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1500 questions
23
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8 answers
What is a good reason to change calculus texts?
Our college is switching to an Early Transcendentals calculus text, and this seems like a good time to consider which text we are using in general. Larson, Stewart, Thomas, Briggs/Cochran, etc are all on the table.
However, the books we have no…
Chris Cunningham
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1 answer
Where does the word "roots" come from when talking about zeros
We often use the word roots when referring to the solutions of an equation. For instance, when we have a polynomial $P(x)$, we call its zeros the roots of $P(x)$.
For some polynomials we can relate the zeros with a root function of some kind, say…
Jean-Sébastien
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23
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13 answers
Historical tidbits to liven up calculus classes
What are some examples of math history that can be mentioned in calculus classes, either to liven things up or to provide additional perspective / insight on the material being learned?
For example, when discussing complex numbers, one might tell…
littleO
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Is the reciprocal function continuous?
I'm curious the views of those who teach calculus.
As you know the continuity of a function at a point is defined in terms of the limit in the typical course. I'd like to ask a pair of questions:
Consider $f(x)=1/x$. Is $f$ continuous ?
Let…
James S. Cook
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23
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9 answers
The definition of natural log and e
I'm asking this question from the point of view of an introductory non-rigorous calculus instructor. Calculus textbooks have different approaches about how to define $e$ and $\ln$. For example, my current textbook defines $e$ as the number such…
Chris Cunningham
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23
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9 answers
"A computer program IS a proof": Introducing rigor via programming
This provocative essay
Igor Rivin.
"Some Thoughts on the Teaching
of Mathematics—Ten Years Later."
Notices of the AMS, Jun/Jul 2014.
(PDF download link).
suggests that a discussion of Igor's "principle":
A computer program IS a…
Joseph O'Rourke
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23
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3 answers
What are the differences between graduate and undergraduate classes, relevant to course design and teaching?
I will be a postdoc in the fall and will be teaching my very first classes aimed at graduate students. One will be an intro class, and the other a topics class.
There are of course many differences between undergraduate and graduate courses. I'm…
Aru Ray
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How can we handle grocery store/bus stop conversations better?
When chatting with a new acquaintance for a few minutes, our profession often comes into the conversation and then takes over. We're all familiar with this line at grocery stores, airplanes, trains, and more.
MATH? Oh, I was never a math…
Chris Cunningham
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23
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2 answers
Teaching and "The Two Cultures"
This is a rather broad (and perhaps too philosophical) question about undergraduate and graduate mathematics education.
Gowers, in his article "the two cultures of mathematics", observes differences between the problem solving and theory building…
Jon Bannon
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23
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What are some good low-prerequisite examples for the heuristic advice "If you cannot prove it, prove something stronger."?
One useful trick in mathematics is to prove something stronger instead of the question asked.
This works well in induction proofs (because strengthening the claim also strengthens the induction basis):
Example: Prove $\frac1{1\cdot 2} +…
user11235
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23
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9 answers
Why do we teach the Rational Root Theorem? (high school algebra 2)
Main question: Does anyone have any good/interesting applications of the rational root theorem or ways to teach it that don't involve conveniently ignoring computer-based tools in order to avoid rote checking of long root candidates lists?
Longer…
Cassius12
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2 answers
Can we avoid confusion over using "let" as a quantifier?
I've encountered the following misunderstanding.
I pose a question (to undergraduates in the U.S.), for example:
Let $P$ be a polygon of $n$ vertices.
Is it true that every triangulation of $P$
has the same number of triangles?
This question…
Joseph O'Rourke
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23
votes
5 answers
Why are the contents of contest maths so different from contents of degree-level maths?
I wonder why topics examined in high school math contests are so different from the maths learned by those who are seriously studying a math major at a university. Firstly, contests like IMO, ARML, AMC and most of the others seem to focus on a very…
Ma Joad
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Dyscalculia and studying mathematics (as major)
I am a bit afraid to ask this, but the question has bothered me for some time now. I have a student in my analysis class having a medical certificate of dyscalculia. This entitles her to write tests and exams in a special environment and using extra…
András Bátkai
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23
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3 answers
What can be said about Lie groups in a first abstract algebra course?
Lie groups are among the most important examples of groups in mathematics and physics, but they are rarely discussed in introductory undergraduate abstract algebra courses, which tend to focus on finite groups.
Partially, this is because you can't…
Jim Belk
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