Hi everyone,

I’m a Data Science undergrad looking to build a strong foundation in pure mathematics on the side. I recently finished studying proof writing (Velleman's How to Prove It) and I'm about to jump into real analysis/calculus (Spivak's Calculus).

The main issue is that since I’m self-taught, I don’t have a mentor to check my proofs or answer highly specific questions when I hit a wall. I was thinking of using AI tools like Gemini Advanced or NotebookLM as "private tutors" to guide me through these books.

Has anyone tried this for proof-heavy or rigorous math? Is it feasible, or do AI models still hallucinate too much for this level of rigor?

If you don't recommend AI, what alternatives would you suggest for someone self-studying without a formal academic environment?

Does anyone has solution manual or can find me for the book functional analysis with application to linear pde by Alberto bressan

i do understand that being adhd doesn't stop me from learning math and i know that there are adhd people who love math and are really good at it.

but i never liked math (probably because nobody noticed i was adhd when i was a kid and only tried to force the neurotypical approach down my throat) and now, i need to learn some math before the end of september because i have a test (which has "**Quantitative Logical Reasoning**" questions in it) that could get me a good job, which i've been looking for since i'm still unemployed.

i do know baasic math, but advanced math is what breaks me because every freaking class i watch about it just wants me to memorize stuff, which is borderline impossible for me because of adhd. i need to UNDERSTAND the concept and how it works and why it works like that. otherwise, i can't learn it :(

is there a way for me to learn math? does anyone have any advicce or reccommendations?

I transferred to a prestigious school in 3rd grade and was bullied almost k-drama style. To better explain myself, I used write poems and literature starting at the age of 5 in my native language but spoke little no English (only knew my abc’s). When I transferred to that school, the students there have already studied English with great quality of education for three years then, and I started getting bullied by teachers, students and even my principal for some reason because I barely knew English. Since then I was petrified of interacting with teachers and stopped with my passion for literacy because they would torment me for acing classes taught in my native language.

The teachers leading up until junior year didn’t help with that fear. I was transferring a lot because of different reasons and junior year, I finally got humane and loving teachers and was just starting to get a grasp of my education and starting learn but I graduated. So now in my first year of undergraduate studies in Entrepreneurship the classes are so hard but I’m able to keep up with it with extra effort. I’m understanding my best learning style as well, however the math class…💔. Just off me atp because I suck soooo bad at math it's eating me alive. Math is just full of formulas that I haven’t learned yet.

I'm trying my best to stay afloat but I'm just too far behind in math no matter how much attention I pay during lectures and seminars, I don't get it. I've been replaying lectures and re-reading the slideshows and I understand it at first, right? And then... the math problems just start spiraling. Basically, just when I start to go like "Ouu nicee I'm actually starting to kind of get it!! Can't wait to put these formulas to work... and then I see the problems given for homework or during seminars and WHY WHY WHY?!!??! WHY DOES THE FORMULAS AND EQUATIONS START SPEAKING ALIEN LANGUAGE 50 MINUTES INTO THE LESSON?? I'M TRYING MY BEST:' ( to not feel stupid and | just get slimed out by the problems and I'm loosing seminar and homework points.

So if anyone is willing to help me out in Matrix and the Gauss Jordan method asap, I would be very grateful and I can also help you back in anyway it’s possible for me to.

I will appreciate any help or insight into how I can pace up to undergrad mathematics or tutoring or anything:)

​I am currently an 8th-grade student (2AC) preparing for mathematical olympiads (IMO).

​I have been working through Mathematical Circles (Russian Experience) and have already completed the chapters on Introduction, Parity, and Combinatorics 1.

​I would like to ask two quick questions:

​Do you think continuing with this book is the best strategy at my current level, or should I supplement it with other specific resources?

​What is the most effective approach for self-study when working through these problems alone (e.g., how long to spend on a problem before checking a solution, how to take proper notes)?

I’m not sure if this is an appropriate question for this place, but out of curiosity, I’ll ask anyway. I want to see integration from a basic understanding to a grad level or possibly higher level of explanation.

I'm thinking about going to college, but I'm currently relearning basic math and struggling with equivalent fractions. My future course is called "Elementary Statistical Methods." Will I need to know how to work with equivalent fractions and fractions on a number line for this course? What math skills should I focus on learning first?

I took a look at my progress bar graph I keep where I track the scores of some mock tests. Over the course of 2 months, I have nothing. No improvement. At all. My score is still floating around the same range. 2 months of hard work, of dedicating my time and effort into this, and just nothing.

I had a mistake log, I practised every day, I tried my best to think about problems but often times would just end up staring and then seeing the solution. What more could I have possibly done? This feels like my dream of being a great problem solver and being able to learn the language of the universe is shattered. There must be something in me, something fundamentally broken that I haven't improved even a little bit even after giving my heart and soul for this.

And I break down every time I think about it. Honestly, I dont even know how many of these I can take. I dont know how long I can tolerate feeling this stupid, even when Im doing everything I can. I just never have the first step and end up staring at the problem, even when I change up the difficulties.

I don't want to give up, I really don't want to, but Im not sure if I'll even get somewhere if I keep going, maybe I'm just not meant to.

Have you all ever felt like this due to Math? Sounds stupid to ask, feeling so shattered because of a subject, but if you did and got through it, hearing it could really help right now

So be me; who screwed around in all of high school and basically already started a calculus class as of this month in a California Community College, and I barely passed Pre-Calc.

I was wondering if someone(ANYONE!!!) can give me a thorough crash course of books/YT videos/playlists I can use to start studying calculus(as an idiot).

I was lurking and heard about some books like:

Calculus For Dummies(Ryan Mark)

Calculus Made Easy(P. Thompson)

The Cartoon Guide to Calculus(Larry Gonick)

Calculus: Early Transcendentals(James Stewart)

And ofc Paul's Notes (if no one knows what that is; https://tutorial.math.lamar.edu )

Other than that, I have no idea. I am locked in right now, though. But if someone can give me an A-Z crash course of everything I should study, from basics/fundamentals to the big stuff. It'll be so APPRECIATED!!

Hey guys! Just finished my university Calc 2 5-week summer class

I got a B+, and I'm pretty proud of myself.

Despite having gotten a C in calc one the quarter prior during the actual school spring quarter

However, I've always had a bad foundation in math due to not having a teacher for an entire year of my 8th-grade year, and when I entered high school, I was behind my peers

This sounds wild, but I had unbelievable trouble learning how to factor while taking Calc 2 because one particular question required me to factor, and even back in Calc 1, I had struggled to simplify or factor something that multiplies and adds to certain numbers

I wanted to close that gap and have math as a hobby. It's not my major at all, but I'd like to be someone people could count on to teach them math, but I'm not sure where to begin

Can anyone here please take a look at some of the claims made by Ali Fazely on the supposed mathematical miracles linked to the number 19 of the Quran, especially using prime and composite numbers? I genuinely don't even know what to think at this point

For example (and this is both used as evidence for the removal of Quran 9:128-129 as well as trying to demonstrate the nature of the supposed divine code of the number 19 in this book):

The number of verses in the Quran from 1:1 until 19:98 (since it's part of the whole code 19 stuff) is 2346 (not including 9:128-129). The factors of 2346 are 23x2x3x17 which have the prime indices of 9127 similar to Quran 9:127 being the cutoff point as proposed by Rashad Khalifa (the person who developed this whole idea of the Quran being shaped around this number 19 in the first place). Finally if you place the digits 2346 in a permutation table, the 19th permutation is 6234, the total number of verses in the quran if you remove 9:128-129.

Link to the book here, starting on page 44: https://pdfcoffee.com/the-ultimate-mathematics-of-the-quran-pdf-free.html

I don't understand how this is happening, since it's one thing if he only used this method once selectively, but he continues to use it similarly over and over. Wanting to understand whether or not there is more to this, or it's simply pattern recongition and being able to use many numbers at hand.

If someone could take some time out of their day to analyze some of the claims being made and techniques being used, it would truly mean the world to me. This stuff has been stressing me out and I'd like someone who can objectively and non-biasedly look at the following and help me out with it.

How is the quadratic formula useful? If I divided -b plus or minus the square root of b^2-4ac divided by 2a by itself, I would get one.

They say the quadratic formula shows up in the Pythagorean theorem. If I divide a^2 + b^2 = c^2 by itself, I get 1.

So if I divide a triangle by a triangle, I’ll get one. I can just stick a one to anything and solve it. How did this become valuable?

I've seen tons of people who can solve problems in a blink of an eye without any problem. I'm curious on how you can keep a consistent practice of improving while still loving the subject itself. Like how can you achieve that level of understanding? not just repetition that'll just soonly lead to memorization, but actually understanding why the answer is the answer.

I'm no where near that level, but i want to learn from the people who reached that level, or what youre doing to reach it?

Recently in math I have begun to learn geometry (proofs and such.) and everyone in my class is complaining that it is so hard and proofs are impossible to do. However I find it quite easy and fun. Last year we did algebra and everyone in my class was so effortlessly good and I had to actually study. But this year in geometry it's way more intuitive and there really seems to be a beauty to this subject more than just doing computation.

However I don't understand why geometry is so much easier for me as compared to the rest of my class. To understand I decided to study for a test with my classmates to see ther thought processes. I realized that they learned math in a way that was much more rotr memorization based. They seemed to be studying simply to optimize to get the best score and spent a lot of brain cycles only trying to memorize the material they thought would be on the test.

However I simply can't memorize by rote and I don't understand how people do that. For me, I feel the need to read the whole chapter and understand it cover to cover even if the material isn't on the test. Otherwise, I just feel very bored and drained.

This discrepancy between me and my class also could be because everyone was taking after school tutoring and I have never (and probably will never) taken after school math classes to get ahead in material. Now we are all just starting from scratch learning a new subject.

Additionally a lot of people do Competitive math in my school (like AMC and such) and while even I have participated in the contest (got AMC 10 qual recently!!) I find the questions to be more about knowing the patterns that come up over and over again in those types of exams.

Sorry if this came off a bit ranty I just had to get this off of my chest for some reason

Anyways would love to hear ur thoughts!

Hii, freshman in college taking precal with trigonometry. I took a gap year from math during my senior year of high school and I don’t remember anything.
First day in precal i remember some concepts after our first review but my professor was going through it quickly and completely lost me. Once I figure something out, he hits me with other formula or way to solve problems and it just makes me so much more confused. I feel so hopeless and it’s my second week. I’m a slow learner but I just need a clear explanation and then I’ll be set, I can pick up things fast but just carefully explain it. Anyways if anyone has any tips for me to memorize formulas or tricks with precal, please share, since he has us take closed note quizzes and exams. I also have my first quiz tomorrow so if anyone can help me memorize polynomials and solving equations that will be great I have a quiz soon….

[algebra] rational and irrational roots

I'm not entirely grasping the concepts being explained:

If n is a positive even integer and x is positive, then ^n √ x indicates the positive real nth root of x. (Even roots of negative numbers are not real numbers) If n is a positive odd integer and x is any real number, then ^n √ x indicates the real nth root of x.

The example given was ^3 √ -8 rational. Which was fine I understand. I can do the math for this and the root is negative

I then received the problem: ^3 √ 125. I don't know the math so I used my phone calculator and it is irrational. Understood.

2nd problem: ^3 √ -125. I assume since the 3 is odd and -125 is a real number that the answer would be irrational again, but I checked with my calculator which gave me the keep it real prompt. So I went back to the example and tried with my calculator and I got the same response, so now I'm confused.

Is the second problem supposed to be marked as not real or irrational? Why is my calculator noting them as both not real if the nth root is odd?

Sorry if this seems super basic, but all the math I use for work involves medications and nothing to do with geometry.

I recently did a rappell over a cliff face and I want to know how to calculate the distance of the rappell itself given limited data.

The rappell involves 3 points, A B C. A is the anchor end of the rope, B is the edge that I repelled over, and C is the bottom of the rappell where I was back on the ground.

AC is exactly 100 feet. I had a middle marker in my rope and it was perfectly at the ground. The other data set I have is that 75 feet from A is exaclty halfway between B and C. I had a 75 foot tag line that stopped right in the middle of the cliff face.

Is it possible using only these 2 distances to calculate the value of BC?

hi all.

after two years of math undergrad, I have decided to pursue medicine after an experience with healthcare that really sparked something in me. that being said, I do plan on coming back to mathematics after med school but in the meantime I'd like to still study some on the side, just as a hobby :p my interests mainly lie in algebra but I like some analysis and discrete mathematics too. that being said, I don't think I was the brightest student in my cohort, or at least not so on taking exams as I struggle greatly with pacing and knowing when to move on from some nitty gritty thing that really shouldn't alter my understanding of something but it does. some of the time it is because of a gap in my knowledge, other times it's just my personality I assume. combine that with often starting to study a bit too late and you start to get the picture. oh well there's ADHD too that comes to play but that in my experience is heavily influenced by how well I'm generally prepared and since I've been diagnosed for basically my whole life, so it is not something that is unique to school.

that all being said, I'd like some advice and experiences from peeps who have at least some formal mathematical education (post-high school) and have gone down this route. my biggest questions are:

1) how do you know when you've functionally understood something rather than conceptually understanding something? that is to mean, when you are able to do exercises correctly or are able to give counter examples (something I find extremely hard to do) rather than just knowing what a theorem entails.

2) other than textbooks, what are some other sources you use(d)? I know for example that Sheldon Axler has video's on his own textbook and that MIT has some courses but most of these are very first year of undergrad oriented, what for beyond that?

3) did you have any other obligations during your study period and if so, how did you keep it balanced? since I'll be a med student, you can imagine that there will have to be some planning involved (especially since I still have other interests that I love)

4) favorite textbooks you've studied so far and what made it so great to you?

I think that's about all for now.

thanks for taking the time to read and have a nice day.

​

So my teacher made me sign up to AMO, right now Im in grade 10, but since im an international student I will enter the 9th graders contest. To test my knowledge before studying, i solved the contest with no studying whatsoever and i got 27, im atleast hoping to get an honorable mention in the actual competition, if anyone has experince please recommend me resources.

Note: There is around 2 months until the competition and my goal is to learn the easier and common topics rather than the hard ones, so yeah i probably wont be able to learn a few of the topics.

Here are the topics for those who dont know.

​Arithmetic and Algebra

​Geometry, Graphs and Mensuration

​Pythagoras’ Theorem and Trigonometry

​Statistics and Probability

​Non-routine problem solving (including number patterns, divisibility tests, spatial visualisation, logic problems and cryptarithms)

Let R be a set, and let the universal set be

U = {1, 2, 3, R}.

Suppose R = {1, 2}.

Then, is it correct to say that

Rᶜ = {3, R}?

Since R = {1, 2}, this would mean

Rᶜ = {3, {1, 2}}.

I'm confused about whether this is actually valid. Does treating R itself as an element of U cause any problem with the axiom of extensionality or any other axioms of naive set theory?

Also, what does it mathematically mean for the set R itself to be an element of its complement?

For context: Just started reading the Naive Set Theory Book

I did my Leaving Certificate in june and needed a 60% for honours maths. I didn't get it so I applied for two make up tests. I didn't get them. I was so confident with one of them, I thought for sure I passed but it wasn't good enough. I am heartbroken and angry because all I've ever wanted to be was an engineer, I make robots and other projects but as soon as I have to do maths I fail.

Does anyone have tips or books to help. The maths book we used for LCHL maths was useless. We do a good mix of algebra, calculus, statistics, probability, trigonometry, geometry etc.
I also want to progress, perhaps even start learning topics for university.
Im desperate, I can't take another failure, I already feel like the worlds stupidest person as it is.

By different dimensions, I mean row vectors and column vectors of the same size. Is dot product product only concerned with the number of elements inside the two vectors only? We could transpose one of the two vectors and then multiply them but wouldn't transposing make it a different vector of different properties?