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  1. #1 What Are you Learning 
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    What branch of mathematics are you all currently studying (whether it be in a class-room setting in a university or secondary-school or in your free time)?


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    I'm learning Differential Equations and Linear Algebra at the moment, all through textbooks on my own time, and sadly without formal training in a school because I don't qualify for attendance in a university...


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    I don't qualify for attendance in a university...
    Aren't you a professor,,,, or does it just say that you are a professor after you hit a certain number of posts?
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    post count title. at 2000 I'll be an isotope
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    Quote Originally Posted by Arcane_Mathematician
    I don't qualify for attendance in a university...
    Why - anyone can attend a JC to begin.
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    This semester I am not learning very much at the moment. Last spring I did had studying a lot in the areas of combinatorics, differential equations, and some abstract algebra. This semester I am taking a class on euclidean geometry, analysis, and history of math. Hopefully these classes will pick up sometime soon. For my research this year I am studying lectures on nonpositive curvature, one particular space will be the subject of my research, but I cannot comment further on that at the moment since I am not doing the research yet. I am only learning background information.
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    Quote Originally Posted by Arcane_Mathematician
    I'm learning Differential Equations and Linear Algebra at the moment, all through textbooks on my own time, and sadly without formal training in a school because I don't qualify for attendance in a university...
    Good for you.

    One of the sad things about the way math is taught is that it is a chore (and can be a bore). How many people after finishing school go to the library and take out a math book? Folks will read novels, take out history books and even take out foreign language course books...but Math?

    It's a bit sad that math is something to endure and get through almost for the sake of it and then cast aside once out of academia.
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    Quote Originally Posted by raptordigits
    One of the sad things about the way math is taught is that it is a chore (and can be a bore). How many people after finishing school go to the library and take out a math book? Folks will read novels, take out history books and even take out foreign language course books...but Math?

    It's a bit sad that math is something to endure and get through almost for the sake of it and then cast aside once out of academia.
    It is very sad that every time I go to the math section of my university's library, most of the book's I choose to read have never been checked out, some of them in circulation for over 10-15 years.
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    Quote Originally Posted by pbandjay
    Quote Originally Posted by raptordigits
    One of the sad things about the way math is taught is that it is a chore (and can be a bore). How many people after finishing school go to the library and take out a math book? Folks will read novels, take out history books and even take out foreign language course books...but Math?

    It's a bit sad that math is something to endure and get through almost for the sake of it and then cast aside once out of academia.
    It is very sad that every time I go to the math section of my university's library, most of the book's I choose to read have never been checked out, some of them in circulation for over 10-15 years.
    Which university ?
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    Yeah, that might be a feature of that particular university. When it comes to math books that are used for courses, my experience is that they're very difficult to check out of the library (b/c someone else has gotten to it first).
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    At my university, I've been the first to check out some math (and computer science) books too, though they weren't books that were used for classes. Of course, sometimes I wonder if they hadn't recently replaced a full list. (They usually just paste a new one over the old one.)
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    that's probably what's going on, unless you can tell that the book itself is in mint condition.
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    Quote Originally Posted by salsaonline
    Yeah, that might be a feature of that particular university. When it comes to math books that are used for courses, my experience is that they're very difficult to check out of the library (b/c someone else has gotten to it first).
    My experience is that anything worth checking out is checked out, often by facult for extended periods.

    I simply built up my personal library, so that most books that would interest me I own.
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    Not exactly the most practical solution for people who aren't swimming in cash.
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    Differential Equations and Linear algebra aren't taught at any JCs near enough for me to attend, and certainly no level of mathematics beyond them.
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    Quote Originally Posted by salsaonline
    Not exactly the most practical solution for people who aren't swimming in cash.
    I obtained most of my books as a graduate student. I assure you that I was not swimming in cash. As I recall I made $386/month. Admittedly books were a bit less expensive then, but incomes were lower too.

    However, I think that the prices of science and mathematics books have risen faster than either the mean inflation rate or incomes. Some of them now are astoundingly expensive. Many are simply not available either.
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    Out of all my text books, the one I was the most upset over price-wise was my real analysis book. It was a little, thin hardback, but it cost over $70. Completely ridiculous, but required for class. All of my other books were much bigger and (usually) somewhat cheaper.
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    Quote Originally Posted by MagiMaster
    Out of all my text books, the one I was the most upset over price-wise was my real analysis book. It was a little, thin hardback, but it cost over $70. Completely ridiculous, but required for class. All of my other books were much bigger and (usually) somewhat cheaper.
    Which book was it?

    Rudin's Principles of Mathamtical Analysis used to be reasonably priced, but I have see it more recently at over $140, which I find ridiculous. It is however, probably the best book on real analysis at that level.
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    I build up my own collection of books over time as I learn, and if a book isn't very good, then sell it back, otherwise keep it for reference.

    The key is that most people will not (or cannot) learn many expansive areas of advanced mathematics simultaneously, so you don't really need to buy all your books all at once, and for me at least, learning a certain area of mathematics properly takes time...time in which I'm not spending money on more books.

    All you need are a few good reccommendations to get the right book, and you can always sell it back anyway.

    Hasn't anyone here heard of amazon?? you can buy cheap second hand books usually in good condition and also sell them back, you should seriously check it out, I've got loads of bargains on there.
    PHI is one 'H' of alot more interesting than PI!
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    Quote Originally Posted by Nabla
    I build up my own collection of books over time as I learn, and if a book isn't very good, then sell it back, otherwise keep it for reference.

    The key is that most people will not (or cannot) learn many expansive areas of advanced mathematics simultaneously, so you don't really need to buy all your books all at once, and for me at least, learning a certain area of mathematics properly takes time...time in which I'm not spending money on more books.

    All you need are a few good reccommendations to get the right book, and you can always sell it back anyway.

    Hasn't anyone here heard of amazon?? you can buy cheap second hand books usually in good condition and also sell them back, you should seriously check it out, I've got loads of bargains on there.
    You should also consider Alibris.com and Abebooks.com. Both are sources of used science and mathematics books, many of which are no longer in print. Check all of them before buying as prices for used books in good condition vary widely.
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    I don't remember the name of the book any more, and I sold that one back after that semester. Since I've been in grad school though, I've haven't had to buy many books, so I have no idea how much something similar would be now.
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    Quote Originally Posted by Arcane_Mathematician
    Differential Equations and Linear algebra aren't taught at any JCs near enough for me to attend, and certainly no level of mathematics beyond them.
    True enough, but enough JC units will land you in SJ State.
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    Quote Originally Posted by Ots
    Quote Originally Posted by Arcane_Mathematician
    Differential Equations and Linear algebra aren't taught at any JCs near enough for me to attend, and certainly no level of mathematics beyond them.
    True enough, but enough JC units will land you in SJ State.
    enough General Ed courses, and if I could pay the tuition, I'd most certainly go that route, but seeing as how I don't qualify for most financial aid programs, and I really REALLY don't want to go into debt, I'm sol.
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    Quote Originally Posted by Arcane_Mathematician
    Quote Originally Posted by Ots
    Quote Originally Posted by Arcane_Mathematician
    Differential Equations and Linear algebra aren't taught at any JCs near enough for me to attend, and certainly no level of mathematics beyond them.
    True enough, but enough JC units will land you in SJ State.
    enough General Ed courses, and if I could pay the tuition, I'd most certainly go that route, but seeing as how I don't qualify for most financial aid programs, and I really REALLY don't want to go into debt, I'm sol.
    For some reason I was under the impression that you either studying engineering or planned to study engineering. In either case you will eventually need to attend a university and not just a JC.

    You might want to look into available scholarships in addition to loans. I don't blame you for not wanting to incur debt, but if you can land a good job after graduation the trade vs the debt from student loans is usually favorable.
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    I was studying mech engineering, but it was only because it was the closest offered major to a mathematical one, and I signed on to it before I learned how far the field of mathematics goes. And, I really want to learn Math more than Engineering and physics, though I do love both of those, I can't really see myself getting a teaching job with a math degree, I'm much more suited to be a tutor. Either way, though, I'm only in school for to learn, I have no real desire to go forth and get a great career out of it.
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    Just finished Differentials, Complex nubmbers, Matrix Applications and Veectors
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    The Linear Algebra book I ordered has arrived, and so far so good, the first 2 chapters seem to be review from my last semester of calculus, plus an overview of notations.
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    Quote Originally Posted by Arcane_Mathematician
    The Linear Algebra book I ordered has arrived, and so far so good, the first 2 chapters seem to be review from my last semester of calculus, plus an overview of notations.
    Which book did you buy ?
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    Linear Algebra by Serge Lang
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    Quote Originally Posted by Arcane_Mathematician
    Linear Algebra by Serge Lang
    I think that will be a good one.

    I don't know that specific book, he wrote a lot of books. But generally speaking Lang's mathematics books are very good. His algebra book is a standard for first-year graduate students, and his real analysis book (I think it is now called Real Analysis II) is also excellent. His other books also rend to be good.

    I saw him once in a colloquium that we both attended.
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    It seems very comprehensive. All of the mathematics so far aren't presented in undefined ways, nor are trivial topics explored in depth. I'm definitely enjoying myself
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by Arcane_Mathematician
    Linear Algebra by Serge Lang
    I think that will be a good one.

    I don't know that specific book, he wrote a lot of books. But generally speaking Lang's mathematics books are very good. His algebra book is a standard for first-year graduate students, and his real analysis book (I think it is now called Real Analysis II) is also excellent. His other books also rend to be good.

    I saw him once in a colloquium that we both attended.
    I remember going to a professor's office to ask about enrolling in the graduate algebra course (I was an undergrad at the time). The professor wasn't there, but an old man occupying the adjacent office saw me and asked if I needed anything. I told him that I was seeking advice about whether or not I should enroll in the class. To that I added that the textbook looked very good ("Algebra", by Serge Lang).

    I don't remember exactly what he said, but it suddenly dawned on me who he was. "Oh! You're Lang!" I exclaimed.

    At that he launched into an impromtu discussion in the hallway over the concept of winding numbers of curves and the proper way to define them using an integral.
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    Currently studying;
    -calculus,Integration-(logarithmic function, trigonometric function, higher derivative, rates of change)
    -kinematics-(velocity -acceleration via integration and differentiation, vector addition of integral applications, area under hyperbolic functions)
    -relative velocity, vectors in 3 dimensions and 2 dimensions

    these are the last few topics we are studying for our A-level higher maths in igcse
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    Currently studying quadrilateral equations mixed with some algebra in Factor 2 (called Grunnbok and Oppgavebok in Norwegian language) Primary Educational Book and Assignment-book, Junior High :P
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    Currently, multivariable calculus, including double and triple integration. Some number theory as well.
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    I have to take College Algebra next semester. I know, I know..sad..
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    Pre-university Algebra, Including:

    1)Real Numbers,rationalizing, Quadratics Expressions, Inequalities, COmplex NUmbers

    2)Polynomials, Polynomial Division (Long, sysnthetic),All those theorems for Polynomials, and graph of polynomials.

    3)Functions and graph, Transformation fo graph, Composite functions, Inverse Functions, Quadratic functions, rational functions.

    4)Exponential and logarithmic functions, and their graphs.

    5)Matices and systems of equations, Transpose Matix, Inverse matrix (3x3),Gauss-Jordan and Gaussian elimination method, Cramer's Rule, Adjoint matrix.


    Well, that's what I learned in the last semester. I'll be continuing with Pre-University Calculus in the next semester.
    Wormgate, Solar Sail, Antimatter Generator, Tachyon Coated-steel
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    Single Variable Calculus is the course that I will start with next week. After that there will be some Linear Algebra and Geometry.
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    After that you should hit up multi-variable calculus before you go for Linear algebra
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    Quote Originally Posted by HyoureiKyouran
    Single Variable Calculus is the course that I will start with next week. After that there will be some Linear Algebra and Geometry.
    HyoureiKyouran,
    Arcane_Mathematician is correct; you'll want to learn some standard multivariable and vector calculus before you move on to linear algebra (which you should take with differential equations, or at least, before or after).
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    As a computer scientist, I'd recommend linear algebra over multivariable calculus or differential equations. Actually, it seems to me that those three can really be taken in any order. You're not likely to use multivariable calculus in the first differential equations class, and neither is likely to apply too heavily to the first linear algebra course. I guess that'd depend on your professors though.
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    Quote Originally Posted by MagiMaster
    As a computer scientist, I'd recommend linear algebra over multivariable calculus or differential equations. Actually, it seems to me that those three can really be taken in any order. You're not likely to use multivariable calculus in the first differential equations class, and neither is likely to apply too heavily to the first linear algebra course. I guess that'd depend on your professors though.
    Multivariable calculus is still worth learning, however, as it's used often in other branches of mathematics. For example, in continuums (spaces that have a metric that can be infinitesimally subdivided) we make frequent use of the partial derivative when finding a so-called "deformation gradient." Another example is the covariant derivative (the derivative of a vector translated onto the tangent space of the manifold of which it lies on) that's used in tensor calculus.
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    I'm just about half way through my Linear Algebra book. Not as bad as I feared.
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    Quote Originally Posted by Ellatha
    Quote Originally Posted by MagiMaster
    As a computer scientist, I'd recommend linear algebra over multivariable calculus or differential equations. Actually, it seems to me that those three can really be taken in any order. You're not likely to use multivariable calculus in the first differential equations class, and neither is likely to apply too heavily to the first linear algebra course. I guess that'd depend on your professors though.
    Multivariable calculus is still worth learning, however, as it's used often in other branches of mathematics. For example, in continuums (spaces that have a metric that can be infinitesimally subdivided) we make frequent use of the partial derivative when finding a so-called "deformation gradient." Another example is the covariant derivative (the derivative of a vector translated onto the tangent space of the manifold of which it lies on) that's used in tensor calculus.
    I didn't say it wasn't worth learning, but for a computer scientist, linear algebra is definitely the most useful, followed by differential equations, then multivariable calculus. For a mathematician, that may not be true. My main point though was that the three are pretty independent, at least in the introductory courses.
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    probability theory, econometrics and statistics, which I need for my job.
    how do you keep up the motivation when self studying? Although quite intersting, studying maths can be very, very exhausting.
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    Quote Originally Posted by Ellatha
    Quote Originally Posted by HyoureiKyouran
    Single Variable Calculus is the course that I will start with next week. After that there will be some Linear Algebra and Geometry.
    HyoureiKyouran,
    Arcane_Mathematician is correct; you'll want to learn some standard multivariable and vector calculus before you move on to linear algebra (which you should take with differential equations, or at least, before or after).
    I look into it a little myself then, since the order of my courses at the university is single variable, linear algebra and then multivariable.
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    Quote Originally Posted by Ellatha
    Quote Originally Posted by HyoureiKyouran
    Single Variable Calculus is the course that I will start with next week. After that there will be some Linear Algebra and Geometry.
    HyoureiKyouran,
    Arcane_Mathematician is correct; you'll want to learn some standard multivariable and vector calculus before you move on to linear algebra (which you should take with differential equations, or at least, before or after).
    Not necessarily.

    Linear algebra is usually taught after one has had a standard three-semester course in calculus, the last semester of which includes some multi-variable ideas such as partial derivatives.

    However, there is no logical dependence of linear algebra on multi-variable calculus, but if multi-variable calculus is done correctly (as is typical beyond the third year) one does need linear algebra in order to study calculus of several variables. It is necessary to understand the notion of a linear function in order to understand what the derivative is in higher dimensions and to even be able to state properly fundamental theorems such as the open mapping theorem and implicit function theorem.

    Linear algebra can be taught either by itself or in conjunction with systems of ordinary linear differential equations with constant coefficients. If it is done in conjunction with
    ODEs in an elementary class that sometimes is illuminating. In a more advanced class it may take up time that could be spent on more important aspects of linear algebra itself. I have done it both ways, and can honestly say that I don't have a preference -- although I do like the insight into ODEs that comes with viewing a system as just a single vector differential equation.

    Linear algebra is usually taught in two forms. There is an elementary class that discusses the absolute basics -- vector spaces, bases, transformations, matrices, determinants. Then there is a more advanced class at the junior-senior level that treats the subject in more detail, and discusses things like the characteristic polynomial, Cayley-Hamilton theorem, spectral decomposition and normal forms, etc.

    The former class is what is typically taught to sophomore mathematics majors and is terminal for engineers and scientists, but to study more advanced mathematics you need more algebra.

    ODE's is some thing that you can study at about any time. It is also taught at many different levels. You can pick up what you need in physics and engineering classes if necessary, or you can study them at more theoretical level in pure mathematics classes. It tends to be somewhat of a "bag of tricks" as opposed to a unified theory, particularly at the introductory level.
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