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  1. #1 new in mathematics 
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    Hello everyone.
    I have never really studied mathematics, I've been doing literature studies, now at 20 (almost) I would like to learn maths.
    Do you think it's possible?
    How can I get started knowing that I've never liked maths before.


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    what do you know already and are there any particular sections of maths that you are interested in?


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  4. #3 Re: new in mathematics 
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    Quote Originally Posted by kidvisions
    Hello everyone.
    I have never really studied mathematics, I've been doing literature studies, now at 20 (almost) I would like to learn maths.
    Do you think it's possible?
    How can I get started knowing that I've never liked maths before.
    Not having a background in math is not a problem Not having a strong liking for math could be a problem.

    Try studying a book on elementary abstract algebra or elementary point-set topology and see if you really have a liking and and interest. Michael Artin's book Algebra or the first few chapters of Bartle's Elements of Analysis (which discusses the topology of the line and of Euclidean spaces) might be good places to start.
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  5. #4  
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    Quote Originally Posted by Nevyn
    what do you know already and are there any particular sections of maths that you are interested in?
    Blank board!I absolutely remember nothing
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  6. #5 Re: new in mathematics 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by kidvisions
    Hello everyone.
    I have never really studied mathematics, I've been doing literature studies, now at 20 (almost) I would like to learn maths.
    Do you think it's possible?
    How can I get started knowing that I've never liked maths before.
    Not having a background in math is not a problem Not having a strong liking for math could be a problem.

    Try studying a book on elementary abstract algebra or elementary point-set topology and see if you really have a liking and and interest. Michael Artin's book Algebra or the first few chapters of Bartle's Elements of Analysis (which discusses the topology of the line and of Euclidean spaces) might be good places to start.
    thanks, I think I will like it, I read an article about topology onc and I was triggered by it!
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  7. #6  
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    It might be a good idea to go to the library and ask for a beginners math book.
    Then just jump to the next chapter when you already know it.
    "So much of contemporary life is about opportunities for self-congratulation."
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  8. #7 Re: new in mathematics 
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    Quote Originally Posted by William McCormick
    Quote Originally Posted by kidvisions
    Hello everyone.
    I have never really studied mathematics, I've been doing literature studies, now at 20 (almost) I would like to learn maths.
    Do you think it's possible?
    How can I get started knowing that I've never liked maths before.

    Get a job apprenticing to someone in custom cabinets, railings, stairs, or even a small hometown architect.
    William This post makes no attempt to answer the question asked.
    Off-topic parts deleted.

    -G-
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  9. #8  
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    :-D Never too old to learn math! Internet has good stuff, Libraries, tutors... where theres a will, theres a way! Get old highschool math book, so many options!
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  10. #9 Re: new in mathematics 
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    thanks, I think I will like it, I read an article about topology onc and I was triggered by it![/quote]

    I do not know how can you understand topology if you do not understand basic. If you are really new to math it will be wise to by basic schum's outline on Algebra. Topology is abstract, and sometime hard language of math can discourage people. Never think math as hard or complicate, what I mean don't let math dominate; you should dominate math.
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    I must admit I'm a little confused by the original poster's interest in learning math. If you genuinely don't remember any of the math you've learned so far, what leads you to believe that you will be interested in it if you pick it up again? I don't mean to discourage you. But you should be honest with yourself about what your goals are and what led you to those goals in the first place.

    I wouldn't say anything if you were asking advice about learning algebra and calculus. But it sounds like you want to dive straight into things like topology and group theory. Why?
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  12. #11  
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    Quote Originally Posted by salsaonline
    I must admit I'm a little confused by the original poster's interest in learning math. If you genuinely don't remember any of the math you've learned so far, what leads you to believe that you will be interested in it if you pick it up again? I don't mean to discourage you. But you should be honest with yourself about what your goals are and what led you to those goals in the first place.

    I wouldn't say anything if you were asking advice about learning algebra and calculus. But it sounds like you want to dive straight into things like topology and group theory. Why?
    Well, most people in school unless you are in the industrial arts department, ever really learn how to deal with geometric figures. The math department can give you all kinds of formulas. And don't get me wrong I use some of those formulas, like a secret pirates map. But most I cannot remember.

    Neither can anyone else from my experience, if they are working with only a certain set of formulas day to day. Even the best machinists have to go to the book to get formulas.

    It is really just a good idea to know they exist, to know what the strength and weakness of the formula is. So you do not waste a lot of time. Or start something that there is no formula to get you out of.

    To be honest math is like a hammer. If you do not know how to build the hammer is useless. That is why most never get into math or building. You need them both.

    But from studying geometric figures you can come across some neat stuff about them.

    http://www.Rockwelder.com/geometry/G...letriangle.pdf

    Combined with knowing there exists a mathematical formula, to check the workability of using one or any of these procedures in that link. You can get some wild stuff done. Often the size of the object needed to create some of these effects is just to large or small to be practical. Math is good at finding that out without actually building it.

    Most of the things you learn in math class, as being very powerful tools. Are crushed in the field by very rude, large men that do it day in and day out. They know the formula you are talking about. However it proved so unworkable they do not even want to go back to that place. Why none of this ever gets back to the math department I do not know.

    You take the three four five triangle. You want to square up something. Maybe a form. Sounds like a great way to do it. I mean you just take a few measurements and away you go.

    But then the reality sets in. What are we going to use to create this giant triangle out in the field? The stuff we want to square up has to be in place. It has to be straight. This is not the reality. String stretches as much as an inch over twenty five feet. Most people do not have three fiberglass surveyor tapes and a half hour to get three guys to hold them.

    So often it just gets sighted by a known square object.

    Where that three four five triangle is great. Is for measuring where to cut into a large pipe to create a branch pipe, to hit an existing opening in a wall within 25 feet. You still need two guys, and a tape measure .
    But there are tricks to even making that useful. You have to be able to understand what the reference being crooked to the branch pipe, means to the outcome. Or it is all for nothing.

    If mathematicians apprenticed, I believe they could not only make a fortune, by designing new equipment, they could see the collapse, in all fields. And make a better world.


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    William McCormick
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  13. #12 Re: new in mathematics 
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    Quote Originally Posted by sondivp456
    thanks, I think I will like it, I read an article about topology onc and I was triggered by it!
    I do not know how can you understand topology if you do not understand basic. If you are really new to math it will be wise to by basic schum's outline on Algebra. Topology is abstract, and sometime hard language of math can discourage people. Never think math as hard or complicate, what I mean don't let math dominate; you should dominate math.[/quote]

    Schaam's outlines IMO are a pretty lousy venue for learning mathematics. They tend to be long on computations and short on true theoretical understanding.

    Point-set topology actually requires almost no background, only what is sometimes called "mathematical maturity" and a desire to learn the subject. It is particularly undemanding in terms of background when you limit yourself to the topology of the real line and Euclidean spaces. Rather than requiring a lot of background an understanding that subject actually makes understanding calculus at a theoretical level easier. That is the reason that it is covered in the first few chapters of the book by Bartle that I recommended. Frankly it is not possible to understanding basic mathematics without understanding elementary point-set topology, the issue is not how one can understand topology without understanding basic mathematics but rather how one can claim to understand basic mathematics without understanding the rudiments of topology.
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    Quote Originally Posted by salsaonline
    I must admit I'm a little confused by the original poster's interest in learning math. If you genuinely don't remember any of the math you've learned so far, what leads you to believe that you will be interested in it if you pick it up again? I don't mean to discourage you.
    Well it sure reads like you do mean so to do

    But it sounds like you want to dive straight into things like topology and group theory.
    Now where did you find that in the OP?

    Look, I have no idea why DrRocket made the suggestions he did, but I have to say I agree with them. Here are my reasons, which may not be his:

    When we first learn mathematics, we are taught to use objects called "real numbers", and we are told they have certain properties. It turns out that these properties are a synthesis of the properties of an ordered set, the properties of a topological space, the properties of a vector space, and so on. This makes the real numbers almost (totally?) unique

    Having finally got our heads around the real numbers, we are then encouraged to "deconstruct" all we have learned and accept that there are, say, sets that are not ordered, topological spaces that are not vector spaces, and so on. This is a challenge for many people, to throw off ingrained learning

    Far easier, I would think, to start with the "deconstruction", and build up. As DrRocket said, point set topology is as good as any place to start, and so is linear algebra - both use extremely familiar constructions, at least to start with
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  15. #14  
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    Quote Originally Posted by Guitarist
    Quote Originally Posted by salsaonline
    I must admit I'm a little confused by the original poster's interest in learning math. If you genuinely don't remember any of the math you've learned so far, what leads you to believe that you will be interested in it if you pick it up again? I don't mean to discourage you.
    Well it sure reads like you do mean so to do

    But it sounds like you want to dive straight into things like topology and group theory.
    Now where did you find that in the OP?

    Look, I have no idea why DrRocket made the suggestions he did, but I have to say I agree with them. Here are my reasons, which may not be his:

    When we first learn mathematics, we are taught to use objects called "real numbers", and we are told they have certain properties. It turns out that these properties are a synthesis of the properties of an ordered set, the properties of a topological space, the properties of a vector space, and so on. This makes the real numbers almost (totally?) unique

    Having finally got our heads around the real numbers, we are then encouraged to "deconstruct" all we have learned and accept that there are, say, sets that are not ordered, topological spaces that are not vector spaces, and so on. This is a challenge for many people, to throw off ingrained learning

    Far easier, I would think, to start with the "deconstruction", and build up. As DrRocket said, point set topology is as good as any place to start, and so is linear algebra - both use extremely familiar constructions, at least to start with
    I totally agree.

    The plain fact of the matter is that to learn and understand graduate level mathematics, undergraduate mathematics is not really needed. It is quite possible to learn topology, algebra and analysis at the first-year graduate level without having taken much in the way of undergraduate mathematics. It is in fact quite possible to take such courses in a setting in which the students supply nearly all of the proofs, the professor offering only occasional comments and usuall remaining silent, without the usual undergraduate classes as prerequisites.
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    Math is a really general and wide subject. Algebra is the real basic point in math, so if you really don't remember any math I would start with Algebra 1: CPM (College Preparatory Mathematics) by Kysh Sallee and Hoey Kasimatis. This book takes you step by step and is really good for math beginners. Then I would read Discovering Geometry: An Inductive Approach by Michael Serra to gain a more in depth approach to math. After that you will just have to decide what sort of math you want to go into.

    For example:
    -calculas
    -theories
    -advanced linear algebra
    -topology
    -advanced trigonometry
    -or you could even lead into chemistry or physics
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  17. #16  
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    Quote Originally Posted by DrRocket
    I totally agree.

    The plain fact of the matter is that to learn and understand graduate level mathematics, undergraduate mathematics is not really needed. It is quite possible to learn topology, algebra and analysis at the first-year graduate level without having taken much in the way of undergraduate mathematics. It is in fact quite possible to take such courses in a setting in which the students supply nearly all of the proofs, the professor offering only occasional comments and usuall remaining silent, without the usual undergraduate classes as prerequisites.
    It is certainly possible from a logical point of view. But is it practical? I venture that it is not, especially if you don't have any particular goal in mind.

    I think it's a big mistake to dive into these abstract formalisms without any concrete examples to compare the formalisms to. If you don't have some experience with connectivity, compactness, sequences, and limits from calculus, what sort of appreciation will you have for these concepts when you see them in point set topology? There's a reason why most math programs want you to learn things like calculus and linear algebra before you start taking graduate courses--they motivate a lot of the ideas that enter into the more advanced subjects.

    You can go about things backwards if you're truly determined--learning the advanced formalism first and learning the motivating examples later. But it's going to be a struggle. And why do it anyway? Is point set topology intrinsically more interesting than calculus? It's a tool that a lot of interesting subjects use, but the material that a newcomer to mathematics would be able to cover on his/her own is not that interesting by itself.

    Moreover, I find it strange that when someone says they don't know any math, but want to learn, people sometimes seem adverse to giving the most natural advice: go learn algebra and calculus. Is it just me, or are those the most basic skills required of almost anyone who studies math? Even research mathematicians need to be able to integrate a function or multiply two polynomials.
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  18. #17  
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    Quote Originally Posted by salsaonline
    Quote Originally Posted by DrRocket
    I totally agree.

    The plain fact of the matter is that to learn and understand graduate level mathematics, undergraduate mathematics is not really needed. It is quite possible to learn topology, algebra and analysis at the first-year graduate level without having taken much in the way of undergraduate mathematics. It is in fact quite possible to take such courses in a setting in which the students supply nearly all of the proofs, the professor offering only occasional comments and usuall remaining silent, without the usual undergraduate classes as prerequisites.
    It is certainly possible from a logical point of view. But is it practical? I venture that it is not, especially if you don't have any particular goal in mind.

    I think it's a big mistake to dive into these abstract formalisms without any concrete examples to compare the formalisms to. If you don't have some experience with connectivity, compactness, sequences, and limits from calculus, what sort of appreciation will you have for these concepts when you see them in point set topology? There's a reason why most math programs want you to learn things like calculus and linear algebra before you start taking graduate courses--they motivate a lot of the ideas that enter into the more advanced subjects.

    You can go about things backwards if you're truly determined--learning the advanced formalism first and learning the motivating examples later. But it's going to be a struggle. And why do it anyway? Is point set topology intrinsically more interesting than calculus? It's a tool that a lot of interesting subjects use, but the material that a newcomer to mathematics would be able to cover on his/her own is not that interesting by itself.

    Moreover, I find it strange that when someone says they don't know any math, but want to learn, people sometimes seem adverse to giving the most natural advice: go learn algebra and calculus. Is it just me, or are those the most basic skills required of almost anyone who studies math? Even research mathematicians need to be able to integrate a function or multiply two polynomials.
    It is eminently practical if you have a desire and a need to learn some real mathematics. I did it.

    If you don't have a goal in mind then, whatever the particulars, you are not going to accomplish anything. That applies whether the subject is mathematics or cooking.

    Point set topology is not only more interesting than what passes for mathematics in elementary calculus, it much better motivated. Calculus is one of the least motivated and least logically presented subjects in university mathematics. There is lots of emphasis on manipulation of symbols and very little on concepts. Despite your statement, compactness is not a subject that is taught in most introductory calculus classes.

    In fact one othe motivations for the development of point set topology in the early part of the twentieth century was to isolate and understand the mathematics that underlies calculus. Point set topology is quite often the first time that students see real mathematics, where the objective is to understand what is going on rather than just "find the answer".
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    I see where you're coming from, don't get me wrong.

    Students do encounter compactness in some sense--they're usually taught the extreme value theorem, and they certainly develop some feel for the difference between continuous functions on open intervals and continuous functions on closed intervals.

    To address a second point: absent the motivation that comes from more basic mathematics, how is point set topology "better motivated" than calculus? Any reasonably good student can see right away why concepts like instantaneous rates of change are worth studying, and can at least have some appreciation for the definition of the derivative as a limit of a family of secant lines. Contrast that with the very much more obscure definitions a beginning student encounters in topology. For example, consider the basic axioms in topology: 1. The union of any collection of open sets is open. 2. The intersection of any finite collection of open sets is open. Will a student who has almost no math training be able to understand intuitively why we allow all collections in axiom 1., and only finite collections in axiom 2. ?

    One last point. I agree completely that a lot of lower level calculus courses are taught poorly (especially in high school). Students indeed often focus more on manipulating symbols than on the underlying concepts. But I never suggested that the original poster learn calculus poorly. I just said he/she should learn calculus. I have to assume that when I give this kind of advice, people understand implicitly that I mean "acquire a solid understanding of the subject" and not "take the easiest most superficial course you can find." And is it really fair to assume that every introductory calculus course emphasizes cookbook solutions to problems, and ignores critical thinking and concepts? My experience is that there are always a few dedicated faculty out there who really put thought into their presentation of the subject, and shrug off any concerns that their popularity might suffer from making the course too difficult. After all, they are mathematicians too, and they know the difference between teaching ideas and teaching recipes.

    Let's not get so down on calculus. Even Edward Witten said he thinks it's one of the most amazing mathematical innovations we have.
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