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1500 questions
17
votes
11 answers
Natural occurrences of a to the (b to the c)?
Are there some natural contexts in which a double exponential occurs,
$x$ to the ($y$ to the $z$):
$$
x ^ {(y ^ z)} \;, \textrm{or} \;, a ^ {(b ^ c)} \; \textrm{?}
$$
Of course one can contrive many problems that ask computational questions…
Joseph O'Rourke
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17
votes
4 answers
What are some of the open problems that can be suitably introduced in a calculus course?
I feel it may be a good idea to introduce some related open problems in a calculus course. Surely I am not expecting my students to solve any one of them, though I cannot say it is absolutely impossible; but I think it is good to let the students…
Zuriel
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17
votes
5 answers
(How) Do American undergraduate math programs teach complex numbers?
What kind of exposure to complex numbers can you expect in mathematics majors at American colleges?
I teach at a very large public university. It occurred to me that it is possible to graduate in their math majors with the exposure to complex…
shuhalo
- 443
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17
votes
1 answer
Research supporting "recipe-style" calculus in senior high school?
Anecdotally, I've heard it said that in (Australian) grades 11 and 12 calculus needs to be taught in a procedural way involving merely recipes for doing calculus, rather than teaching for understanding common in lower grades.
In primary school…
pdmclean
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17
votes
5 answers
How do you revise?
I'm not too sure if this is the right place for my question, but I couldn't think of anywhere more suited.
I am a first year university Math student, I am currently revising for six end of year examinations. My problem is that I am struggling to…
Mark
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17
votes
9 answers
How important is knowledge of trig identities for use in Calculus
I have a question regarding tutoring a calculus student. They need to prove trig identities such as $$\frac{1}{1-\sin x}+\frac{1}{1+\sin x}=2\sec^2x.$$ Doing this kind of problem is very tedious and time consuming. Is it really so necessary to focus…
Burt
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17
votes
5 answers
Would a 1990's educated person need additional content knowledge to tutor high school mathematics today?
Have there been any major content (not pedagogical) changes in the basic US high school mathematics curriculum since the mid-1990's? More specifically, if I wanted to become a tutor of high school math today as someone who learned his…
Robert Columbia
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17
votes
4 answers
What is the motivation for characterizing second order linear PDEs as hyperbolic, elliptic, or parabolic?
I'm teaching an Intro to PDEs course (I'm an analyst, but PDEs are a bit outside my bailiwick) and I'm covering the basic examples: Heat, Wave, and Laplace. How should I move from these examples to motivate the definitions of hyperbolic, elliptic…
Ben Willson
- 301
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17
votes
6 answers
How to deal with a "protest" assignment?
I just received one assignment (by email) from a student. Out of 6 questions, "I don't know" is the answer to 4 of them.
There is also a comment at the end of the assignment which suggests
my lectures are not helpful for solving problems
I am…
user11702
17
votes
2 answers
"Always/Sometimes/Never" vs. "True/False" questions for mathematical reasoning
Has anyone performed a study on the differences between student interpretations of these words?
Background: When I taught high school geometry and later undergraduate precalculus, I noticed that even when explicitly taught how to read and interpret…
Opal E
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17
votes
2 answers
Why do most of the books in mathematics not include answers?
I am currently going through the Topics in Algebra by I.N. Herstein. The problems are pretty good, but there are no answers. The same is the case with Mathematical Analysis by Rudin.
Why is this?
Even though some would argue that it robs the…
tattwamasi amrutam
- 343
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17
votes
8 answers
"Real world" examples of implicit functions
When teaching implicit differentiation in freshman calculus I lack good examples which might help students relate the theory to applications in other sciences.
So I'm looking for (relatively simple) examples from physics/engineering/life…
Michael Bächtold
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17
votes
4 answers
Making solutions to all problems freely available
I teach at a community college, almost all physics but also a math course now and then. My current practice is that I assign homework worth a very small number of points (1 point per problem, as opposed to about 20-25 points per problem on exams),…
user507
17
votes
7 answers
Unique steps leading to a non-unique answer
When asked to show a math problem has a unique solution, students sometimes think that if an algorithm leading to a solution has unambiguous instructions at each step (no need to make choices at any point) then the solution they find has to be the…
KCd
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17
votes
8 answers
Examples of basic non-commutative rings
I am teaching an intro to ring theory, and after grading the first quiz, I realize most of my students are under the assumption that rings must be commutative. I have given them the example of matrices over the reals, but clearly we need to spend a…
David Steinberg
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