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They are extracted from my concise books for adult learners on MATH & PHYSICS https://minireference.com/static/excerpts/noBSguide_v5_previ... and LINEAR ALGEBRA https://minireference.com/static/excerpts/noBSguide2LA_previ...
I don't want to self-promote too much here, but maybe HN users who have read the books can add a comment to say what they thought.
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this is an excellent recommendation. it did not work for though. i was not the one that was at the advanced level and the one that was got bored rather quickly with us minions. Happend 5 different times. if you could find one who willing, this recommendation will def help.
Other people's help is indeed one of the most effective ways to learn. My problem with that is simply finding such people - given my extremely introverted disposition it's much harder for me than for normies - and also what you say, ie. finding people who would not quit after three sessions. Then I thought, why can't I just buy the time of someone competent? There are many students who tutor high school kids, shouldn…
One way to find them is to contact your nearest research university’s department of math/physics/whatever and they can help match you with someone, or just post a flyer in their department office.
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Herstein Topics in Algebra or Dummit and Foote.
goofy suggestion. those are both either grad or senior undergrad books depending on where you are. much better suggestion is A Book of Abstract Algebra by Pinter (really gentle) or A First Course in Abstract Algebra by Fraleigh
Here's my personal opinion about how you should approach this. It's all well and good to want to cover undergraduate math courses. When you are actually enrolled in a university, you will have enough inertia and motivation to complete the courses. However, when you are self-studying you are doing it all on your own. It's hard to be as thorough and cover everything. And so I ask, what really is your goal here? You don…
Is this sentence incomplete or am I missing the context of the word "compelling" here? > be able to write up a compelling Can someone clarify what this means?
Mathematical notation is meant to be read out loud. It's shorthand for English, or whatever your natural language is. You should be comfortable seeing a sigma sign and thinking in your head, "the sum as ehn goes from one to infinity of eff of ecks squared times ..."
That's just the basic part of it. There's lots of cultural shorthands that are just kind of osmosed, seldom overtly acknowledged (for example, the precise meaning of "without loss of generality"). Maybe you can acquire them by watching videos, but if you can find people that you can hang out with that can teach you the cultural aspects of mathematics, that would help a lot. Picking up a book and reading and working through it and understanding it gets a lot easier once you have the culture down.
https://www.cambridge.org/core/books/course-in-modern-mathem...
It covers most of the mathematics needed for quantum field theory (which is a big chunk of applied mathematics) starting right from set theory.
If you choose the project/problem based approach I recommend https://projecteuler.net
You will learn a ton solving these problems (the programming aspect is the trivial piece in most cases).
The hard but maximally useful thing to do, in my opinion, is to regularly meet with at least two other people and a blackboard and beat your heads against it together for about 3 hours at a stretch. Do this at least weekly--and preferably more often. Self study in between meetings is obligatory. One of those people should be at about your level. The other should be farther along. All three of you should trust each ot…
One thing that worked for me was to have a community of fellow mathematicians to study with. There's a lot of cultural stuff that is kind of hard to osmose from books, such as for example, how to pronounce things that you read. Mathematical notation is meant to be read out loud. It's shorthand for English, or whatever your natural language is. You should be comfortable seeing a sigma sign and thinking in your head, "…
You don’t typically obtain that kind of maturity until graduate school, maybe upper undergrad if you’re quite good.
The University of Oxford has all of their notes and exercises available online https://courses.maths.ox.ac.uk/overview/undergraduate If you get stuck you could try asking on https://math.stackexchange.com/ Although, if you can, finding someone else to work with, and someone else who already knows some math to ask occasional questions would probably help you a lot.