# Update

I’ve fallen into a bit of mathematical stagnancy since the first week or so of living here but after much ado, I’ve finally become regimented enough to start doing work and doing math and juggling other obligations, etc. etc.

What can I say? Moving is hard business!

Since falling off the mathematical (and career) wagon, I have managed to buy some new math books (uber sale; it’s my weakness) and to completely build a 95%-ish complete version of a new professional homepage which I hope to deploy within a week or so. As of a few days ago, I also managed to climb back on to the career (sans math) wagon, and as of today (well, yesterday; it’s 4:30am “tomorrow” for me right now), I also managed to do some low-key math with my BFF L. Hoping that pans out.

Later today, I’m going to head to IAS and spend the day doing math things and listening to postdocs talk about stuff I’ll likely never be mature enough to comprehend. Hoping this is day 1 of a lot of consecutive days of doing that and/or things like it. We’ll see.

Mathly yours…

# Update since the update

The last time I posted something meaningful here (not counting the 2014 year-in-review and the most recent claim of attempting necromancy), it was June 2014 and I was about to embark on a summer of traveling. Around that same time, my son was 21 months old, I was working part-time at Wolfram, and I was a pre-doctoral candidate whose academic situation had gone (apparently without being blogged about) from two doctoral advisors with two separate projects to a single advisor plus a second non-advisor faculty colleague.

Typing that out makes me realize how much has changed.

For those of you keeping score, it’s now August 2015, and 13 months after the last update, lots and lots of things have changed. For example, my son is now one month away from being three years old. There’s also a lot of professional stuff, too. Let’s go somewhat chronologically.

• I spent summer 2014 traveling.
• Afterwards, I was offered a full-time position at Wolfram as Math Content Developer. I accepted and took the year off from teaching.
• I landed a lead role in a really awesome math-related project at Wolfram.
• I went to a great conference at Yale and really enjoyed New England. New Haven is absolutely incredible.
• I passed my advanced topics exam (ATE) and became a doctoral candidate. My work was on Gabai’s colossal (first) work on Reebless foliations in 3-manifolds, and while I definitely learned more significant math than I’ve ever learned, I feel like there’s so much in that paper than I’m years away from understanding.
• I went to the Tech Topology Conference soon after becoming a candidate.
• Not long after, FSU had a pretty gnarly conference on Clifford analysis.
• I flew up to Baltimore to interview for an NSA gig. I didn’t get chosen.
• I went to the 40th annual spring lecture series at the University of Arkansas and had a complete blast. I ended up slipping on ice, busting my ankle up pretty badly, and having some travel woes near the end but when all was said and done, I met some cool people (Benson Farb, Allen Hatcher) and saw some really great talks. Oh, and great coffee!
• I went to Rhode Island College and gave an invited lecture on limit sets and computer visualization. It was an honor and I couldn’t have hoped for a better first invited lecture experience.
• I finished a pretty uneventful spring semester at FSU. Lots of work. Lots and lots of work.
• Once summer (2015) rolled around, I got accepted to some pretty great things:
• I was fortunate enough to be awarded a pair of scholarships from the FSU math department.

And now, here we are! It’s officially September 1 (1:07am now): That means Fall semester has started at FSU (which means I’m now a fourth year doctoral student; eek) and things are back in full swing. It never gets familiar, really, no matter how many times it happens. C’est la vie, I guess.

I’ve got a bunch of stuff going on, professionally:

• I’m still trying to make progress on my dissertation research (3-manifolds and, eventually, foliations).
• I’m studying Dirac operators / spin manifolds / hypercomplex structures / supermanifolds / miscellaneous things that seem to get more and more into the realm of theoretical physics as we progress. This is with my non-advisor faculty colleague.
• I’m trying to get a small research project going with an undergraduate at FSU on topological quantum computing (maybe Microsoft will take interest?).

Non-professionally, things have also happened. I got pretty serious into working out for a bit; later, I lost track due to travels, though I’ve since made some pretty considerable body transformations due to a healthier diet. I’ve also tuned back my Wolfram hours to give me more time to do student things; I’ve upgraded my workstations (desktop and mobile); I’ve made the switch from Windows to Linux (full-time rather than as a hobby)…

…that may actually be about it!

So there! Now we’re caught up! That means that I can pick up next time with an actual update / piece of newness / whatever. And who knows – maybe there will even be some math thrown in here! gasp

Good night, everyone.

PS: Oh! I was also introduced to Mnemosyne by a mathematician considerably better than myself! So far, I’m a pretty big fan.

# Random Update, or A Prologue to Travel

Okay, so I’m almost never around these parts anymore. That’s probably obvious to anyone who lands on the home page. Aside from “the random question regarding Hatcher problems” (read: the random pointing out of something very stupid I did when attempting to solve problems from Hatcher), I usually don’t receive many updates regarding this place either.

Truth be told: This place is essentially a wasteland. That makes me at least mildly sad.

I’d like to attempt to remedy that at least somewhat, and in order to attempt such an endeavor, I’ve brainstormed a plan. Before sharing, perhaps I should preface:

I’m about to be traveling quite a bit.

In particular, I’m going to be leaving on Friday (20 June) for approximately five weeks. My travels will include extensive bus rides that will land me in Ithaca, New York, Boston, Massachusetts, and Newark, New Jersey (en route to Staten Island, NY) and will include a variety of math- and computer science-related things.

Much excitement is expected on the professional front.

I figure this makes for at least a somewhat worthwhile opportunity to update this thing, though, since I could use it as a sort of travel diary. Truth be told, I’ve never traveled much, so I don’t know what exactly a travel diary entails; I figure I can come here, vomit out some photos and maybe a video diary or two, and hope that the inspiration I get by being surrounded by greatness will provide me the motivation to at least type up a summary entry or two on some fascinating stuff.

Long story short: Ostensibly, I should be able to post without having to rigorously type up mathematics I’m working on (or attempting to work on). That’s a win.

So yea…I’m at T-minus 51(ish) hours before my first bus departs. There’s lots to do, and so I won’t stick around here much longer. I will try to cough up a legitimate update, though; it’d be silly for me to start a travel diary without at least trying to piece together some sort of update on the journey behind the journey.

In the meantime, I hope this finds the internet in good spirits.

Yours in math,

C

So since coming back around here last week, I’ve been working on an update.

Of course, I’d be lying if I said I’d been working non-stop on an update, but I have, in fact, been working on one. I’d say I’m a solid 75% finished with it now, even though it’s (a) not going as quickly as I’d expected and (b) probably not going to be written the way I’d anticipated. Oh well; such is life, I guess.

I’m down to my last seven days of Wolfram employment, and to say I’m a sad robot is understatement of the year. I’m hoping the hustle and bustle of a new school term with new responsibilities and opportunities and excitements will curb that somewhat, but at this point, I’m not 100% convinced.

Among new things that have happened in the last week:

• FSU made office assignments for the new year. Apparently I’m staying put. As much as I’d have liked a new office (you know, since my CEILING COLLAPSED AND DESTROYED ALMOST EVERYTHING I HAD THERE(!!!)), I don’t like the hassle that comes with doing something new. I’ll already be doing enough new things; figuring out a new office situation isn’t something I want to add to that list.
• Fall schedules have been entered. I’m officially taking the third semesters of abstract algbera (field theory + categories, I think) and topology (advanced algebraic topology), as well as a course on complex manifolds (taught from an algebraic geometry perspective, I’d guess) and Riemannian manifolds. I’m excited. Sincerely.
• I’ve gotten my change of residency file 95% compiled. Monday will be the day to finish it off and submit it.
• I’ve finally started training for my new gig with Pearson. I’m less than thrilled with the progress so far. We’ll see.

Otherwise, things have been kinda the same: I’ve been doing a lot of Wolfram stuff, I’ve been taking more time away to hang with my family, and I’ve been somehow managing to not think about the nervousness I’ll invariably feel when new TA responsibilities, etc., pick up.

Things are good, I’d say, even though I’ve got a lot of things I need to start doing otherwise. I need to start reading the books potential advisers have suggested; I need to start doing more independent research; I need to start getting back in school mode.

For the first time in a really really long time, I’m enjoying being in not-school mode. I wonder if this is that changing tide I always heard so much about.

Anyway, expect a new content entry soon enough. And maybe some to follow that one. We’ll see.

Peace.

# Back again

So, I knew it had been a while since I’d been around here, and even longer since I’ve posted anything of substance. Little did I know, however, that it had been almost a month since I’d been around and almost two months since coming here and posting anything even remotely of substance.

That’s definitely not how I envisioned this blog thing going.

Here’s a small list of what I’ve been up to:

• I snagged that gnarly internship at Wolfram that I posted about back in the day. It saddens me to say that today is the beginning of week seven there; the contract I signed was for eight weeks which, as I’m sure you can deduce, means that my time is almost up. Never in my life have I done something that’s made me enjoy working as much as this internship has. I’ve loved every single second of it and just thinking about it ending makes me tear up a bit.
• I took a summer class in foundations of math. That class has already come and gone. We covered nonstandard analysis, basic set theory, cardinals, ordinals, and a bit of other stuff throughout, and despite the fact that the overall course wasn’t the most well-oiled, beneficial thing I’ve ever experienced, it was enjoyable overall. The workload was intense, though – like, seriously, intense – and there were weeks that that class + my TA duties + my Wolfram internship had me logging 120 hours of work. I’d be lying if I said I don’t enjoy hard work, though, and in this instance, it paid off: I managed to secure an A in this course and bring my overall graduate GPA up to 3.71. That’s a victory I’ll take.
• I applied and got passed over for a really gnarly graduate fellowship offered by my department. I was really excited leading up to it and was really really down afterwards. I haven’t thought about it since, though, so I guess that means it wasn’t too detrimental to my existence.
• I’ve been in frequent conversation with one of the professors in my department who I most admire and he’s helped me schedule a study-plan to better myself for the potential of working with him / working in his area. He does work in Geometric Topology but has expertise that spans lots of other areas, too, including dynamical systems, chaos, and geometric group theory. I’m hoping to have an adviser picked by the end of fall and as of now, he’s in my top-3. Working with him would be an honor, and that is in no way and overstatement.

There are many things missing from that list that sadden me a bit. For one, I got to spend very little time with my family over the break. I also got to spend very little time maintaining the independent studies I’d lain out and begun earlier in the summer. School starts back in just a couple weeks and one of the things I’m most glad about is being able to spend a little more time working towards that goal. I’m also pretty excited about my classes this semester, and about getting more acquainted with professors in the department so as to narrow down my list of potential advisers.

I’m excited about my career right now. That’s always a good thing.

I’m going to try to get myself back into the swing of updating here. Perhaps that’s something I can work on tomorrow, say, but there’re no promises.

Good night, WordPress. I hope this is delivered to peaceful eyes and rested minds.

Peace.

# Revisiting, and something light

Well, today was the fourth day of my official employment with Wolfram. This job is absolutely amazing; I couldn’t be more stoked. It’s saddening, of course, that I’m not spending my days engulfed in the books I’d been looking at earlier in the summer; it’s also a bit saddening that I have less time to spend with you beautiful people. Regardless, things are pretty amazing and overall, I couldn’t be happier.

I wanted to take some time to swing by here and say something, though, and fortunately for me, my TA duties this semester have yielded me something of precisely the right balance of depth (or lack thereof) and length (or brevity) to be fitting for tonight’s (this morning’s) pit stop.

On Wednesday (July 3), I was sitting in a precalculus class, doing Wolfram stuff and vaguely listening to what the instructor was talking about at the time. The topic? Logarithms. As someone who’s solo-taught precalculus before, I know precisely how little students understand – or like – or care – about logarithms. I also know how much we try to convince them to believe without their understanding which – among others – has to be a primary cause for their confusion and disdain.

One thing we try to get them to believe? The change of base formula. The change of base formula says that given a base $b>0$, $b\neq 1$, the quantity $\log_b(x)$ is equal to the quantity

$\log_b(x)=\displaystyle\frac{\log_c(x)}{\log_c(b)}$ where $c>0$, $c\neq 1$.

This information is shared with students at that level largely so they can feel comfortable evaluating an expression like $\log_{15}(31)$ in their calculators given only the capacity to utilize $\log(x)=\log_{10}(x)$ and $\ln(x)=\log_e(x)$ functionality. Surely, they never really need to know it.

And then I realized…

In all my years in mathematics, I’ve never actually seen this rule proven before. That, of course, sparked my interest, and so I went back to my office and jotted the (surprisingly simple) proof on my whiteboard just to appease my curiosity. Here’s the way that goes:

Proof of The Change of Base Formula.
Let $y=\log_b(x)$ so that $b^y=x$. In particular, then, it follows that for $c>0$, $c\neq 1$,

$\displaystyle\frac{\log_c(x)}{\log_c(b)} = \frac{\log_c\left(b^y\right)}{\log_c(b)}=\frac{y\cdot\log_c(b)}{\log_c(b)}=y=\log_b(x)$. $\square$

I think I may force my next round of precalculus students to know that. It keeps ’em fresh, on their toes, where they gotta baayayaeeee….

Did anyone just catch my reference to ‘Heat’? Or, rather, my reference to Aries Spears’ reference to ‘Heat’?

I hope everyone’s 4th was safe and that there were only minimal injuries due to inebriation, explosives, and general tomfoolery.

Until next time….

# The Alpha: Day 1 with Wolfram

So today, I officially began the first day of my summer-long journey through research internship with Wolfram. I’m probably going to remain sparse on the details of what I’m actually doing there – though interested parties can find some information here – but suffice it to say that it’s going to be awesome.

It’s going to be awesome, once all the technical hindrances get worked out. And yes, as of now, there are many technical hindrances. But that’s neither here nor there.

In my journey towards the apex of mathematical paradise, I’m forever acquiring (and seeking to acquire) access to resources I wouldn’t have been able to access otherwise. As of now, I’ve been an employee for about seven hours (maybe six) and already, I’ve found a really really cool resource because of my tenure there:

Behold, the Digital Mathematics Library.

So far, this place is a treasure trove of information – some new-ish, some archaic – and I can honestly say I’m beyond stoked.

Beyond stoked.

Perhaps we’re not as far from recognizing Terence Tao’s (and also Ingrid Daubechies’) vision of universal mathematical access.

Great minds, coming together to support the present and future of great minds.

Somebody pinch me.