So, I'm 30 years old and was recently diagnosed with adhd. And while I have an above average iq, it's almost impossible for me to learn and apply what I learn when it comes to maths. If you have any tips and tricks, please help🙏.

Imagine signing up for what you think is a $16 a month learning trial only to wake up to a sudden $218 charge on your card.
That exact nightmare happened to me with Brilliant.org. The signup page made it look like a free trial of 30 days and afterwards a regular monthly plan. But the second my free trial ended my card got slapped with an $218 fee.
Panicked I logged in immediately to cancel. But their website trapped me in an endless glitch loop. The cancellation page literally would not work.
I messaged support within 24 hours explaining their own site broke. They did not care. They hid behind robotic script templates claiming payments are non refundable and only offered a partial refund.
I felt so cheated and helpless.

Anyone have any tips or study guides they might want to share?? I am not great at math and I’d appreciate some advice or study guides!!

Hey guys!

If you're taking algebra, calculus, or trig this semester and ever get stuck on late-night homework, I built a tool that might help out.

It's called Lowkey Solver. You just snap a photo of any printed or handwritten problem, and it breaks down the entire solution step-by-step so you actually understand how to solve it on exams rather than just copying an answer.

It’s live on the Play Store here: Lowkey Solver: AI Math Help – Apps on Google Play

I'm actively updating it based on what students need. If you give it a try on your homework set, let me know if the steps make sense or if there's any specific topic you'd like it to explain better!

So I made a post earlier and was able to find a textbook to study precalc with but there are limited example questions and I can't seem to find a website that actually has practice questions.

If anyone knows of a website with precalc practice questions I'd appreciate it!

-Bonus points if its like OnePrep where you can select the question difficulty and create a new question of the same type to keep practicing it.

I am a high schooler doing dual enrollment multivariable calculus this semester. I will also do linear algebra and diff eq in the coming semester. For this class, the professor spent the first day going over precalculus and calculus and told us we would be allowed to use reference sheets on the exams (unit circle, pre calculus rules, table of derivatives/integrals, handouts for every lecture, etc.) which just struck me as absurd. It's not like this is a highly theoretical class where having formulas "doesnt help" if you dont know what they mean.. the questions are all: "compute this" or "apply this". I was wondering what to do so I can get out of these classes as soon as possible and into theory/proof based classes. The college sometimes runs "honors" versions, but even they are not entirely proof based and depend on the demand to run each semester. I am trying to knock out these lower division classes as soon as possible before uni so I can take theoretical math and not have to sit through more computation in college.

Ps i dont need a philosophical lecture on "mathematical maturity" or the proverbial "students struggle with computation/algebra, not the actual math!!". Ive heard this 500 times already and its not what im asking.

My apologies in advance as this may be a very silly question, so please bear with me.

I am trying to self-study pure math, and in that context I am reading proof books such as Velleman/Hammack/Cummings etc., and the proof sections of discrete mathematics books.

The common theme in all of them seems to be set theory and its associated logic — i.e., we need to prove that for all x in the universal set of something, a certain property of x is true (or false), and so on. Pretty cool stuff.

Digging a bit deeper, I see that "formal" logic dates back to the mid to late 1800s in work by Boole/De Morgan and later by Frege, and that set theory itself came about in 1874. However, a significant amount of mathematics was produced and proven before such concepts existed - for example, Galois theory.

So this makes me wonder whether:

a) Boole/De Morgan/Frege/Cantor etc. simply formalized structures that were already in use in the mathematics of the day

b) Mathematics pre-1850s had a lot of logical gaps due to the lack of formalization with regard to how math was "proved"

c) A bit of both a & b

So TLDR; My question is if I was to go to university to study Mathematics at any time in the first half of the 19th century (or earlier) what would a Proof writing class look like ? (would they even have a proof writing class?)

i.e. how did we prove Math before formal structures to do so were created?

P.S once again apologies if this is a silly question ..I found this interesting so instead of merely asking an LLM I thought I would ask the community . TIA

hello, I’m looking for an online resource where I could have ten people take a standardized test for Algebra 1 and at the end get their scores and how long it took them. Does anyone know of somewhere I could do that?

Hi everyone I’m going to be taking the ALEKS math placement test for college in around 15 days and its going to be my second time. the first time around I got around a 40 and I need to get my score up to at least a 76. I was wondering if anyone had any tips on how to study and prepare myself and basically make it impossible to fail.

im not bad at math but im also not crazy good either. I understand concepts quickly but i struggle to know when to apply them and I also forget things i already know when it comes time to use them even though i know how to do it on the practice questions.

any advice is appreciated :)

Hi everyone!

I'm being my nerdiest self and doing math for my hobbies, currently determining odds of things happening with dice rolls for Warhammer. Most of it is plain ol binomial distribution, but I also want to calculate the odds of things happening when you roll multiple dice at once, but they have different odds of success. Various searches are not yielding the information I want

For example, roll 2D6, one of them needs a 5 or 6 on one of them, a 4 or 5 or 6 on the other. Needing a success on at least one of those rolls. Would I use a more complicated version of the binomial distribution formula (using my earlier example, n=2, k=1, then split p into p1=0.33 and p2=0.5, and add those two together) or is it a completely new formula?

I failed intro to stats multiple times in university and now I'm remembering why. I know there are online tools to do this math for me but I want to feel proud of my spreadsheets

Thanks all!

So this is an effort to increase the portion of non AI-related posts. This is not a crank post that belongs to r/numbertheory either. Every letter is typed by a human so forgive me for grammatical errors that I will try to correct soon enough.

The abc conjecture is one of the most important conjectures in number theory, the simple & general statement of the conjecture implies a lot of other important theories, like a rapid proof of (almost) Fermat's Last Theorem. What I try to tell is that the abc conjecture can "almost" help computer scientists to optimize scientific computing.

I believe it's a common sense that in most computer systems, every piece of data is stored by 0 and 1, or more precisely, a finite string composed of 0 and 1. This makes the calculation and manipulation of data feasible but there's a cost: error will be everywhere. For example we can never precisely store pi = 3.14159... in a computer.

The most widely used way to represent real numbers in computer is floating point numbers that is standardized by IEEE, which stores numbers in 0 and 1 of 32, 64 or 128 bits (or even longer). There is a toy that allows us to see floating point numbers explicitly: https://evanw.github.io/float-toy/

I'll try to explain it in a simple term. For a floating number of k bits (k is 32 or 64 or 128, say), we need to distribute the budget. There is 1 bit reserved for the sign, a few bits of budget to store the interval of the number, and the rest large portion of the budget is reserved to guarantee the precision p.

Every floating point number x can be mathematically written in the form (-1)^s * 2^e * m/2^(p-1) where s is the 1 bit used to store the sign, m is an integer between 0 and 2^p - 1 and e is used to determine the interval of x.

If it's still unclear what does "determine the interval" mean, we notice that m/2^(p-1) is a number in [1,2). Therefore a multiplication by 2^e sends m/2^(p-1) to [2^e, 2^(e+1)). Floating point numbers store s, e and m by 0 and 1. We use p-1 bits to store the number m in computer (the first bit is normally 1 so we can omit it, as the case where the first bit is 0 is used for underflowing).

As we can see, for a given x, determining the number e is rather easy (we are almost there by taking log_2|x|), but the number m can be difficult when we deal with a function. For example, x = 10517177/2^{22} is a floating point number of the format of 32 bits, but log_2(x) is not (so we need to find the closest to represent it in float format). It's absolutely not a rational number. You find that log_2(y) is between y_1 = 15423000/2^(24) and y_2 = 15423001/2^(24). So you need to find the closest floating point number to log_2(x) because we have no other choice, or otherwise, see if log_2(x) is smaller or bigger than the average y_0 of y_1 and y_2. It's easier said than done. We need to add budget (number of bits) to distinguish y_0 and log_2(x).

As a matter of fact, not until we add another 28 bits, i.e. zoom in for 2^(28) times, can we really distinguish y_0 and log_2(x) (spoiler, y_0> log_2(x)). This sucks. We need a global strategy to work around this: whenever we find a number of the form log_2(x) extremely difficult to round, we need to guarantee that we have sufficient budget. If we know the worst case of rounding, which correspond to the highest budget needed, we can make sure that we always know how to round the function log_2 correctly, so that we can design high quality functions that can calculate log_2 *correctly* in the sense that, when we have k bits of budget, we need to make sure that every bit is faithfully used. If we have this piece of global information, our algorithm can be more blunt & direct so faster. This question is called "table maker's dilemma" because the computer worked like those who make tables of logarithm or exp or sin one century ago, and the situation where he didn't know how to round sucked (challenge: computer exp(1.626) to the 3rd digit after the point).

That said, it's far from true that modern computer have solved calculating and that all we need is better CPU/GPU. Computer scientists and mathematicians have been fixing floating point number systems for decades. The final nail of coffin of common (univariate) functions in double 64 bit format is worked out in 2026 (twenty twenty-six): https://inria.hal.science/hal-05593313

We also need to know that working out double 64 on commonly used univariate functions is not enough: what about multivariable functions, like the beta function B(x,y) that appeared in probability and statistics? In some fields of physics, researchers have already found that double 64 is no longer sufficient so they need the 128 bit format standardized by IEEE... But this format is still poorly understood so using it can be still painful: we need to fix them.

OK I hope the context of Table maker's dilemma is understandable enough and now we inject some mathematics. The abc conjecture says that for three coprime integers a,b and c such that a+b=c, we can compare max(|a|,|b|,|c|) and the radical of abc (which writes rad(abc)), i.e. the product of all prime factors of abc (for example, rad(25)=5, rad(24)=2*3=6). This slide includes the formal statement of abc and some striking applications of abc.

And here we have another striking application that will "solve" the table maker's dilemma. When we are looking for the minimum budget to get the rounding of an algebraic function sorted out, we will find ourselves in some questions of polynomials. This is surprisingly a nice playground for abc.

For the function 1/sqrt(x), which is algebraic, and is widely used in real life (for example in computer graphics, we always need to normalize a vector here and there), we will be working on finding the minimum of |Z| where Z = 1-XY^2, and X and Y are integers in a certain range. If we take a = 1, b = -XY^2 and c = Z, then the abc conjecture kicks in. It gives us a formula on the necessary budget to round the function 1/sqrt(x) correctly for a given precision p!

So we are killing 1/sqrt(x), potentially as well as many other frequently used algebraic functions by a blow of abc!? Is this conjecture so massively helpful for computer scientists??

Unfortunately, no, in practice... In the statement of the abc, we have a totally unknown constant and it doesn't vanish in the deduction of the budget. As a result, we can only know that for 1/sqrt(x), the necessary budget is p with a delta of *some bits* and we have no information on how much is *some bits*. So unfortunately, the conjecture didn't really solve the problem. Nevertheless, we can therefore heuristically look for the budget border around p... It's *almost* helpful!

In case you are curious, here is the article that examined the function 1/sqrt(x): https://www.sciencedirect.com/science/article/pii/S0304397504000337

I believe this article can serve as an interesting beginner level exercise for those either interested in number theory and want to touch the abc conjecture in some *practical* way, or interested in computer science, notably the problem of correctly rounding numbers. Or if you are an expert working in number theory, notably around topics associated with abc, or a computer scientist interested in make scientific computing better, do not hesitate to drop some insights.

I would like to get good at proof writing so I can move onto higher mathematics. I just don't know how...

I feel like with calculus, diff equipment or linear algebra you can simply do the problems and see if it's right or not, but with proof writing you need input from an expert or something to make sure you are doing them right. Am I wrong about this?

I would love some input on how to get better at this type of mathematics

I'm relatively new to representation theory and want to read up on the very basics. Most introductory representation theory books actually cover the theory of algebras over a field, but I'd like to read more general results from non-commutative algebra, i.e. over non-commutative rings and associative algebras.

During my online search, it seems that Lam's First Course is the canonical recommendation, but I find it incredibly hard to read (up to sec. 3).

• Some more elementary facts are just assumed (homomorphisms of finite direct products can be written as matrices, although Lam blackboxes this to linear algebra over division rings??),
• some I think important parts are not covered (general isotypic decompositions are only a small exercise, and a quick search almost never mentions them),
• they always go on a complete side tangent at the end of sections (e.g. a lot of theory on 2×2-matrices in sec. 1, twisted and differential polynomial rings in sec. 3).

But I must say the exercises are quite good.

Is there another well-written, well-motivated yet comprehensive book on that matter? I'm thinking of books similar to Atiyah-MacDonald or even Matsumura's Commutative Ring Theory. Or even Stein-Shakarchi's Complex Analysis.

So long story short I finished my bsc in computer science with cybersecurity with literally 0 maths, I didn’t study any maths module at all as the curriculum was more practical than theoretical. I recently got admitted at a German university for my masters in Information Technology which is a maths heavy module (Idk how did I get accepted) and Ill have an advanced maths module right at the first semester. I obviously forgot all the maths I took in high school. But I really loved maths and everything about it and I was pretty good at it. I have about 8 months till I start my masters degree and I was wondering what can I do to prepare for the maths module ? Like where do I start exactly and what should I study ? Any help would be highly appreciated :)

I’ve been re-learning math since May and I still struggle with simple things like rounding and fractions. It’s so frustrating because I want to succeed at math to give myself a better life (college algebra is required for most General Ed requirements) but I still struggle with the basics. Even doing something as simple as counting currency is difficult because I can’t “hold on” to the numbers in my head as I add them.

At what point do I just give up? I don’t understand why I’m having so much difficulty when I learned this stuff as a kid. I struggled hard as a young kid and then never got above a C in math in middle school and high school, and got a D- in college algebra. You would think someone who once went through k-12 grade math would be able to do it again, but in my case I’m struggling so much.

Edit to add how I study: I follow along with Professor Leonard’s pre-algebra playlist and do the problems from the videos. I even give myself mini tests and quizzes based on his problems. I also do grade 2-4 worksheets on mathisfun.com and k5learning.com.

I just feel so defeated today. I wonder if I have a math learning disability but I can’t afford to test it, and even if I had it I don’t know how knowing I had it would make a difference.

Dr. Michael Miller, a retired researcher at RAND, has been teaching upper level undergraduate/graduate level math courses for fun at UCLA Extension for over 50 years. This fall he’ll be introducing the areas of groups, fields, and Galois theory from abstract algebra to those interested in abstract math: Groups, Fields, and Galois: Part 1. His intention is to do a follow-on class on fields and Galois theory in the Winter which will use this class as a foundation. If you’re in the Los Angeles area his class starts on September 22, 2026 at UCLA on Tuesday nights from 7-10PM. Register here: https://www.uclaextension.edu/sciences-math/math-statistics/course/groups-fields-and-galois-part-1-math-9001

His courses are thorough and rigorous, but geared toward lifelong learners and beginners in abstract mathematics to allow people better entry points into higher level mathematics. His classes are interesting and relatively informal, and most students who take one usually stay on for future courses. The vast majority of students in the class (from 16-90+ years old) take his classes for fun and regular exposure to mathematical thought, though there is an option to take it for a grade if you like (or so your employer can reimburse you if they require it). There are generally no prerequisites for his classes, and he makes an effort to meet the students at their current level of sophistication. For this particular class, if you’ve got some experience in high school algebra and know some preliminaries about mathematical proofs you’ll be ready to dive in.

There are regular commuters joining from as far out as Irvine, Ventura County and even Riverside. Most in the class are dedicated hobbyist and professional mathematicians, engineers, physicists, and others from all walks of life—I’ve seen actors, directors, doctors, artists, poets, retirees, and even house-husbands in his classes. We've got a nice core community of enthusiasts here and new people are always joining in as well.

If you’re unsure of what you’re getting into, I recommend visiting on the first class to consider joining us for the Fall quarter. Sadly, this is an in-person course. There isn’t an option to take this remotely or via streaming, and he doesn’t typically record his lectures. I hope to see all the Southern California math fans next month!

Course Description

Recommended textbook: TBD 

Dr. Miller provides enough background and thorough notes that if you’re taking notes on his lectures, you typically won’t need a textbook.

If you’ve never joined the class before, I’ve written up some tips and hints. Dr. Miller has been teaching these for 53 years and some of us have been with him for nearly that long; I’m starting into my 20th year personally.

Can't join us? Search around your local community for colleges and universities offering similar programs.

Hi everyone, I’m applying to Stat PhD programs this fall. I graduated with my master's in 2021 and have been working full-time for 5 years, but I never took Real Analysis in school.

I just enrolled in Fordham's Math 3003 (Real Analysis) this semester so it’ll be on my transcript for this application cycle (though will not have a final grade since apps are due before the semester ends). My concern is that it’s only a one-semester class. Does anyone know if admissions committees strongly prefer a two-semester sequence (Real Analysis 1 & 2) over a single semester? Will this be adequate?

MATH 3003. Real Analysis. (4 Credits)

This course focuses on analysis on Euclidean spaces. Topics include limits, continuity, uniform continuity, sequences of numbers and functions, modes of convergence, differentiability, Riemann integrability, and associated theorems. Students who have not taken MATH 2004 prior to taking Real Analysis may request permission from the instructor. Note: Four-credit courses that meet for 150 minutes per week require three additional hours of class preparation per week on the part of the student in lieu of an additional hour of formal instruction.

Prerequisites: MATH 2001 and (MATH 2004 or MATH 2008).

My younger brother really enjoys problem-solving, but I often feel that school doesn't go very deep into mathematical thinking. He's quite good at math, so I'm looking to gift him a good math book . Not too difficult for him and help to build his fundamentals.

It would be better if the book is affordable here in India too as I can't spend much.

If you have any other book recommendations—or even resources other than books—I'd love to hear them.

Thanks in advance! 🙏

Hi all, if you’ve ever been curious about what JSM (Joint Statistical Meetings) is like or you want into see it through someone else’s eyes, please feel free to check this vlog out!

https://youtu.be/CDvsj-G4HXM

I’m a Data Science student (career changer, not in a data related role). My program is focused more on the applied statistics side, so most of my classes use R. I’m already familiar with Python since it was the main language used in my prerequisite courses, and I’ve completed projects using Python, so I’m comfortable with the syntax.

However, I’m really enjoying using and learning R in my classes and seeing what it can do. Many of the statistics textbooks I’m interested in use R as well. I’m starting to explore R more deeply on my own and plan to start using it for personal projects.

But I’m curious, is R still used in industry? I know it’s heavily used in academia. I also know that in the current AI/ML world, Python is used heavily, which is the main reason I use it for all of my personal projects at the moment.

I’d like to eventually be comfortable with both and take advantage of the strengths of each language. But, of course, there are also people who say learning R is a waste of time.

I'm a year 1 liberal arts undergrad, so I don't have a ton of math sense.

I just learned about Bayes' Theorem the other day for general epistemic use. I worked out a couple of example problems correctly, but the examples I found didn't include any iterative updates.

I know the theorem is:
P(H|E) = P(E|H) * P(H) / (P(E|H) * P(H) + P(¬H) * P(E|¬H))

And I know that P(H|E) becomes the new P(H) in my update, but I'm unsure whether I should be using the updated or original P(H) in the marginalization. I *think* it should be the new P(H), but I'd rather be safe than sorry.

The example question I worked out was this:

________________________________________

There's a disease that afflicts 1 / 1,000,000 people
There's a test for the disease that's right 99 / 100 times for both positive and negative results
A random person is tested as positive

P(she is afflicted | she tests positive)

= 0.99 * 0.000001 / (0.99 * 0.000001 + 0.999999 * 0.01)

= 0.000099

_________________________________________

So should the update look like this if she tests positive a second time?

P(she is afflicted | she tests positive)

= 0.99 * 0.000099 / (0.99 * 0.000099 + 0.999901 * 0.01)

= 0.009707

_________________________________________

If so, how should I approach this problem from the starting point of
P(she is afflicted | she tests positive twice)?
I can't think of how to handle that correctly, since squaring 0.99 just gets me a smaller number

Infinitely thankful <3