Some ebooks, mostly from /u/lewisje's post

Currently a second year undergrad student taking real analysis. This is my first proof based math class and I have not taken discrete maths before either. I’ve already taken up to calc three and linear algebra, did pretty well in them.

The professor is using Understanding Analysis by Abbott, and the lectures mostly make sense to me. However, his problem sets are very very long and do not follow the textbook questions. He seems to come up with them from his brain…and he posts them every Saturday..which is also great.

I find myself really struggling to know what steps to take and where to go after reading a question asking to prove or show something. This makes me very worried for future exams.

Any and all advice would be really appreciated!

In the chapter on "Infinite Series", one of the problems is to prove the following:

(1+x)^a = \sum_{k=0}^{\infty} [\binom{a}{k} x^k] for |x| < 1, for any a

Surely, this is not true for x = 0 as the LHS is 1 and the RHS is 0. So, does one not need the caveat that x \neq 0 ?

Additionally, what is the definition of \binom{a}{k} if a is fractional? Is it just a placeholder for a(a-1)...(a-k+1)/k! ?

I attach an image of the problem in the comments.

Like how does a niche operation designed to number a matrix such an importn concept. Like it feels so niche and unique but this function is there everywhere please help me conceptualise it.

Thanks in advance!

So I just finished book of proof by Richard hammack which is a book on how to Write proof (duh) whith most of the problem solved including a lot of hard one ,but now I'm bit lost on where to move on to develop advanced proof writing skill so I can tackle subject like topology n' abstract algebra cuz that's why I'm trying to learn those skill in the first place so it would be cool if u could give me some suggestions (I'm a self-taught idk if this info matter) on how to develop those skill ty in advance

I've struggled with math for years, and sometimes I feel like my foundations are way weaker than they should be.

For those of you who used to be really bad at math but eventually improved a lot, what did you do differently? Did you start over from the basics, change your study habits, or approach the subject differently?

I'd love to hear your experiences and what actually worked for you.

Hii everyone. So, my parents have failed to put me into any sort of school basically my whole life (never tried homeschooling as well). Now I'm nineteen and I really don't understand any form of math, even the easiest questions, and I've been really wanting to get into learning it, so if anyone has any recommendations on videos, websites, apps. Anything. I would greatly appreciate it :D !! The easier it is to understand, the better (I have a learning disability.)

I’m an A level student and I failed in math all throughout highschool but somehow managed to pass with a B in my GCEs. I studied the subject for a while earlier this year to build logic and intuition so I practiced a lot, I couldn’t even factorize so I started from algebra and worked my way up to trigonometry before I COMPLETELY stopped studying math. I would focus a lot on derivations and the “why” behind each step so I don’t remember having memorized anything. I have picked the subject back up again and it’s been a few months since I last did sums and it feels like I have completely lost my intuition. I cannot do trig identities as well anymore and I can’t solve any quadratics or circle equations without looking at the solution. Is this because I haven’t been revising and the concepts got rusty? This is pretty demotivating because I was doing perfectly alright earlier this year.

Im in calculus 2. first year. and we're having a test on series and sequences in almost exactly 2 weeks. on the last test i made a bunch of stupid mistakes and got a 57.5. now my grade is a 74.5. i really need to get at least a B (80%) overall and there are 3 tests left including the final (all 15%, except final which is 25%.... rest is HW and quizzes and class participation which im not very worried about)

i started studying ahead of the class so ive already learned all the series tests. did a practice test today by looking at a previous exam and it went terribly. im not prepared at all. i cant fail again but i feel like im going to. its only my first semester and i feel like dropping out. i thought i was smart but i feel like a complete idiot. wjat do i do

any recommended resources??? i have already used pauls math notes. Using previous exams/lecture notes. what else

in general ive been having trouble factoring polynomials because the steps dont seem to mean anything, and it seems more like simplifying than factoring even though i guess those are similar?

but onto more pressing matters. my book factors trinomials with substitution as such:
consider trinomial 3x^2 - 2x - 8
step 1: multiply ax^2 + bx + c by a to transform x^2 into (ax)^2.

i dont understand why we do this, no other video has done this before. i'd understand this step if the 3x^2 term was to equal 3(3x^2) which i think would be 9x^2 but it doesn't equal that. in general, i dont know what "transform x^2 into (ax)^2" really means. or why we do this when other videos have a common binomial substitution which i can do easily. after the supposed multiplication of 3 to every term, we have:

(3x)^2 - 2(3x) - 24
(Why isn't 2(3x) just 6x???????? why is - 24 not -24x since in some places we multiply by 3x and others by 3??)

replace ax with a variable p. p = ax.

we now have p^2 - 2p - 24. the typical factoring commences where c = pq and b = p + q.

we now have (p - 6)(p + 4). we substitute ax back into p.

(3x - 6)(3x + 4)

3(x - 2)(3x + 4) factoring out common factors we end up with (x - 2)(3x + 4) im under the impression the common factor of the second binomial was 1 which i've never seen before. but that doesn't make sense as what did we divide 2 by then?

and then since we started by multiplying the trinomial by a , we must divide by a, and this obviously doesn't make sense to me as someone not behind the reason we multiplied by a. the answer is (x - 2)(3x + 4)

we have the easier and obvious method of AC grouping (i dont get it but its consistent so whatever) but we also have substitution and im scared i might get a question asking me to factor by substitution specifically in our upcoming midterm.

help to understand or other resources much appreciated.

I'm a college student a few weeks into an intro to proofs course (logic, sets, induction, relations, functions, etc). I've seen proofs before, but I'm having a hard time adjusting to working with arbitrary elements and figuring out how to put proofs together. For example, when I'm asked to show two sets are equal, I understand the definitions but can't figure out where to start.

The class is flipped, so I feel like I'm mostly teaching myself from the instructor's notes. I'm worried about falling behind and want to make progress while there is still time. What helped you get through your first proof-based class? Any study habits, ways of thinking, or resources that you'd recommend?

Hello, I'm a first year university student and my course doesn't offer any mechanics modules so I was wondering what specifics I should cover (classical mechanics, Newtonian, etc.) and in which order. Also any suggestions on resources.

tldr: I really want to get bridge mathematical gaps after struggling in high school after seeing how it can be applied, stuck with many holes in my algebraic knowledge and would like any recommendations for this specific dilemma. Thank you!

I'm currently starting my bachelors degree in Computer Science, I have a deep love for games and want to dabble behind the scenes with game engines, 3D graphics and such. I'm well aware mathematics play a large role in this topic such as calculus and linear algebra for the algorithms and physics of certain mechanics.

My excitement has intertwined with fear due to my previous experiences in high school so long ago, especially with my overall disinterest of it general math back then that's caused gaps, I barely survived it in high school. Now that I actually have something to apply and learn math for, it excites me, but I feel slightly discouraged and not good enough for it.. especially haven’t fully grasped algebra concepts well. I also really struggled to take math notes!

Granted, I've realized I had a learning disability when I first started college, which makes a lot of sense as I can name so many points in my education where I would simply just zone out, but it doesn’t make me feel better about myself. I now have a few motivators; I want to heal the inner child in me and take control of my education after years of being frustrated from looking at my math homework. Im seeing math in such a different light when it is applicable, implementing cool, game physics mechanics looks really exciting. And of course.. to get my degree haha. Any recommendations would be appreciated! I could have searched this up, but I wanted to gather some anecdotal experience from others on here, especially if any of you have an experience similar to mine. :)

I can't seem to understand this one problem. could somebody help me solve for X?

(lnx)^3-ln(x^25)=0

Looking for someone to help me with an undergraduate Real Analysis math course.

Willing to pay but i’m also a student so please be reasonable.

**Edit:

Thank you all for your willingness to help! I have found someone from this post and am no longer looking for a tutor :)

The statement : Show that every predicate in two variables can be presented as the composition of the elmentary predicates AND , OR and Negation.
I understood that steps where
1. Truth rows are constructed purely from AND and NOT
2. False row is achieved by combining the expression in 1 with OR.

How does it then “prove” that the mechanism works for every predicate?

I have been studying complex numbers for the past couple of months (I'd say I'm fairly confident with them at this point).

The one thing that drives me crazy about this topic is how you can solve those long Euclidean geometry and trigonometry problems in what, like, minutes, and that too with such insane elegance.

So I just wanted to find more geometry and trig problems of this kind, but I couldn't find any good material anywhere. I just wanted some suggestions about what resources I should refer to.

BTW, I'm just 16, so don't expect me to know very high-level stuff, but you can expect me to have a solid foundation in algebra and geometry.

(English isn't my first language btw, so excuse any errors lol.)

Hi r/learnmath,

A common struggle I’ve seen (and experienced myself) when learning mathematics is the gap between reading theory and actually solving enough problems to build true intuition.

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If you're currently studying for high school exams, college STEM courses, or just self-studying math for fun, give it a try. Any suggestions on topics you'd like more problems in are very welcome!

Hey guys, I am working through Lang's Basic Mathematics and was hoping to find people in the same boat to discuss concepts with, clear up doubts and bounce ideas off of. If anybody is interested, feel free to DM me. Doesn't matter what point you're at in the book, we can still find a way to make it productive for each of us.
My intention is to develop a rigorous understanding of precalculus before proceeding to undergrad calculus, so anybody looking at Gelfand's 3 books is also welcome to reach out.

I have to take an Accuplacer test, so I decided to try a practice test just to prepare myself and i quickly realized I dont remember anything. I used to be super good at algebra so im pretty upset with myself.

I tried Khan academy but I really dont have the money for a subscription and I have to take this test tomorrow to enroll for fall classes.

Ive watched several videos but im just not understanding where these people are pulling these numbers from. Ive looked at the formulas. I just dont understand it.

I was trying to avoid taking extra refresher type classes but im afraid I might have to :(

The thing about vacuous truths is that, you can you this to generate statements that are true but practically useless if the premise never happens. Take the Mean Value theorem for instance. For all functions f, and for all a,b \\in R (f is differentiable on the open interval (a,b) and f is continuous on the closed interval \[a,b\]) implies \\exists c in (a,b), f'(c) = \\frac{f(b)-f(a)}{b-a}. This theorem would still be true even if you work in a function space where no function is both differentiable and continuous on the interval (a,b). It would be vacuously true. The most useful statements in math are those where you can find examples, counterexamples or both. So a mathematician could simply write a statement that useless because the premise never happens.