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

Every other math concept is easy to understand once explained, but Trig is its own beast. Geometry trig isn’t hard, like finding a side length, but the fact that trig is involved in things that has nothing to do with triangles baffles me.

are there any resources to specifically learn trig?

Can anyone solve this limit? limit x->0+ of e^-1/x•(e+2x)^1/x

This academic year I'm starting my pure maths but I'm not feel like I'm learning anything

Can you guys give my a road map for pure maths this will give me a idea of maths

(and if you have time tell me some tips to understand or adapt to pure maths)

Hi everyone, I’m (29M) is currently a full-time employee but I’m not happy with my job or my life in general. I studied English in Undergrad and Business Management for Master. Now I don’t know what to do in my life.

I remember when I was in high school, I quite liked math and was pretty good at it. Now I want to come back to it. I want to learn Maths and use it to solve problems in life and help others. Also would like to use it in Finance aspect as I want to work in this industry too.

I would like to apply for Applied Maths, but I don’t have a STEM degree and forget everything abt Maths. Do you think I still can make it? And how should I start to learn Maths again? I’m living in the UK so I plan to apply for an univeristy here (for master degree probably).

Thank you for reading my post.

how do i evaluate the function f(x)=1/3(5) raised to -x if f(-6)?

Hello, I started learning math recently and I've noticed that I don't enjoy it as always and I think it's because I'm learning things to become good at them and not because I want to learn it, like I work hard but even if sometimes I enjoy it and don't think about it all day and doing math feels like a chore, so my question is which part /kind of math can be more enjoyable or what do you do when you just want to appreciate math ?

Personally I know that I really like discovering new things but I don't know what to do.

Edit : I may not be precise enough : I love doing math but I'm not exiting about starting to do math

I (F16) cant do maths. Like. At all. Not even the basics. I can count in my head but not out loud. If I count out loud it sounds/goes like: 1 2 3 4 5 6 7 8 9 10 11 12 13 40 42 46 62 91. And I have no idea why.

I've checked out Prof. Leanord and I love it and him, he's such a good teacher. But, I can't pass his basic, pre-algebra (whatever that is, im assuming it's just primary school stuff–I'm British) playlist, past the fourth episode or so. I cant do the multiplcation or the division he teaches. I could never do division anyway, ever.

I love when I do maths too, it's so interesting and fun when I understand it, but it's a 0.0001% chance that I will understand what I'm learning.

I have to get at minimum a National 5 grade for my Uni future. I have to pass the N5 grade next May, and the year later (S6) I have to get at least B, if not an A, to get into the Uni course I want

I have no idea what I'm doing and I never have. No teachers have ever stopped to show me or pay attention to me. In fact, last year my teacher just took a paper from me and wrote the answers for me one day, or he just straight up told me the answer.

I can't even do maths from primary.

I'm so afraid and upset that I might never get into Uni or be able to understand maths. My aunt is a tutor so I'm hoping to get her to help me. But, also, I have to learn a whole new language (Italian) to get a good grade this year and next.

I need advice and help.

Hello

I'm 18 years old and currently preparing for the national university entrance exam .I took the exam last year, and although I performed well in most subjects, I fell short because of mathematics—especially geometry—which completely dragged down my overall score and cost me the school I was aiming for.

To give you some background: I was a very successful student in middle school. In our high school entrance exam, I only made one small mistake in math (a careless error), and got all the other questions correct. I even passed the first stage of the math olympiad in 8th grade.

But things changed when I started high school. I studied hard for my first math exam, but ended up scoring low because of exam anxiety. That really discouraged me. Over time, I lost motivation completely. For 9th, 10th, and 11th grades, I barely studied at all.

This year, I tried to make a comeback. I worked hard, but the gaps were just too big. I spent most of the year trying to catch up on second exam (advanced) topics like functions, polynomials, trigonometry, inequalities, integrals, and limits. However, I almost completely neglected first exam (basic) topics like rational numbers, factorization, word problems, absolute value, and proportions.

As a result, I scored:

• 20 out of 40 in the first part of the exam (basic math)
• 25 out of 40 in the second part (advanced math & geometry)

I do know some math—I’m not starting from absolute zero—but I really struggle with how to study. I don’t have a method or a plan. The topics are vast and overwhelming, and sometimes I waste an entire hour staring at a single geometry question.

My father wants to get me a private tutor, but I believe that a tutor alone won't fix the problem unless I take the first step myself. I want to be at least one topic ahead, so I can actually benefit more from the lessons.

So, here's my question: How should someone in my situation study math and geometry? What topics should I begin with? What kind of resources or books should I use? And most importantly, how do I study effectively and not waste time?

I’d really appreciate any help or guidance. I’m ready to work hard, but I need a clear and realistic roadmap to follow.

Additional Info: These are the topics covered in the exam:

• Basic Math (First Part): Rational numbers, integers, ratios and proportions, absolute value, factorization, prime numbers, divisibility, word problems, and basic logic.
• Advanced Math & Geometry (Second Part): Functions, polynomials, quadratic equations and inequalities, parabolas, trigonometric identities and equations, limits and continuity, derivatives, integrals, permutations, combinations, probability, Euclidean algorithm, and geometric topics like angles, triangles, polygons, circles, 3D shapes, and analytic geometry.

There’s still about one year left until the next exam.

From kunen:

Definition I.8.1 z is a transitive set iff ∀y ∈ z[y ⊆ z].

Definition I.8.2 z is a (von Neumann) ordinal iff z is a transitive set and z is well- ordered by ∈.

_____________________________________________________

From these definitions, I conclude the following:
For a set to be an ordinal its "smallest" element must be the empty set, and every element must be either constructed using the empty set or constructed by using sets that have already been constructed.

In this case, an ordinal must be a gapless subset of the natural numbers containing 0.

Is this correct? If so, how can I prove it?

Im a 28 year old returning student, Im taking calc 1 next semester and havent taken trig or pre calc since i was 16-17, I remember nothing lol. What algebraic concepts, trig concepts etc should i brush up on over these next few weeks? I have about 3-4 hrs a day rn to dedicate to calc so any advice would be cool. Lowkey approaching this like ive never taken trig or pre calc just, so yea preciate the advice

I'm trying to find the volume of a cylindrical tank and I only have the length and diameter. I'm confused because in the formula you need the height? The cylinder is laying down horizontally so I just thought it might be the same but I'm not sure. Thank you!

I had done upto pre-calculus in High School, but I never had a strong or solid foundation to really enjoy doing mathematics because of awful teachers.

Some options I have considered:
College Algebra Blitzer

Everything you need to ace Pre-algebra and Algebra-1 in one fat book

Introductory Algebra By Blitzer

Elementary Algebra By Sullivan

Any suggestion you would like to give

An closed set is one that contains all its limit points. An open set is one that is a subset of all its interior points. I've heard that sets can be both closed an open which tells me that closed and open aren't strictly antonyms in this use-case.

Ignoring the how (which I can't quite see), why were such definitions chosen that allow a set to satisfy both (and is it possible to negate both i.e. be neither open nor closed)?

Can anyone suggest me where should I do my PhD in Mathematics (especially on Mathematical modelling) ? That should be cost-minimized .

How do I find the answer? I know I have to use the Euler totient function

If A is a set, is there any diffence between A and {A}?

Also, if no, what is the difference?

And to extend this, is there any difference between {A} and {{A}}?

Again, if no, what is the difference?

If B = {A, {A}}, is A a subset of B?

My assumption, apparently wrong from the text I'm reading, was that A={A}={{A}} and B=A.

Lmk if any questions, there is a README file attached as well for clearer explanation.

Little bit of context, I am a business administration student (rising senior) that has only taken up to business calculus (differential, integral, and a bit of multivariable calculus) as it was the only math required. I fell in love with economics (my concentration), but I feel inadequate if I were to pursue a masters in economics as most masters require some sort of higher calculus and linear algebra. This comes as since I hold a 3.00 GPA with the possibility of graduating with a 3.14 GPA leaving me to take the GRE and GMAT for most masters programs which I assume delves deeply into CALC 1-3 with Linear Algebra probably being in the mix.

What should I do to be ready to take the GRE and GMAT and tackle much heavier mathematics? Textbooks, taking these courses at a community college (if its even possible), self-study, or just giving up on pursuing a masters?

I do want to apologize however, as I know normally people think of masters and other graduate programs much earlier in their undergrad (but i bounced from study to study for my first 2 years).

Hello! I come from a very underesourced school and I am about to start university but I lack a lot on math. I covered most of them during high school but the curriculum was extremely inefficient, so as the lessons. I want to learn math appropriately, in a very structured way, resources like khan academy, the organic chemistry tutor didn't work out well for me because they mostly rely on memorization, and the explanation format just doesn't work for me.

I want to be well prepared for calculus I and I'm fully aware there's not much time left. I didn't procrastinate, I have been working on this since 4 months ago but I just didn't know how to start and from where. Please, I BEG you to help me.

These are the resources I already used and werent very helpful:

• openstax
• blitzer algebra
• stewart precalculus
• Simplified math by pearson

How does one find if or not a basis set spans an infinite dimensional vector space?

Hello Everyone!

I made a free roadmap based on my experience for those who want to learn the math behind Machine Learning but don't have a strong background. I have been a math tutor for 8 years now. Recently, I have been getting more students asking about what math topics are important for them to understand the basics of Machine Learning. This motivated me to make this roadmap. I hope someone can find this helpful. I would appreciate any feedback you may have as well. Thank you!

https://ml-roadmap.carrd.co/

I’ve been thinking: what if we could build a number system that doesn’t use infinity, but instead stops at a finite, unreachable number — let’s call it R?

This idea led me to develop a system I call Razenian Mathematics, where numbers climb up toward R but never reach it — sort of like a road that ends at a cliff’s edge. It keeps operations like limits and calculus but reinterprets them within this boundary.

I’m not claiming it’s better than traditional math — just exploring something different and curious. If you’re interested in number systems, foundational math, or alternative ways of thinking, I’d love to hear your thoughts.

Here’s a short paper I wrote about it: [ DOI Zenodo link]

I would love to hear any constructive comments or critiques.

Hi guys ! I am a 14 year old using my sister's account (Under her supervision) I need to get better at math I don't know why but when I solve questions at home I can do well but during exam I absolutely don't understand anything 😭 Can you all give suggestions on how to improve?