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Thread: When does math get challenging?

  1. #1
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    When does math get challenging?

    I am taking statistics and calculus 1 this semester and for the most part my statistics class has been more challenging than my calculus 1 class. In stats we are starting to learn about probability and it seems not very unintuitive.


    Calculus 1 has been a breeze. However I feel like I am mindlessly conforming to these math problems, that is I do not know what is happening visually or graphically with each function when I find the differentiation, continuity, or limits of the function.

    Obviously this is a subjective question and has many different answers but for the most part math has not been too difficult for me yet.
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    Re: When does math get challenging?

    If want a challenge and you want a better understanding of calculus try your hand at a math major's book on real analysis.

    I used "Real Analysis" by Royden, but that's probably a bit dated by now.

    One of the guys here that actually teaches can probably suggest a current book.
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    Re: When does math get challenging?

    Quote Originally Posted by math951 View Post
    I am taking statistics and calculus 1 this semester and for the most part my statistics class has been more challenging than my calculus 1 class. In stats we are starting to learn about probability and it seems not very unintuitive.
    Calculus 1 has been a breeze. However I feel like I am mindlessly conforming to these math problems, that is I do not know what is happening visually or graphically with each function when I find the differentiation, continuity, or limits of the function.
    You did not tell what level you are asking about.
    If this is secondary, then it sounds as if you are cursed with awful AP instructors.

    If you are in college, you may have been ill-advised. Years ago, I was part of a regional conference on the New Calculus. The leader was a well-known mathematician at one of the hands-full of southern Ives. At the end of his talk, someone ask if this was an example of what his Univ taught freshman mathematics majors? If so, why would anyone pay the cost of his school??" The answer was so informative: "My good man, freshman mathematics majors at D___ don't take calculus."

    So tell us more about your situation.
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    Re: When does math get challenging?

    Quote Originally Posted by Plato View Post
    You did not tell what level you are asking about.
    If this is secondary, then it sounds as if you are cursed with awful AP instructors.

    If you are in college, you may have been ill-advised. Years ago, I was part of a regional conference on the New Calculus. The leader was a well-known mathematician at one of the hands-full of southern Ives. At the end of his talk, someone ask if this was an example of what his Univ taught freshman mathematics majors? If so, why would anyone pay the cost of his school??" The answer was so informative: "My good man, freshman mathematics majors at D___ don't take calculus."

    So tell us more about your situation.
    My situation: I did horrible in high school, I graduated with a cumulative 2.4 gpa. Granted, I never tried in high school (I probably spent 100 hours of homework my whole 4 years there). I took algebra 1 freshman year, geometry sophomore year (failed class), geometry junior year, then consumer mathematics for senior year. I went to junior college last summer, started with intermediate Algebra. Now 4 semesters later, I am in Calculus 1. I have a 4.0 cumulative gpa, am a honor student, etc. (not trying to boast). Moreover, what do you mean by that quote? Is freshman and sophomore mathematics horribly taught for junior college students ? At fist when you said "D____" I was thinking of profanity, but I assume now you are talking about a certain university. Are you saying that in general, calculus is taught wrongly?? For the most part, my statistics professor is a wonderful person, a motivator, and teaches us everything, where we can understand what we are actually doing. He even related to my class by him going the JC route, and him struggling ,etc. He told us how most of the mathematics teaching, or education teaching in general just works along the lines of follow what I do and do not question what I do, either. Almost as if in math, the purpose of some classes are to just memorize the steps, then forget them afterwards, and I have been a victim of this - as I have done this sometimes, but I try to branch away from that type of studying/learning. My statistic professor explains what a standard deviation is, and why we use the formula, and how it applies to real life etc. However, on the flip-side, my calculus professor said that to enjoy this class you must try to apply it to real life as much as possible, so while he does talk about applications sometimes, for the most part, it is just following properties and theorems of limits and continuity, differentiation, thus far. I have told people in person, (this is my opinion) that the way to truly understand mathematics is to understand what is going on with the problem visually on a graph, then to be able to apply it in to real life application. Why is it when I was tutoring last semester at my junior college, we had tutors that are in calc,2,3 and even differentials, and they were unable to help the tutees' with word problems from intermediate algebra classes? Why, because I think word problems are very hard to understand and apply. Algebra is purely just signs of expressions, just take some memorization and repetition, and you will be fine. But to apply it into real life, atleast, that is what I see the difference from a good mathematician and an average one. For the most part, many of the fellow math posters on here can do what I just said, and they can take any problem I need help on without any reference of notes, it is pretty incredible IMO.
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    Re: When does math get challenging?

    paragraphs are your friend :P
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    Re: When does math get challenging?

    Quote Originally Posted by Plato View Post
    You did not tell what level you are asking about.
    If this is secondary, then it sounds as if you are cursed with awful AP instructors.

    If you are in college, you may have been ill-advised. Years ago, I was part of a regional conference on the New Calculus. The leader was a well-known mathematician at one of the hands-full of southern Ives. At the end of his talk, someone ask if this was an example of what his Univ taught freshman mathematics majors? If so, why would anyone pay the cost of his school??" The answer was so informative: "My good man, freshman mathematics majors at D___ don't take calculus."
    To me, rather than "informative" this answer seems ambiguous. It might be that "freshman mathematics majors" take a college "pre-calculus" class (not too uncommon years ago) or it might mean that "freshman math majors" would already have taken an AP calculus class in secondary school.

    (Actually, I wonder about the phrase "freshman mathematics majors". In most colleges students are encouraged not to choose a major until at least their sophomore year.)

    (Math951, is "not very unintuitive" anything like "intuitive"?)
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    Re: When does math get challenging?

    Quote Originally Posted by HallsofIvy View Post
    (Actually, I wonder about the phrase "freshman mathematics majors". In most colleges students are encouraged not to choose a major until at least their sophomore year.)
    That has not been my experience at all. In fact I have been two places that want to do that only to be blocked by powerful departments. I do know some schools that will admit some freshman with non-declared majors. But found out that is a bookkeeping ploy. That way they do not have to start the "progress to graduation clock" until a major is declared.
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