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0

The only known way to learn to write proofs up to the mathematical community's standards is: experience.


1

Depends how you naturally prefer to learn, but if you're like me and like an intuitive taste before the formalities, Calculus I and Calculus II are very good video introductions on Coursera. There are many additional courses such as Massively Multivariable Open Online Calculus Course with gradual "inline" mini assessments. Also, I find the University of ...


0

There are several classic books that provide preparation in calculus. James Stewart's Calculus (8th edition)  is one of the most widely used text books, covering the usual differential, integral, and multivariate calculus. Ron Larsons' Calculus is a popular alternative to Stewart, and covers similar material. I personally used Serge Lang's A First ...


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Starting with your Euler equation \begin{align} x^{2} y'' + \alpha x y' + \beta y &= y'' + \frac{\alpha y'}{x} + \frac{\beta y}{x^{2}} \\ &= 0 \end{align} we can see that our ODE will be undefined at $x = 0$ unless $$\frac{\alpha}{x} \ \ \ (1)$$ and $$\frac{\beta}{x^{2}} \ \ (2)$$ are analytic at $x = 0$. For example, if $\alpha$ and $\beta$ ...


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In Singapore math questions of this nature, they almost always preface the question statement with the phrase: "not drawn to scale". That phrasing might seem redundant, but in cases like this, it becomes so very important. Even if the figure is printed as a perfect square, the disclaimer that the figure is not to scale means that no conclusions at all ...


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Who is right? Is there a chance that we're both right? I don't have anything to add to what is already said in other answers. How should I handle this? I told my student that I would email the teacher, but I'm not sure that's a good idea. Take the high road. Unless your pupil is in a great danger (losing scholarship or similar), I ...


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I can't help but say something... As noted in other answers, this is clearly a trick question, playing on deliberately misleading visuals, and potentially on delicate (non-universal!) semantic conventions. (I am disturbed by the idea that, for example, a "square" is not a "rectangle", because, supposedly, "rectangle" only refers to (actual) rectangles that ...


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The answers are replying you your question #1, but not question #2. Who is right? Is there a chance that we're both right? How should I handle this? I told my student that I would email the teacher, but I'm not sure that's a good idea. As explained by other answers, you are right. Rather than feel humiliated, the student could explain why it ...


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It's a trick question. The answer, as you concluded, is a trapezoid. The figure is deliberately drawn to look like a square to fool the unwary. The best procedure to teach your student how to determine and prove such things for herself. Once she can prove to herself the figure is a trapezoid, your "reputation" is irrelevant. Math does not depend on ...


-5

One might also point out that a square is also a special case of trapezoid, rectangle, rhombus, quadrilateral and parallelogram, so any of those answers would technically be correct, assuming the object in question was, indeed, a square. However, I think what everyone is missing is that while in a classroom the "right" answer is the one the teacher is ...


6

Of course the mathematically correct answer is as the OP and others have stated. However, if you showed this drawing to an architect, engineer or carpenter they would probably assume that all sides are 9 inches - you don't usually indicate all measures, but assume that the missing lengths are equal to the opposite sides.


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In our 5th grade math group, our teacher came across this multiple choice problem that we thought about for a short period of time. We discussed the answer, which we concluded would be a trapezoid, square, or a rectangle. We also discussed what the tutor should do about this problem. We had varying answers, from the tutor having a conference with the teacher ...


38

The point is that mathematically, you can't tell from the picture. It might be this: It is easy enough to describe a construction of this with compass and straightedge, so it is definitely a legitimate geometric figure by any reasonable definition. The same "diagnostic test" from which this came (thanks to Barry Cipra for finding it) has numerous other ...


112

Of course, you are right. Send an email to the teacher with a concrete example, given that (s)he seems to be geometrically challenged. For instance, you could attach the following pictures with the email, which are both drawn to scale. You should also let him/her know that you need $5$ parameters to fix a quadrilateral uniquely. With just $4$ pieces of ...


1

I hope not! I graduated (last week) from a university that offered one semester of abstract algebra and one semester of real analysis as the highest division math courses. I will be attending a (fairly good, I think) graduate school in the fall. Of course, this doesn't help much but, I hope that where you come from does not affect your ability to succeed ...


3

The right vertical side of 9 inch is free to rotate about any of two vertices 1. upper-right vertex & 2. lower-right vertex without changing any of the conditions provided. This rotation shows that the quadrilateral is a trapezoid (having two right angles & two parallel sides not necessarily equal in length). Thus, the resulting figure (given ...


77

FWIW, this question appears to come from a diagnostic test which can be perused at http://www.mathmatuch.com/presentations/diagnostic_test.pdf -- where the official answer is given as J (the square). So it's not just the teacher who is wrong. (Remark: I found the site by googling on "identify the figure shown" and "trapezoid" then looking for "76" and "J" ...


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I agree with @davidgstork re: the first question. As for your second question, it's important to get the word out that it is a trapezoid, but you'll need to draw a few diagrams that actually show the trapezoids that conform to the conditions. (As they say on standardized tests all the time, just because it looks like a whatever, doesn't mean it ...


148

Clearly the figure is a trapezoid because you can construct an infinite number of quadralaterals consistent with the given constraints so long as the vertical height $h$ obeys $0 < h \leq 9$ inches. Only one of those infinite number of figures is a square. I would email the above statement to the teacher... but that's up to you. As for the "politics" ...


3

Reading, in pretty much any form, will almost always benefit you. Chances are you won't have a solid grasp on the material if you don't complete the problems, but this sort of reading will allow you to become informed about the larger ideas at play in various areas of mathematics and will help inform your future learning. It sounds like you'll end up taking ...


0

You might try looking for a book, or using an MOOC like the one at MIT or some other university.


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For your first question, it really depends. If you're going into a sub-branch of algebra, you will very likely have at least a little interaction with algebraic geometry. Knowing some of the basic ideas and terminology is useful, but if you were going to need much more than that, you would know it well in advance. If you are not going into algebra, but ...


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The books mentioned over here i think would help you and also with these books you can get an idea of what all stuff you require http://www.math.uiuc.edu/~schenck/grad.html


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As Gerry Myerson points out in a comment to your question, you should ask the appropriate people at your university. Since this is a late answer to your question, I hope you have already done so, but perhaps this answer will benefit others. Searching online for applied mathematics programs in biology reveals many courses (e.g. Brown University's Applied ...


2

You know, Exams are like tournament or competitions. Some people are great at practice but when they enter a championship, and feel under pressure, they under perform. I am telling you this because I am student athlete , and I did track and field for 4 years while doing my double major in computer science and mathematics. So with that being said, I highly ...


1

Sometimes, you do questions, you practice a lot but you don't get the same output. Don't care much about what you're getting as the output unless and until your input is in doubtful situation. Give it your best and the results will be shown, no matter the conditions be! Mathematics is a subject, which requires loads of practice and concentration while ...


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Depending on the size, you can ask questions. Questions are always welcome in smaller talks. If it's bigger, just listen, make notes of things you might want to discuss afterward either with other people there or the speaker. Why talks are so great is that you're actually THERE with the person who's supposedly an expert.



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