Comment author: cursed 11 February 2014 08:33:42PM *  4 points [-]

I'm interested in learning pure math, starting from precalculus. Can anyone give advise on what textbooks I should use? Here's my current list (a lot of these textbooks were taken from the MIRI and LW's best textbook list):

  • Calculus for Science and Engineering
  • Calculus - Spivak
  • Linear Algebra and its Applications - Strang
  • Linear Algebra Done Right
  • Div, Grad, Curl and All That (Vector calc)
  • Fundamentals of Number Theory - LeVeque
  • Basic Set Theory
  • Discrete Mathematics and its Applications
  • Introduction to Mathematical Logic
  • Abstract Algebra - Dummit

I'm well versed in simple calculus, going back to precalc to fill gaps I may have in my knowledge. I feel like I'm missing some major gaps in knowledge jumping from the undergrad to graduate level. Do any math PhDs have any advice?

Thanks!

Comment author: ricketybridge 12 February 2014 02:46:59AM *  1 point [-]

For what it's worth, I'm doing roughly the same thing, though starting with linear algebra. At first I started with multivariable calc, but when I found it too confusing, people advised me to skip to linear algebra first and then return to MVC, and so far I've found that that's absolutely the right way to go. I'm not sure why they're usually taught the other way around; LA definitely seems more like a prereq of MVC.

I tried to read Spivak's Calc once and didn't really like it much; I'm not sure why everyone loves it. Maybe it gets better as you go along, idk.

I've been doing LA via Gilbert Strang's lectures on the MIT Open CourseWare, and so far I'm finding them thoroughly fascinating and charming. I've also been reading his book and just started Hoffman & Kunze's Linear Algebra, which supposedly has a bit more theory (which I really can't go without).

Just some notes from a fellow traveler. ;-)

Comment author: ricketybridge 12 February 2014 02:40:07AM 4 points [-]

Sometimes I feel like looking into how I can help humanity (e.g. 80000 hours stuff), but other times I feel like humanity is just irredeemable and may as well wipe itself off the planet (via climate change, nuclear war, whatever).

For instance, humans are so facepalmingly bad at making decisions for the long term (viz. climate change, running out of fossil fuels) that it seems clear that genetic or neurological enhancements would be highly beneficial in changing this (and other deficiencies, of course). Yet discourse about such things is overwhelmingly negative, mired in what I think are irrational kneejerk reactions to defend "what it means to be human." So I'm just like, you know what? Fuck it. You can't even help yourselves help yourselves. Forget it.

Thoughts?

Comment author: adbge 11 February 2014 06:30:24PM *  1 point [-]

It sounds like you're saying that my aversion to failing at something else is irrational. Would you mind pointing out the error in my reasoning? (This sort of exchange is basically cognitive behavioral therapy, btw.)

Many of the things that you have said are characteristic of the sort of disordered thinking that goes hand-in-hand with depression. The book Feeling Good: The New Mood Therapy covers some of them. You may want to try reading it (if you have not already) so that you will be able to recognize thoughts typical among the depressed. (I find some measure of comfort from realizing that certain thoughts are depressive delusions and will pass with changes in mood.)

As a concrete example, you said:

I'm just not smart or hard-working enough to do anything more interesting than pushing paper (my current job).

These are basically the harshest reasons one could give for failing at something. They are innate and permanent. An equally valid frame would be to think that some outside circumstance was responsible (bad economy, say) or that you had not yet mastered the right skill set.

Comment author: ricketybridge 11 February 2014 11:51:53PM *  0 points [-]

I am thoroughly familiar with Feeling Good and feel that I can argue circles around it. My original statement (that I'll fail at everything) is an example of "overgeneralization" and "fortune telling." But this sounds to me like just a way of stating the problem of induction: nothing can ever be certain or generalized because we don't know what we don't know etc. etc. However, science itself basically rests on induction. If I drop a steel ball (from the surface of this planet), will it float, even if I think positively really hard? No. It won't. Our reason makes conclusions based on past evidence. If past evidence suggests that attempts lead to failure, why ISN'T it reasonable to assume that future attempts will lead to failure? Yes, the variables will be different, I guess, but it's still a gamble. If you think I should give it a go anyway, then you may as well advise me to buy lottery tickets, imo. And I just can't dredge up the sufficient motivation to pursue something with chances like that.

An equally valid frame would be to think that some outside circumstance was responsible (bad economy, say) or that you had not yet mastered the right skill set.

Kind of funny that you suggest blaming external forces instead of taking personal responsibility, but okay. I would say the latter is the case for me: I did not master the sufficient skill set, even after ten years or whatever. The people who are successful in my field do so MUCH earlier. So, okay, I didn't master the right skill set. I don't see how that's supposed to make me feel any better. It doesn't change my shitty situation. And it only makes me question, well why didn't I? I wanted to; I attempted to. Clearly, I did something wrong. I either don't have sufficient talent at my field or talent at learning to have mastered those skills.

But those are innate and permanent traits, which you (and many others) apparently consider invalid, which I don't really get, but I'll accept it for the moment. So due to non-innate and temporary faults, I failed to achieve my objectives. Again, how is this supposed to make me feel better? Because I'm supposed to believe those faults have mysteriously vanished, or I can work to improve them? Even if that's so, the rewards that are reasonable to expect from attempting to improve them seem so minimal at this point that, again, it doesn't seem worth bothering about. I'm willing to concede that this is depressive thinking, but it seems to me more like a difference of opinion than disordered reasoning: some people think hard work with little reward or low chance of a big reward is fun; I do not. It's no different that my hating a movie you like and vice versa.

Comment author: btrettel 11 February 2014 05:53:59PM *  2 points [-]

I agree with Lumifer that your priority should be treating your depression. Also, consider that your depression likely is making you pessimistic about your prognosis.

For about 5 or 6 years I had a treatment resistant fungal infection. I had to try 6 different antifungals until I found one that had some effect, and I tweaked the dosage and duration for most of those to try to make them work better. The last medication I tried didn't work completely the first time, so I increased the dosage and duration. That totally wiped out the fungus. If you asked me if I ever thought I'd get rid of the fungal infection 6 months before I finished treatment, I'd have said no.

Knowing which antifungal medications didn't work actually was the key to figuring out what did work. My doctor selected an antifungal medication which used a mechanism different from that of any other treatment I tried. I suggest that you look at which mechanisms the drugs that you have tried use and see what other options exist. There are many more depression treating drugs than antifungal drugs, and many more mechanisms.

You mentioned a few other non-pharmaceutical options you've considered. If you haven't already considered it, I might suggest exercise. There seems to be reasonable evidence that exercise helps in depression. Anecdotally, I've read of several people who have claimed that running in particular cured their depression when nothing else provided much help. (I've suggested this to others before, and they generally think "That'll make me feel worse!" People generally seem to discount the idea that as they get into better shape, exercise will become easier, enjoyable even.)

Comment author: ricketybridge 11 February 2014 11:14:02PM 0 points [-]

consider that your depression likely is making you pessimistic about your prognosis.

Yes, I've heard this before, but I don't see why any reasonable, non-depressed person would be pessimistic about it. As I've said, it's not like this is the first time I've ever been depressed in my life and I'm irrationally predicting that I can't be cured. And I've heard stories like yours before: people who were depressed until they found the right combination of medications. But in my situation, my psychiatrists have gone back and forth between different combinations and then right back around to the ones I already tried. Changing them up YET AGAIN just feels like shuffling the deck chairs around on the Titanic (but of course I'd say that). If there are tons more different medications to try as you assert, none of my psychiatrists seem to know about it.

To be fully clear, anti-depressants have had an effect on me. I definitely don't feel unbearably miserable and anxious as I do without them. They just haven't gotten me to 100%.

I GUESS I could ask my psychiatrist to try yet another combination I haven't tried before. But it just sounds like a nuisance, frankly.

As for exercise, yes, I've heard that countless times. I used to be much more active, and don't recall it ever having a palpable effect on my mood. Nowadays, it's just not gonna happen. I've tried to get myself to exercise, with some occasional success, but with my work schedule, when it finally comes time to do it, I flatly refuse. You could say, "you just gotta find something you enjoy!!" But I'm depressed! I enjoy nothing! (/sarcasm) I guess I could make sure to make time for hiking (probably what I enjoy the most) or get a membership at an expensive gym near work (which would be the most convenient arrangement for me) but the fact that exercise never particularly had an effect on me makes me not particularly motivated to do so.

Comment author: hyporational 11 February 2014 10:18:27AM 0 points [-]

What side effects make ECT worse for you than depression and the risk of death? Have you looked into ketamine trials?

Comment author: ricketybridge 11 February 2014 10:41:34PM 0 points [-]

I asked that of someone else when they made the same statement about ECT. The most common side effect is memory loss. You prompted me to look into the details, and I guess I wouldn't mind losing a couple months of memory (usually the only permanent effect). However, the jury appears to be out on ECT as well, so it may not even be worth it.

I actually looked at that exact website you linked to about ketamine. I'm all for it! However, all those studies are also across the country from me. Although you could say that quitting my job and staying across the country for 2 months is worth the chance of treating my depression, I'm not certain that the possible benefits outweigh the risk of being unemployed, and potentially for a long time, given the current labor market. After all, I could end up just in the control group and have no treatment at all, or the treatment could be ineffective.

Also, just for the sake of clarity, I was wrong: I'm actually not clinically depressed; I have dysthymia, which is a chronic low-grade depression (i.e. I can still function, go to work, seem normal, etc.). Maybe this is why none of my psychiatrists have recommended ECT, even when I was suicidal? Idk.

Comment author: Lumifer 11 February 2014 03:46:34AM 4 points [-]

it sounds like you're saying that my aversion to failing at something else is irrational.

That's really irrelevant at this point. If you are clinically depressed, this is sufficient to explain both your failures and your lack of belief in your ability to succeed.

I am not a doctor and don't want to give medical advice, but it seems to me that getting your depression under control must be the very first step you need to take -- before you start thinking about new careers.

Comment author: ricketybridge 11 February 2014 04:04:58AM 0 points [-]

If my depression does explain my failures, then I really am pretty much destined to fail in the future since this appears to be treatment-resistant depression and as I described, I've run out of treatment options. Thanks anyway.

Comment author: Lumifer 11 February 2014 02:21:19AM 3 points [-]

Yes, I am definitely clinically depressed

So, um, don't you want to try to fix that? Until you do your judgement of your own capabilities is obviously suspect, not to mention that your chances to succeed are much diminished.

Comment author: ricketybridge 11 February 2014 02:36:22AM 1 point [-]

Sigh, well, I've been trying to fix it for about ten years (so as long as I've been failing. Coincidence?? Probably not). I'm on 2 anti-depressants right this minute (the fourth or fifth cocktail of which I've tried). I've gone through years of therapy. And the result? Still depressed, often suicidally.

So what else am I supposed to do? I refuse to go to therapy again. I'm sick of telling my whole life story over and over, and looking back on my past therapists, I think they were unhelpful at best and harmful at worst (for encouraging me to pursue my ludicrous pipe dreams, for instance). Moreover, talk therapy (including cognitive behavioral therapy, which some say is the most effective form) is, according to several meta-studies I've looked at, of dubious benefit.

I could try ECT, but apparently it has pretty bad side-effects. I've looked into submitting myself as a lab rat for deep brain stimulation (for science!), but haven't been able to find a study that wouldn't require quitting my job and staying somewhere across the country for two months. So here I am.

But if we can sidestep the ad hominem argument for a moment, it sounds like you're saying that my aversion to failing at something else is irrational. Would you mind pointing out the error in my reasoning? (This sort of exchange is basically cognitive behavioral therapy, btw.)

Comment author: Lumifer 11 February 2014 02:00:19AM 3 points [-]

Have you considered that you might be clinically depressed?

No one succeeds constantly. Success generally follows a string of failures.

Comment author: ricketybridge 11 February 2014 02:16:46AM *  1 point [-]

lol I almost added a sort of disclaimer addressing that. Yes, I am definitely clinically depressed -- partly due to my having failed so epically, imo, but of course I'd say that. ::eyeroll:: However, I don't see the benefit in just discounting everything I say with the statement "you're depressed." Not that you did, but that's the usual response people usually seem to give.

No one succeeds constantly. Success generally follows a string of failures.

Yeah, so they say. But you have to admit that the degree of success and the length of strings of failures are quite different for each person. If that weren't true, then every actor would be a movie star. Moreover, success is never guaranteed, no matter how many failures you've endured!

Comment author: Lumifer 11 February 2014 01:50:07AM 1 point [-]

...could range...

We're not speaking generally. You will have to make a decision about your life so you need to estimate your costs for a specific career move that you have in mind.

...if I decide to get a masters or something

You need to focus and get specific.

Comment author: ricketybridge 11 February 2014 01:56:19AM 0 points [-]

There's no point in getting specific if I think I'll fail at anything I try to do.

Comment author: Lumifer 11 February 2014 01:08:28AM 2 points [-]

In the context of a costs-benefits analysis, what are your costs in trying another career?

Comment author: ricketybridge 11 February 2014 01:42:08AM *  1 point [-]

Purely financially speaking, the costs of a career transition could range from opportunity costs to hundreds of thousands of dollars in debt if I decide to get a masters or something. Opportunity costs would be in the form of, say, foregoing income I would get from more intently pursuing my current field (e.g. becoming a paralegal, which is probably the most obvious next step) instead of studying another field and starting all over again with an entry-level position or even an unpaid internship.

Although less pay might sound rather benign, the idea of making less than I do now (which isn't much) is rather horrifying. But then again, so is being condemned to a lifetime of drudgery. And I could potentially make a lot more in a different career track, meaning I would break even at some point.

Between those two extremes include things like spending several hundred dollars on classes or certifications.

I'm not married and don't have kids, so luckily those sorts of concerns don't enter the equation.

The emotional costs of trying another career (if you want to take those into account as well) would be utter heartbreak from failing yet again (if that's how it turns out).

Another intangible cost is leisure time. Instead of pursuing another career on my off-hours, I could be playing video games, sleeping, working out, hanging out with friends, etc. Although those things might seem like not a big deal to sacrifice in the name of a better career, after wasting years of my life on fruitless pursuits, I can't help but feel that "hard work" just isn't worth it. I may as well have been playing video games that whole time.

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