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Roy Goodman

@roygoodman.net
46 followers 104 following 45 posts

Mathematician, Professor, Director of Graduate Studies NJIT Math, Founding President SIAM New York-New-Jersey-Pennsylvania section, nonlinear dynamics of waves & vortices, LaTeX nit-picker, sometime spoon carver, lesser of two weevils

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Roy Goodman @roygoodman.net · 22/09/2026
Is there a plan to deal with the corner of Atlantic and 6th/Portland? This corner becomes a complete logjam whenever there's an event at the Barclays Center. This will ensnare the bus, too, if they don't make changes.
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Roy Goodman @roygoodman.net · 11/09/2026
I signed.
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Roy Goodman @roygoodman.net · 06/08/2026
We have a very specific education!
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Roy Goodman @roygoodman.net · 06/08/2026
Buckingham's Pi Theorem!
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Roy Goodman @roygoodman.net · 28/07/2026
It's a good book! People should buy it! Unlocking Justice from Princeton University Press. Available at all reputable bookstores!
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Roy Goodman @roygoodman.net · 28/07/2026
I managed to use my custom domain name as my Bluesky handle. It was straightforward once I found the specific instructions for @netlify.com sites.
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Roy Goodman @roygoodman.net · 28/07/2026
I got my copy of @chadtopaz.bsky.social's book! Hey, author friend! How does COMPAS actually compute its score? Is it just an arbitrary weighted average of risk factors like Consumers Reports does for washing machines, or is there more sophisticated (if biased) math under the hood?
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Roy Goodman @roygoodman.net · 24/07/2026
What's SQ?
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Roy Goodman @roygoodman.net · 23/06/2026
(Left) multiplication of a vector v= (x; y) by A is equivalent to multiplying exp(i θ) (x+ i y).
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Roy Goodman @roygoodman.net · 23/06/2026
A is orthogonal in that tranpose(A) = inverse(A), but B is not. A rotation matrix must be orthogonal. For 2x2 matrices, this implies A=[cos θ, sin θ; -sin θ, cos θ]. This rotates the plane by θ in the positive (counterclockwise sense).
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Roy Goodman @roygoodman.net · 23/06/2026
Rotation and imaginary eigenvalues are related but not identical. Think about the matrices A=[0 1;-1 0] and B = [0 2; -1/2 0]. Both have eigenvalues ±i, but only A is a rotation. You should be able to convince yourself that multiplication by A preserves a vector;s length, but this is not true for B.
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Roy Goodman @roygoodman.net · 23/06/2026
Since y and v were linearly independent (which I didn't mention before), then any vector z ∈ span(v,y), but (A-λI) z ∈ span(v), i.e. (A-λI) z = c v for some c. So the range of (A-λI) is one-dimensional. Is that what you were looking for?
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Roy Goodman @roygoodman.net · 23/06/2026
Therefore, while y is not an eigenvector, (A-λI)y is.
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Roy Goodman @roygoodman.net · 23/06/2026
When algebraic multiplicity exceeds geometric multiplicity, we can then talk about a generalized eigenvector y. This satisfies (A-λI)^2 y = 0, but not (A-λI)y = 0. If we let w=(A-λI)y, then (A-λI)w = (A-λI)^2 y = 0. So, w is an eigenvector, and hence a scalar multiple of v.
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Roy Goodman @roygoodman.net · 23/06/2026
Algebraic multiplicity 2 means that the characteristic polynomial p(x) = (x-λ)^2. Geometric multiplicity 1 means that the dimension of the eigenspace of λ is one, i.e., that if w and v are both eigenvectors, then w is a scalar multiple of v.
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Roy Goodman @roygoodman.net · 23/06/2026
Suppose A has a multiplicity-two eigenvalue λ, but only one eigenvector v. We say it has algebraic multiplicity 2, but geometric multiplicity 1.
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Roy Goodman @roygoodman.net · 18/05/2026
@courtwatchnyc.bsky.social
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Roy Goodman @roygoodman.net · 06/05/2026
You may ask, “Why did Roy respond to my question about living an ethical life by telling you about a sitcom he liked?”
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Roy Goodman @roygoodman.net · 06/05/2026
It's our third time through! We never rewatch anything.
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Roy Goodman @roygoodman.net · 06/05/2026
We're re-watching The Good Place with the 11-year-old. Takeaway: it's hard! Also, so much inappropriate stuff we hope he's missing.
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Roy Goodman @roygoodman.net · 21/04/2026
Who am I going to believe? You or the always intellectually rigorous Bret Stephens? 🤔 www.nytimes.com/2026/04/21/opinion/…
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Roy Goodman @roygoodman.net · 09/02/2026
The links that lead to the PDF of the article and the templates are broken. 💔
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Roy Goodman @roygoodman.net · 21/01/2026
Very rarely, my hands feel dry enough to outweigh my dislike of the greasiness of lotion on my hands. We're in Prague on sabbatical, and it's cold and dry, and my fingers are splitting open. How do you do it?
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Roy Goodman @roygoodman.net · 08/01/2026
Wow, you can turn off the snark when you need to! Great piece. You applied a standard of critical and quantitative thinking that you never see from people who are paid by billionaires to make up reasonable-sounding arguments for their nonsense.
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Roy Goodman @roygoodman.net · 07/01/2026
What a bizarre take! I don't know where to begin with this one. I'm glad that you. Look forward to your piece.
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Roy Goodman @roygoodman.net · 12/11/2025
#mathsky
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Roy Goodman @roygoodman.net · 16/09/2025
It's been in my bookmarks folder since the Netscape era. I just deleted it. Thanks for the reminder.
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Roy Goodman @roygoodman.net · 13/08/2025
📌
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Roy Goodman @roygoodman.net · 17/05/2025
I taught numerical PDE this semester. This was on the whiteboard on his 99th birthday:
A whiteboard with the words "Lax Wendroff" and the iteration formula for the Lax Wendroff method applied to a nonlinear advection equation.
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Roy Goodman @roygoodman.net · 17/05/2025
#mathsky 🧮
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Roy Goodman @roygoodman.net · 17/05/2025
www.nytimes.com/2025/05/16/s...
nytimes.com
Peter Lax, Pre-eminent Cold War Mathematician, Dies at 99
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Roy Goodman @roygoodman.net · 10/05/2025
It's even better. It's DLA: arxiv.org/abs/2504.13400
arxiv.org
Diffusion Limited Aggregation in Ants Biting off Wall Paint
Diffusion limited aggregation (DLA) is a well studied phenomenon in which diffusing particles cumulatively aggregate on a starting fixed seed point, forming a pattern which is fractal in structure. He...
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Roy Goodman @roygoodman.net · 26/04/2025
Math/typesetting/BlueSky geek post: I finally figured out how to get the BlueSky icon in my HugoBlox-based homepage, and removed the link to my deleted account on that other site. roygoodman.net
roygoodman.net
Roy Goodman
Roy Goodman is a professor and Associate Chair for Graduate Studies in the Department of Mathematical Sciences at NJIT
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Roy Goodman @roygoodman.net · 27/03/2025
#MathSky
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Roy Goodman @roygoodman.net · 27/03/2025
Tagging for 🧮. Every year I read the citations and the popular press writeup and learn a bit about math outside my area. In this one, the citation admits, "Yes, this is very technical," and I still don't feel I know what he's done. Can anyone communicate this better? Maybe @stevenstrogatz.com
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Roy Goodman @roygoodman.net · 24/03/2025
That sounds great. Please share a link.
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Roy Goodman @roygoodman.net · 19/03/2025
I carved these wooden Möbius strips and keep them in my office to fidget with and show to visitors.
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Roy Goodman @roygoodman.net · 13/12/2024
So, this must be pi. I googled "search for a string of digits of pi" and found the page below which informs me that 04437805 appears in pi at position 7642 after the decimal point and agrees with your window shade beyond that. www.angio.net/pi/
angio.net
The Pi-Search Page
Search for any string of digits in the first 200 million digits of Pi
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Roy Goodman @roygoodman.net · 02/12/2024
I have read the "The Number Devil" by Hans Magnus Enzensberger with both my kids, and they've read it countless times by themselves afterward. I've looked and looked for another book like this, but have found nothing else comes close. en.wikipedia.org/wiki/The_Num...
en.wikipedia.org
The Number Devil - Wikipedia
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Roy Goodman @roygoodman.net · 15/11/2024
I have always wanted to propose a SIAM mini symposium on the theme of Applied Mathematicians who go by their middle name. I could easily fill three sessions.
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Roy Goodman @roygoodman.net · 19/09/2024
What about @guprofbc.bsky.social ?
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Roy Goodman @roygoodman.net · 16/09/2024
No transit expertise, just a frustrated user. The Northeast Corridor trains have been clustered this way 7 days a week as long as I've been riding both weekdays and weekends, but weekends are worse.
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Roy Goodman @roygoodman.net · 15/09/2024
20+
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Roy Goodman @roygoodman.net · 15/09/2024
It has been like this since they opened the stop at EWR 2+ years ago.
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Roy Goodman @roygoodman.net · 08/06/2024
@guprofbc.bsky.social
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