Michael Joyce

New Orleans, LA

math.tulane.edu/~mjoyce3

Age: 37

I am interested in algebraic combinatorics, especially in the combinatorics of orbits of a Borel subgroup on spherical varieties.
May
16
comment Exercise 1.2 in Hartshorne Chapter I
$ - $ w $ + $ rt.
May
10
answered Strongly convex cones
May
7
comment Language as a barrier to learn math
Your second point reminds me of one of my favorite jokes / observations. A linguistics professor is giving a lecture about the variation of double negatives in different languages. To add some spice to his lecture, he concludes with, "But, of course, in no language does a double positive become a negative." One of the student pipes up in the back and says, "Yeah, right."
May
6
comment When $-x$ is positive
I had the opportunity to hear one Serge Lang lecture, during which he went on a five-minute tirade on the distinction between 'negative' (a unary operation) and 'minus' (a partially defined binary operation), including his complete displeasure at how commonplace it is for people to misuse one term or the other.
May
6
comment Rationale for not dividing both sides of an equation by $x$ (ex: $6x^2 = 12x$)
While I agree with Mark Fantini and Richard that the factoring method is preferable to the divide into two cases method, I strongly agree with benblumsmith that students should learn to become robust in their approach to mathematics. Ideally, students should learn both methods and understand why they are consistent with each other. That can help to reinforce the underlying algebraic principles involved.
May
6
awarded Yearling
May
4
comment Surface Integral, Stokes Theorem, Divergence theorem
Sorry, yes according to your terminology, the above comment was an interpretation of an integral with respect to surface area. It refers to a surface $S$ in 3-dimensional space.
May
4
comment Surface Integral, Stokes Theorem, Divergence theorem
The surface integral $\iint_S f(x,y,z) \, dS$ gives the total mass on a 2-dimensional surface $S$ if the mass density (per unit area) at the point $(x,y,z)$ on $S$ is given by $f(x,y,z)$.
Apr
29
awarded Commentator
Apr
29
comment Teaching a very enthusiastic and bright 5 year old
How about teaching to make a "bank" (with some loose change) as a way to teaching him negative numbers? He can keep track of "deposits" and "loans".
Apr
28
comment Union of the two coordinate axes in $\mathbb{R^2}$ - From the book '' Differential Topology '' of Guillemin and Pollack
In general, it is better to respond with a comment to an answer rather ask a question about an answer in a different answer. But I'm glad from your other answer that you've figured the problem out.
Apr
28
revised Union of the two coordinate axes in $\mathbb{R^2}$ - From the book '' Differential Topology '' of Guillemin and Pollack
added 7 characters in body
Apr
28
answered Union of the two coordinate axes in $\mathbb{R^2}$ - From the book '' Differential Topology '' of Guillemin and Pollack
Apr
28
comment Are there any benefits to having an entire course's homework problems available from day one?
I find what works best for me in service courses is to pass out a list of all homework problems for the semester, organized by the section of the textbook from which they come. Then each week, I assign which sections students must do problems from for the following week. This gives me the flexibility to adapt the schedule to whatever pace we have (and deal with things like class cancellations that happen unexpectedly from time to time due to weather or other circumstances), but it also allows the student to know what is coming and to work ahead if they anticipate the need to do so.
Apr
27
comment Issues with "equals", where does this come from and how do I combat it?
So early curriculum often treats equality as operational = students learn to think of equality as operational = students write nonsensical answers in college because they lack a conceptual understanding of equality? ;)
Apr
23
comment Blow-up toric varieties.
I think your suggestions are great, but, at least for #1, it may be better to start with affine space rather than projective space, depending on the sophistication level of the audience.
Apr
22
revised Linear Algebra Proof confirmation
edited title
Apr
20
revised Bourbaki - Algebra Chapter IV - Section 6, Exercise 9(b)
fixed LaTex formatting
Apr
17
comment What is a fair way of constructing exams with tiered levels of difficulty?
Are they only to do a total of 6 out of the 18 problems in your example test?
Apr
14
comment books well-motivated with explicit examples
There is also Silverman and Tate's "Rational Points on Elliptic Curves" which is even more explicit and introduces the subject to undergraduate students.
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