/sci/ - Science & Math

>>10287660
First, you read the material and make notes. In the notes you re-explain everything you just learned.
Second, you do the exercises, and most importantly, you figure them out for yourself you don't look at the solutions after 10 seconds of not knowing what to do. Actually try and stop being a passive half asser. Plug in corner cases like 0 or sqrt of 2 in all the variables and see if it breaks. Play with it for a few minutes before just giving up and being spoon fed.
Third, you find university class schedules that are open and try and take their exams or midterms or whatever other old tests they have up w/solutions. This is the prove to yourself that yes, you actually understand the concepts and are progressing.
To prepare for this test, you teach an invisible class from your notes. If you can't effortlessly explain every concept in the text like you're talking to 12yr olds then go back and redo (the Feynman learning method).

Solving undergrad level math problems is the same as doing carpentry. You don't just give up when you hinge some cabinet door and find it's rubbing against something because it isn't in the documentation. You also don't just randomly attach the hinge somewhere else either, you think about a) why doesn't this work b) how can I fix this c) logically this should go here d) test new placement e) be satisfied and then move on.

>>10268760
In fact here is your entire curriculum:
>Getting a job
https://lambdaschool.com/
- cost $0.00 (they shave your paycheck for X months)
Work there for 3 years.
>Calculus book
Get a rigorous calc book with proofs, and do all the exercises while you program bullshit.
- cost $20 used book or 'International edition' like Apostol's Calc I
>The Art of Computer Programming
This will probably take you 4-6 years to complete depending on effort. This will be your supplementary comp sci education you never had.
- cost $150 or so for the first 4 volumes.

So total cost: about $200 and you get a F/T job, and (eventually) a compsci degree equivalence out of it if you actually do the exercises.

Go on libgen.io or otherwise obtain the following exercise books:
>Advanced Problems in Mathematics - S.T.C. Siklos (University level problems for highschool math)
>Solving Mathematical Problems: A Personal Perspective - Terence Tao
>Yet Another Introduction to Analysis - V. Bryant (assumes only basic Calculus familiarity)

Obtain the following brainlet reference material which you will use to directly research things:
>Better Explained - Math
>Better Explained - Calculus
>An Infinite Descent into Pure Mathematics (free pdf) - https://infinitedescent.xyz/
>Anything else from the sticky guide

Your learning algorithm:
Start with any exercise book and attempt the first excercise, don't read the chapter.
If successful continue until you finish all the exercises, every single one, no exceptions.
Failure? Research directly the problem in your brainlet guides. Keep notes about everything you learn.
Still failure? Research the relevant chapter of said exercise book.
Still failure? Go on math.stackexchange and search for an answer similar to your problem, then go solve your problem.
>Critical: Do not look at the solutions manual in the appendix of w/e exercise book you're doing
Attempt to prove your answer is correct, research how to do this in the Tao book, the Pure Math book, or math.stackexchange, or Wikipedia
Only when you are absolutely sure you have the correct answer, look it up in the solutions guide.

This is not a meme, it's evidence based teaching: https://infinitedescent.xyz/20180214-exercises-ibl/
This won't take that long either, because like every other skill you'll get better at it with practice

How to fail
>Skipping problems
>Looking up the answers without at least thinking/attempting how you would prove it correct yourself
>Passively reading instead of directly researching the problem you want to solve
>Not keeping notes