're really just the reverse of the regular operations.

    • What's the opposite of addition? Subtraction.
    • The opposite of multiplication is division.
    • And the opposite of exponentiation is "roots" (exponentiation actually has two inverses because it's special, but just learn roots for now).

    Now you probably already get subtraction and division. But you seem to have trouble with roots. Here's a summary for roots.

    What is the square root ? The number that to the power of 2 = n. It may seem confusing, but it's a very easy concept if you see this...

    The square root of 9 is 3. Why? Because 3 to the power of 2 is 9.
    The square root of 16 is 4. Because 4 to the power of 2 equals 16.

    Now what is the square root of 81? What number to the power of 2 is 81? It's easy if you remember that a number to the power of 2 is just times itself.

    Square root of 9 = 3. Because 3 times 3 = 9.
    Square root of 16 = 4. Because 4 times 4 = 16.

    So what times itself is 81 (is the square root of 81)?
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    Quote Originally Posted by brody View Post
    Quote Originally Posted by Andrei View Post

    The way you put it makes it really easy to understand. I don't have problems with the number families although I had some uncertainties with rational numbers. Thanks
    No problem That's good. Understanding integers and natural numbers are critical in basic Algebra.

    And just to help a little more, here's a summary of operations if you're interested...

    -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    There are 3 basic levels of operations you'll need to know: Addition (), Multiplication ()...

    And then there's the third one, Exponentiation (which is the one that involves powers, exponents, and square roots).

    Now, pretend is just some number...

    Exponentiation





    Multiplication





    Now those are exponentiation and multiplication.

    Notice how exponentiation is just repeated multiplication. And multiplication is based on addition. They act like different levels of operations.

    So if you're not sure what is, just remember it's repeated multiplication: which is a big number (16,384 to be exact :P).

    So if exponents are based on multiplication... And multiplication is based on addition... What is addition based on? Right now, you just need to know that addition is self-defined. It simply is addition itself, and you can't really describe any other way for now. So again, remember that exponents are repeated multiplication. And multiplication is repeated addition. Addition isn't really repeated anything.

    Now, I'll present the inverse operations. These are subtraction, division, and roots.

    They're really just the reverse of the regular operations.

    • What's the opposite of addition? Subtraction.
    • The opposite of multiplication is division.
    • And the opposite of exponentiation is "roots" (exponentiation actually has two inverses because it's special, but just learn roots for now).

    Now you probably already get subtraction and division. But you seem to have trouble with roots. Here's a summary for roots.

    What is the square root ? The number that to the power of 2 = n. It may seem confusing, but it's a very easy concept if you see this...

    The square root of 9 is 3. Why? Because 3 to the power of 2 is 9.
    The square root of 16 is 4. Because 4 to the power of 2 equals 16.

    Now what is the square root of 81? What number to the power of 2 is 81? It's easy if you remember that a number to the power of 2 is just times itself.

    Square root of 9 = 3. Because 3 times 3 = 9.
    Square root of 16 = 4. Because 4 times 4 = 16.

    So what times itself is 81 (is the square root of 81)?
    Hey Brody, again thanks for the great support and the patience. I never thought the square roots as opossed to exponention, that make things a lot clearer. I think the square root of 81 is 9. But how do you find out the square root of a bigger number that has lets say three digits?
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    Quote Originally Posted by brody View Post
    Quote Originally Posted by Andrei View Post

    The way you put it makes it really easy to understand. I don't have problems with the number families although I had some uncertainties with rational numbers. Thanks
    No problem That's good. Understanding integers and natural numbers are critical in basic Algebra.

    And just to help a little more, here's a summary of operations if you're interested...

    -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    There are 3 basic levels of operations you'll need to know: Addition (), Multiplication ()...

    And then there's the third one, Exponentiation (which is the one that involves powers, exponents, and square roots).

    Now, pretend is just some number...

    Exponentiation





    Multiplication





    Now those are exponentiation and multiplication.

    Notice how exponentiation is just repeated multiplication. And multiplication is based on addition. They act like different levels of operations.

    So if you're not sure what is, just remember it's repeated multiplication: which is a big number (16,384 to be exact :P).

    So if exponents are based on multiplication... And multiplication is based on addition... What is addition based on? Right now, you just need to know that addition is self-defined. It simply is addition itself, and you can't really describe any other way for now. So again, remember that exponents are repeated multiplication. And multiplication is repeated addition. Addition isn't really repeated anything.

    Now, I'll present the inverse operations. These are subtraction, division, and roots.

    They're really just the reverse of the regular operations.

    • What's the opposite of addition? Subtraction.
    • The opposite of multiplication is division.
    • And the opposite of exponentiation is "roots" (exponentiation actually has two inverses because it's special, but just learn roots for now).

    Now you probably already get subtraction and division. But you seem to have trouble with roots. Here's a summary for roots.

    What is the square root ? The number that to the power of 2 = n. It may seem confusing, but it's a very easy concept if you see this...

    The square root of 9 is 3. Why? Because 3 to the power of 2 is 9.
    The square root of 16 is 4. Because 4 to the power of 2 equals 16.

    Now what is the square root of 81? What number to the power of 2 is 81? It's easy if you remember that a number to the power of 2 is just times itself.

    Square root of 9 = 3. Because 3 times 3 = 9.
    Square root of 16 = 4. Because 4 times 4 = 16.

    So what times itself is 81 (is the square root of 81)?
    Hey Brody, thanks again for the great support and for the patience, I never though square roots as opposed to exponentiation, that makes things a lot clearer. I think the square root of 81 is 9. But how do you find the square root of a bigger number like one with three digits, without staying hours to think? Or is it even possible?
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    Quote Originally Posted by Andrei View Post

    Hey Brody, thanks again for the great support and for the patience, I never though square roots as opposed to exponentiation, that makes things a lot clearer. I think the square root of 81 is 9. But how do you find the square root of a bigger number like one with three digits, without staying hours to think? Or is it even possible?
    Again, no problem. I'm glad to help someone learn, no matter how long it takes.

    ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    Before we move on, do you know how to write out square roots in math form? When we say "the square root of *some number*", it's mathematically written as , where "x" is some number. The sign looks like a checkmark with the line going over the number.

    I asked what is. You're right! The square root of 81 is 9.

    Because , or if you remember that a number squared is that number times itself, then you know that .

    Now I'll teach you something else. Every positive number has two square roots.

    You've probably learned the positive-negative rules. One of them is that a negative times a negative is a positive.

    So, yes 9 times 9 is 81. But -9 times -9 is also 81. So which is the square root of 81? Is it nine or negative 9? It's both!

    That also means the square root of 9 is 3 and -3. And the square root of 16 is 4 and -4.

    Now, it's important to know that if you see , it's only asking for the positive square root. So technically is just 9. If it wants you to come up with both of them, it'll look like , which you would call "positive-negative square root of x". The is a plus-minus sign. You'll use it when coming up with answers to positive-negative square roots. .

    This is important, because you're learning a new symbol. You can write 1 and -1 as simply .

    So what is
    1. ?

    2. ?.

    They're different answers. One will just be the positive square root and the other will have both answers in form.

    ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
    Last edited by brody; March 13th, 2012 at 05:41 PM. Reason: Oops. 1 & 2 have different answers I mean. Edited :)
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    Quote Originally Posted by Andrei View Post

    Hey Brody, thanks again for the great support and for the patience, I never though square roots as opposed to exponentiation, that makes things a lot clearer. I think the square root of 81 is 9. But how do you find the square root of a bigger number like one with three digits, without staying hours to think? Or is it even possible?
    The short answer is you use a computer.

    However, sometimes you can get lucky. There is a theorem in arithmetic that says that every integer can be written uniquely as the product of prime numbers. For example 10 can be written as 2*5. If the number factors into a double, (eg. 25 factors into 5*5) then to take the square root of 25 is to take the square root of 5*5, which is of course 5. This can be a certain way to find square roots but for large numbers you run into the problem that it can sometimes be tricky to factor your number.

    There is an added problem that for some numbers, like 2, the square root cannot be written down with a finite number of decimal places.
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    Hi Andrei,

    I made a square root calculator site that should help with square roots. At the moment I am adding some fun facts that will hopefully inspire others to learn more.
    You can fill in the square root box or the answer box and it will auto complete the other box. If anyone knows some more square root fun facts, just let me know and I will add them.
    Hope that helps!
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    Forum Freshman Andrei's Avatar
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    Quote Originally Posted by brody View Post
    Quote Originally Posted by Andrei View Post

    Hey Brody, thanks again for the great support and for the patience, I never though square roots as opposed to exponentiation, that makes things a lot clearer. I think the square root of 81 is 9. But how do you find the square root of a bigger number like one with three digits, without staying hours to think? Or is it even possible?
    Again, no problem. I'm glad to help someone learn, no matter how long it takes.

    ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

    Before we move on, do you know how to write out square roots in math form? When we say "the square root of *some number*", it's mathematically written as , where "x" is some number. The sign looks like a checkmark with the line going over the number.

    I asked what is. You're right! The square root of 81 is 9.

    Because , or if you remember that a number squared is that number times itself, then you know that .

    Now I'll teach you something else. Every positive number has two square roots.

    You've probably learned the positive-negative rules. One of them is that a negative times a negative is a positive.

    So, yes 9 times 9 is 81. But -9 times -9 is also 81. So which is the square root of 81? Is it nine or negative 9? It's both!

    That also means the square root of 9 is 3 and -3. And the square root of 16 is 4 and -4.

    Now, it's important to know that if you see , it's only asking for the positive square root. So technically is just 9. If it wants you to come up with both of them, it'll look like , which you would call "positive-negative square root of x". The is a plus-minus sign. You'll use it when coming up with answers to positive-negative square roots. .

    This is important, because you're learning a new symbol. You can write 1 and -1 as simply .

    So what is
    1. ?

    2. ?.

    They're different answers. One will just be the positive square root and the other will have both answers in form.

    ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
    First the answer for the is 8 and for is 8 and -8.

    Now for the signs they are not really new to me. I met them a lot of times before.
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    Quote Originally Posted by TheObserver View Post
    Quote Originally Posted by Andrei View Post

    Hey Brody, thanks again for the great support and for the patience, I never though square roots as opposed to exponentiation, that makes things a lot clearer. I think the square root of 81 is 9. But how do you find the square root of a bigger number like one with three digits, without staying hours to think? Or is it even possible?
    The short answer is you use a computer.

    However, sometimes you can get lucky. There is a theorem in arithmetic that says that every integer can be written uniquely as the product of prime numbers. For example 10 can be written as 2*5. If the number factors into a double, (eg. 25 factors into 5*5) then to take the square root of 25 is to take the square root of 5*5, which is of course 5. This can be a certain way to find square roots but for large numbers you run into the problem that it can sometimes be tricky to factor your number.

    There is an added problem that for some numbers, like 2, the square root cannot be written down with a finite number of decimal places.
    Thanks for the help. I asked that because I offen saw in maths classes some bigger number we had to find the square root and so I thought that there might be some kind of formula or method.
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    Quote Originally Posted by Mizen View Post
    Hi Andrei,

    I made a square root calculator site that should help with square roots. At the moment I am adding some fun facts that will hopefully inspire others to learn more.
    You can fill in the square root box or the answer box and it will auto complete the other box. If anyone knows some more square root fun facts, just let me know and I will add them.
    Hope that helps!
    Hello Mizen, your site is wounderfull. Congratulation.
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    Khanacademy have some real good videos on all sorts of math on Youtube. They have a lot of playlists set up from basic arithmetic to algebra and also calculus. You should check them out, some good videos and they give you a few example of each item to work with, whether it be addition, division and so on.

    I have used a few of their videos to brush up on basics that I have not used for many years, such as long division and the likes, and I will also use the videos to re-introduce myself to Algebra and start learning that again. Should help you out a bit though and hopefully you can find what you are looking for on there.
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    Quote Originally Posted by Andrei View Post

    First the answer for the is 8 and for is 8 and -8.

    Now for the signs they are not really new to me. I met them a lot of times before.
    Good.

    so I thought that there might be some kind of formula or method.
    There is, actually. There are two ways you can get an answer, whether it's double-digits, triple... as long as it's not infinite :P

    One is that you can do it is by guess-and-check. Let's say I want to the find the square root of 90. I know and . So I know has to be somewhere between 9 and 10. So you can take a guess, square it... And if it's too high, you lower it a little and try again. Or if it's too low, you raise a little and check then.

    But there is a real way to do it by hand like you do division: Calculate square root without a calculator

    And remember there's nothing wrong with using a calculator. I always use them for roots.
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    Quote Originally Posted by coupe2t View Post
    Khanacademy have some real good videos on all sorts of math on Youtube. They have a lot of playlists set up from basic arithmetic to algebra and also calculus. You should check them out, some good videos and they give you a few example of each item to work with, whether it be addition, division and so on.

    I have used a few of their videos to brush up on basics that I have not used for many years, such as long division and the likes, and I will also use the videos to re-introduce myself to Algebra and start learning that again. Should help you out a bit though and hopefully you can find what you are looking for on there.
    I know Khanacademy and they do have some good videos indeed. Thanks for mentioning.
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    Quote Originally Posted by brody View Post
    Quote Originally Posted by Andrei View Post

    First the answer for the is 8 and for is 8 and -8.

    Now for the signs they are not really new to me. I met them a lot of times before.
    Good.

    so I thought that there might be some kind of formula or method.
    There is, actually. There are two ways you can get an answer, whether it's double-digits, triple... as long as it's not infinite :P

    One is that you can do it is by guess-and-check. Let's say I want to the find the square root of 90. I know and . So I know has to be somewhere between 9 and 10. So you can take a guess, square it... And if it's too high, you lower it a little and try again. Or if it's too low, you raise a little and check then.

    But there is a real way to do it by hand like you do division: Calculate square root without a calculator

    And remember there's nothing wrong with using a calculator. I always use them for roots.
    Ok, so there are two ways to find the square root, by guess or with a calculator. Understood.
    They link is great.
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    Quote Originally Posted by brody View Post
    But there is a real way to do it by hand like you do division: Calculate square root without a calculator

    And remember there's nothing wrong with using a calculator. I always use them for roots.
    Thanks for the link to that interesting site. I know I'll be studying their teaching methods in detail.

    I do think that their iterative method for square-root finding is a bit more complex than it needs to be, though. One of the simplest methods is to divide a guess into the number whose square-root you are seeking. Compute the average of the divisor and the quotient. Use that average as a new guess, and iterate as many times as necessary. At each step, you will know that the answer lies somewhere between the divisor and the quotient, so you can stop whenever you've narrowed the range to the desired number of digits.

    This doesn't converge as fast as, say, Newton-Raphson, but it converges fast enough for a few digits. And it's very simple.
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    Quote Originally Posted by brody View Post
    In my opinion, mathematics is the forefather of all sciences.
    Quote Originally Posted by adelady View Post
    If you're keen on biology, you have no option but to get maths skills adequate to master statistics.
    Quote Originally Posted by Andrei View Post
    I can't speak for biology but a lot of basic physics is built on calculus and geometry.
    2009-11-16-math.gif

    Perhaps the best advice that I can give is to learn the math itself instead of math "tricks". The tricks will only let you go so far, then it's hard to build on them and learn more intense math.

    Also, if you can find reasons why to use each step of math as you learn it, it will feel more natural to you. Unfortunately, some math professors spend entire courses plowing trough the theoretical, and students loose interest and fail because they aren't given real-life applications. For example, you may learn about exponential decays and maybe given an example of radioactive decay (but how often would we run into such a situation?). However, many things in nature decay exponentially. If I'm given a homework problem about the temperature of the coffee in my cup decaying exponentially to room temperature, then that's something tangible that I can wrap my brain around.
    Grief is the price we pay for love. (CM Parkes) Our postillion has been struck by lightning. (Unknown) War is always the choice of the chosen who will not have to fight. (Bono) The years tell much what the days never knew. (RW Emerson) Reality is not always probable, or likely. (JL Borges)
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    Quote Originally Posted by jrmonroe View Post
    Perhaps the best advice that I can give is to learn the math itself instead of math "tricks". The tricks will only let you go so far, then it's hard to build on them and learn more intense math.
    Agreed. When students "learn" (blankly) merely the procedure of doing math because that's "what teachers taught them", they will run into problems in later courses. It's very important to understand the background behind every lesson.
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