noAlchemy

Fun fact about Type II topoisomerase: even though it only has local information (the area where it acts) it manages to move in the correct direction (lower unknotting number) about 90% of the time. AFAIK, no-one knows how.

Good point, but if you wanted to work with an arbitrary distribution in the plane as a generalisation of this I think you'd need to look for an equal-area map from R2 to S2? (eg http://en.m.wikipedia.org/wiki/Lambert_azimuthal_equal-area_...)

Edit: I mean R2 to S2 (although this is bijective)

I know I'm not the GP, but might be able to be some use here. Context: always wanted to do a maths PhD, but ended up stuck running a small business (50-70 hrs/wk) for a number of years. Managed to keep studying through this and have just landed a PhD. Suggestions:

1. You'll be working while you're tired. So your work won't be as good, you won't make optimal decisions 100% of the time, sometimes you will just underperform relative to you at your best. Accept this - your work is still better than all the work you weren't doing before. Slow progress is always better than no progress. Key here is creating space that's just for work. I have a table which is just for studying, and a logon that's only for studying, which actually really helps.

2. Pick a course of study and stick to it. There's a tradeoff here - for a given area of study, you want to choose the best course for you but don't want to waste time trying several different things (likewise languages, frameworks, etc). Pick 2-3 and whittle down quickly (I choose 2-3 MOOCs or textbooks, then whittle down using the first chapter over a week or two). There may be a slightly better course out there you don't know about, but it really won't make a difference.

3. If your intention is to become a professional, pick a specialisation quickly (even almost randomly if you have to). No-one would give me the time of day when I was just generically interested in 'maths' but as soon as I picked a sub-area and started to learn about it, people took me seriously. (Obvious caveats apply about over-specialisation)

4. Start talking to other people. You really need to have done 2 & 3, otherwise you won't have any progress to show, and nothing to talk about, but once you've done enough to talk sensibly to others (which might be less than you think) then you'll be more engaged and less likely to drop out/quit.

5. Accept your limitations. Sometimes work/life will take over - sometimes you can make sacrifices and continue to get work done, sometimes doing this would be too painful and you'll need to take a break to get things in order. The thing here is just to show up.

If I had to choose one sentence from all of this to give as advice, it'd be the last one. Just show up.

I've had a look (but not intensively, it's a back-burner thing for me at the moment). Everything seems very heavyweight and aimed at big businesses with long supply chains.

For a small ecommerce retailer, you don't want much like that; maybe I've missed it but there seems to be a gap for the Basecamp of this niche. A shopify plugin might be a good way to get standardised i/o rather than adapting to proprietary systems

How's your maths? Here's something I'd pay quite a lot for: intelligent inventory optimisation in an easy to use SaaS format. Quite mathematically intensive to do well, so most SMEs don't have the skills, but directly saves money so has a clear value proposition.

Some pointers for an MVP I think might be sensible: Model stock arrival and product ordering as Poisson point process with probability based on recent data Combine with sales data & length of ordering cycle to reach suggested quantity per order (you could make suggestions to account for covering variations in customer ordering based on standard deviations)

I'm thinking of doing this myself for my business but really not finding the time to get it done!

I can support this from the other side. Coming out of a maths degree at a reasonably good university, a lot of the mathematicians who became teachers were those who struggled and pretty much gave up at some point in undergrad. Pushing many of those who will become teachers to mathematical breaking point seems like a bad way of doing things, and I think contributes to this. It's hard to think of a good alternative that still produces enough teachers though.

I'd also say that the other side of this is neglected, namely how to get others to listen better to you.

Those who have issues listening well are probably less likely to be looking out for advice on how to do so, so what can we do when we find ourselves needing to communicate with them?