Fliptomato is a physicist's personal blog, best known for a post on a medical researcher who rediscovered integration.
HN links it mostly as a classic example of researchers rediscovering known ideas, and for a physics learning reading list.
First up, I am no expert, but I have traveled this road for a while so I'll share a bit.
I see Susskind's theoretical minimum is plugged here. Good. That is a fantastic place to start. Start at the beginning. Skip nothing.
Leverage what you know against what you don't. You remember how to find an extremum of a function from Cal 1? The first order necessary condition for an extreme point is that the derivative of the function be zero. Remember that when you get to (deterministic) optimization and a gradient needs to be zero. Next with a constrained optimization you will see the reformulation of an objective function and constraints into one functional by using new variables (Lagrange "multipliers") so that when the gradient of this new functional is zero, not only are you somewhere in the intersection of the constraints and the objective, but you also meet the first order conditions necessary for an extremum to be found. (Second order sufficiency conditions (SOSC) are needed to show that you aren't instead at an inflection point but we are moving fast and breaking things)
Hmm, I didn't say that very well, but there is much intuition to be found in optimization problems. This will serve you well in physics.
Calculus of variations: Nail down cold how to derive the Euler Lagrange Equations for a functional. Hint, Apply the FONC (first order necessary conditions for an extremum) to the functional (now the Action) in question. See Lanczos "Calculus of Variations"…
Perhaps you haven't heard about the doctor who rediscovered the trapezoid rule and had his article published in a respected, peer reviewed biology journal in 1994.[1] The paper is called "A mathematical model for the determination of total area under glucose tolerance and other metabolic curves" — and it got 75 citations (as of 2007). EDIT: Google Scholar lists 178 citations now [‽].
The abstract:
"OBJECTIVE To develop a mathematical model for the determination of total areas under curves from various metabolic studies.
RESEARCH DESIGN AND METHODS In Tai's Model, the total area under a curve is computed by dividing the area under the curve between two designated values on the X-axis (abscissas) into small segments (rectangles and triangles) whose areas can be accurately calculated from their respective geometrical formulas. The total sum of these individual areas thus represents the total area under the curve. Validity of the model is established by comparing total areas obtained from this model to these same areas obtained from graphic method Gess than ±0.4%). Other formulas widely applied by researchers under- or overestimated total area under a metabolic curve by a great margin.
RESULTS Tai's model proves to be able to 1) determine total area under a curve with precision; 2) calculate area with varied shapes that may or may not intercept on one or both X/Y axes; 3) estimate total area under a curve plotted against varied time intervals (abscissas), whereas other…
Absolutely. So wouldn't it be neat if premedical students and business majors had already seen a thorough stats class in high school, so that their college-level stats classes could spend less time on the basics and more time on those subtleties?
(Speaking as someone who's taught calculus-based physics to premedical students, I think it's important to recognize that most folks who've taken a year of calculus really have not internalized those concepts enough to be fluent in applying them. I think it would take a particularly strong math background for someone to really understand the mathematical justifications for statistics, so I suspect class time would be better spent warning students about pitfalls than on hoping that they will draw meaningful conclusions from formal derivations. Heck, medical students are required to have taken calculus, but lots of them (evidently including a journal editor, peer reviewers, and 163 followup papers) apparently don't even know what an integral is: http://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ .)
Something else less related that I find really useful about these chatbots is their ability to take some abstract explanation of some problem/attempts to tackle it, and it'll often spit out a name for it, and explain that this sort of problem is already well studied. That can be really difficult with other more traditional tools.
I feel like this could be a big deal in science in general. People of different fields often do unnecessary extra work (as in reinventing the wheel) because they're not aware that there's, say, 10 years of research on it.
To take an extreme example, just think of the poor fella doing medical research who rediscovered integration[0].
0. https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/
> there's other pretty important stuff that can still bubble up, like the person reinventing the wheel where a well known library could have been used
I wouldn't call not using a well known library "reinventing the wheel". The wheel in that expression is a concept, not a implementation. A library is an implementation of a concept. Writing yourself code instead of using a library is a great way to learn about what that library does and the tradeoffs it makes.
When I think about "reinventing the wheel" as something negative, I think about something like "Medical researcher discovers integration, gets 75 citations": https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/.
There was an example not so long ago of a paper published in, I think, biology, where the author had invented a wonderful new technique for more accurate estimates of the area under a curve.
It was Simpson's rule.
CORRECTION:
It was worse than that. It was the trapezoidal rule:
http://care.diabetesjournals.org/content/17/2/152.abstract
The author named it after themselves:
... The Tai model allows flexibility
in experimental conditions ...
and got 75 citations ...
http://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/
Unbelievable.