Roy Goodman @roygoodman.net · 22/09/2026Is 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. 000
Roy Goodman @roygoodman.net · 28/07/2026It's a good book! People should buy it! Unlocking Justice from Princeton University Press. Available at all reputable bookstores! 000
Roy Goodman @roygoodman.net · 28/07/2026I managed to use my custom domain name as my Bluesky handle. It was straightforward once I found the specific instructions for @netlify.com sites. 001
Roy Goodman @roygoodman.net · 28/07/2026I 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? 000
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). 000
Roy Goodman @roygoodman.net · 23/06/2026A 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). 100
Roy Goodman @roygoodman.net · 23/06/2026Rotation 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. 200
Roy Goodman @roygoodman.net · 23/06/2026Since 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? 110
Roy Goodman @roygoodman.net · 23/06/2026When 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. 110
Roy Goodman @roygoodman.net · 23/06/2026Algebraic 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. 110
Roy Goodman @roygoodman.net · 23/06/2026Suppose A has a multiplicity-two eigenvalue λ, but only one eigenvector v. We say it has algebraic multiplicity 2, but geometric multiplicity 1. 110
Roy Goodman @roygoodman.net · 06/05/2026You may ask, “Why did Roy respond to my question about living an ethical life by telling you about a sitcom he liked?” 000
Roy Goodman @roygoodman.net · 06/05/2026We'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. 000
Roy Goodman @roygoodman.net · 21/04/2026Who am I going to believe? You or the always intellectually rigorous Bret Stephens? 🤔 www.nytimes.com/2026/04/21/opinion/… 000
Roy Goodman @roygoodman.net · 09/02/2026The links that lead to the PDF of the article and the templates are broken. 💔 100
Roy Goodman @roygoodman.net · 21/01/2026Very 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? 010
Roy Goodman @roygoodman.net · 08/01/2026Wow, 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. 000
Roy Goodman @roygoodman.net · 07/01/2026What a bizarre take! I don't know where to begin with this one. I'm glad that you. Look forward to your piece. 000
Roy Goodman @roygoodman.net · 16/09/2025It's been in my bookmarks folder since the Netscape era. I just deleted it. Thanks for the reminder. 020
Roy Goodman @roygoodman.net · 17/05/2025I taught numerical PDE this semester. This was on the whiteboard on his 99th birthday: 000
Roy Goodman @roygoodman.net · 17/05/2025www.nytimes.com/2025/05/16/s...nytimes.comPeter Lax, Pre-eminent Cold War Mathematician, Dies at 99 130
Roy Goodman @roygoodman.net · 10/05/2025It's even better. It's DLA: arxiv.org/abs/2504.13400arxiv.orgDiffusion Limited Aggregation in Ants Biting off Wall PaintDiffusion 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... 110
Roy Goodman @roygoodman.net · 26/04/2025Math/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.netroygoodman.netRoy GoodmanRoy Goodman is a professor and Associate Chair for Graduate Studies in the Department of Mathematical Sciences at NJIT 000
Roy Goodman @roygoodman.net · 27/03/2025Tagging 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 140
Roy Goodman @roygoodman.net · 19/03/2025I carved these wooden Möbius strips and keep them in my office to fidget with and show to visitors. 100
Roy Goodman @roygoodman.net · 13/12/2024So, 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.netThe Pi-Search PageSearch for any string of digits in the first 200 million digits of Pi 1171
Roy Goodman @roygoodman.net · 02/12/2024I 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.orgThe Number Devil - Wikipedia 020
Roy Goodman @roygoodman.net · 15/11/2024I 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. 000
Roy Goodman @roygoodman.net · 16/09/2024No 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. 110
Roy Goodman @roygoodman.net · 15/09/2024It has been like this since they opened the stop at EWR 2+ years ago. 110