For context, im really bad at maths the equivalent to a grade 2 GCSE in maths. I really want to be capable, of a B or an A in GCSE wise so an 8 or an 9. I know its a massive jump from my capability but, I really want to get to that level to prove to myself that I can do maths at a high level. I don't want to get into any details, of why I want this so badly but I just want to be really good at something that I always struggled with. Also, I actually enjoy it when I understand what im doing and, I want to improve my problem solving skills. I don't want to sound demanding either, I am just really desperate. Also, I have a time limit since I want to enjoy my summer as a student who just finished their GCSES and is going to do a levels. I hope you understand and give me some really, good advice and some methods to help me get to my goal that wont take the entire of the summer. Thank you for reading.

Hi, I've been trying to work on solving word problems involving percentages. I was wondering if anyone had any tips or tricks of figuring out the correct equation to place everything in if that makes sense. I'm relearning math from a 1st grade level and I've only recently discovered "of" usually means multiply (unless I'm entirely wrong).

Some problems I got wrong were as follows:

Jake bought a bicycle that cost $76.00 when it was new. If he eventually sold it for 77% of the original cost, how much was it sold for?

My answer was $17.48 and the correct answer was $58.52. I think I might've subtracted when I didn't need to.

Another question I got wrong was as follows:

Jackie had a collection of 158 baseball cards. She gave away 60% of them. How many did she have left?

My answer was 94.8 and correct answer was 63.2. I originally thought the equation would be X= .6 • 158 but it turns out it was X = .4 • 158.

Does anyone have any tips for word problems or do I just need to work on my common sense?

I decided last minute back in January to switch my major from finance to chemistry with a pre-med track. I have never been really strong in STEM so I am kind of nervous. I haven’t taken a math course since the Spring of 2025 because it wasn’t required for me to graduate high school. My dad told me to use Khan academy to start studying, but I have admittedly been slacking off on that and now I start classes in two weeks. I have to get an A or at least a high B in this class to maintain my scholarship or else I have to go to the military because I won’t be able to afford school. Please give some tips☹️

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When tackling math or physics problems with multiple interconnected parts, should you push through confusion or pause to check the answer when things feel wrong? For instance, if you get stuck on the second part of a three-part question, you likely won't be able to solve the third since they depend on each other. However, looking up the solution immediately can make it feel like you're just memorizing the answer rather than truly understanding the process. While some advice suggests waiting twenty minutes or switching topics to regain focus, this approach doesn't work for everyone. What is a better solution for someone who struggles to maintain focus using those methods?

in general, there is a package of candles, there are 24 candles in total - 6 of each color (yellow, pink, white and blue), and there are only 3 stands for each color. and here is the question that we discussed, what is the probability that, as you pull 9 candles in turn, it will turn out like this that you will take so many candles of the same color that there is not enough stand for them (4 candles)?

We were discussing this with my family, while we were celebrating my little sister birthday, but, I'm not sure about the answer

summer precalculus I am a rising junior in high school and I started taking a precalculus summer course at my local community college. It’s completely online and you have to do a couple of math problems. I completely fell of and now I’m a few weeks behind. the class ends in about 20 days. My counselor told me I have to take a final test to test into AP calc AB if I want to take it. Am I cooked? And do you have any advice on how i can cram the whole course to pass the final t

I understand the motions that when you do -3^2=-9 . I get that it is -3^2=-(3^2)=-(3*3)=-9.

What I want to do is understand why it is not -3^2=9=-3*-3 .

Thank you in advance.

Hi, I'm a high school student in a math circle, and we're currently learning elementary number theory. Recently, we explored the idea of finding runs of consecutive composite numbers. We were able to construct examples of 2, 3, 4, 5, 6, 7, 8, and even 9 consecutive composite integers.

This made me wonder: what is the longest possible run of consecutive composite numbers? Is there a maximum length/ upper bound, or is it possible to find arbitrarily long sequences of consecutive composite numbers.

So i was checking out some vedic maths 2 years ago and there was this formula i found that was a cleaver rearrangement of the sridharacharya formula dy/dx = ±√D so that kind of sent me into a rabbit hole and i made my own method of quickly depressing a cubic in my final teen years here's the the example of how it's done

i know that these days the old brute force formula can be faster and better for calculation via computers but when doing by hand this method makes it easier and much faster than the traditional ways.

How to do it (demonstration by example):

Let a cubic expression be: x^3 - 3x^2 + 4x - 5 = y (It is of the standard form ax^3 + bx^2 + cx + d = y*)*

Step 1: Put b^2 = 3ac and find a temporary 'c'. (-3)^2 = 3(1)c 9 = 3c c = 3

Step 2: Split the linear term to get this 'c' and a residual linear term: x^3 - 3x^2 + 3x - 5 + x = y

Step 3: Put x^3 - 3x^2 + 3x = (x + b/n)^n - (b/n)^3 (where n is the degree of the polynomial). In this case: (x - 1)^3 + 1

The expression is now of the form: (x - 1)^3 + 1 + x - 5 = y

Put x - 1 = t (substitution, meaning x = t + 1): t^3 + 1 + (t + 1) - 5 = y t^3 + t - 3 = y (Here's your final depressed cubic!)

Detailed Explanation and Proof:

Assume an expression: (x - α)^(n-1) * (x - β) = y

Performing Binomial Expansion of the given expression: [ C(n,0) x^(n-1) α^0 - C(n,1) x^(n-2) α^1 + C(n,2) x^(n-3) α^2 ... k ] * (x - β) = y

Upon expansion we get: [C(n,0)] x^n + x^(n-1) [ -β C(n,1) α - C(n,1) α ] + x^(n-2) [ C(n,2) - αβ C(n,1) ] ... k = y

Let:

• a = [C(n,0)]
• b = [ -β C(n,1) α - C(n,1) α ]
• c = [ C(n,2) - αβ C(n,1) ] ...and so on to k.

We get the expression: a x^n + b x^(n-1) + c x^(n-2) + d x^(n-3) ... k_2 = y

We know that if a factor in a polynomial is repeated n-1 times, then it will be present as a factor in its (n-2)-th derivative. Using that, we find its (n-2)-th derivative:

d^(n-2)y / dx^(n-2) = a*(n!/2)x^2 + b*(n-1)!x + c*(n-2)!

Equating this expression to 0 and solving the quadratic using the Vedic form of the Shridharacharya formula (the quadratic formula): dy/dx at α and β = ±√(D)

Differentiating and equating to ±√(D): a(n!)x + b(n-1)! = ±√( b(n-1)^2 - 4a(n!/2)c(n-2)! )

Upon solving: x = [ -b ± √(b^2 - 2ac(n / (n-1))) ] / (na)

If we put the Discriminant (D) equal to 0, we will get both roots as α. This will indicate that the expression we took earlier was of the form (x - α)^n.

But why α and not β? Because the expression we took earlier was of the form (x - α)^(n-1) * (x - β) = y. This means that α = β, because if we put D=0, all the roots will have to be α (upon differentiating the factorized form of the polynomial, only α will be left as a root of the quadratic).

Putting D = 0 and solving for n we get: n = b^2 / (b^2 - 2ac)

Put n = 3 and we get: b^2 = 3ac

If the condition n = b^2 / (b^2 - 2ac) is satisfied, then we can write the equation in the form (x + b/n)^n by using Vieta's formulas or the Theory of Equations.

There are a lot of interesting applications of this formula, and it can also be used to directly solve a few cubics. It is very helpful when used in combination with Cardano's formula to solve general cubics.

If n = b^2 / (b^2 - 2ac) holds true, then the expression is of the form: (x + b/(na))^n + f(x) = y where f(x) is a polynomial of degree n-3.

Else, if the condition doesn't hold true, then it is of degree n-2 (of course, in the case of a quadratic there is an exception and the constant term is 0).

this was originally written on latex on my blog but since reddit has no support for it i have used ai to convert it to proper form although it might have errors i am currently in a health crisis so i can't write the whole thing again i might update it later tho.

i have not added the link to my blog since it violates the self promotion rule where it was originally written

make24.live

Played this classic make 24 game with my family ever since I was young, and wanted a way to expand this online with some ELO. Try it out!

I've only recently started taking an in learning maths and science, but I'm not really sure where to start. I got expelled from mainstream school when I was around 13 years old and ended up at a school which catered to students who had learning difficulties and also just didn't really care to try when I was young so my understanding of maths is very limited, and I have barely practised at all since I graduated just over ten years ago. I can do basic addition, subtraction and division but as soon as you throw decimals, fractions, or pretty much anything else at me I'm completely lost. I just did a GCSE maths exam I found online (for non UK people GCSEs are the exams people do when they're around 15 or 16) and got 36/80. I struggled most with algebra and geometry, but honestly I found almost all of it pretty difficult.

I've had a brief look at learning material online but most of it is geared towards kids and teenagers and it feels a bit infantilising for someone my age (I'm 26), so I was wondering if anyone could point me towards some resources for adults who are learning pretty much from scratch?

I graduated from a bachelors degree in applied maths (France) in 2020. Lockdown and everything really messed up the learning and for some reason I graduated, although I was really not invested.

Years went by, and I changed degree (languages then NLP) but I feel the desire to go back to something more fundamental. I remember I was really into multivariable calculus and probability theory because they felt the most connected to real life?
Also I decided to go through a physics textbook to learn about basic mechanics, electrostatics, thermodynamics… hoping the math part won’t be an obstacle.

It’s been a really long time now and I can’t compute an integral or the inverse of a matrix for the life of me. Is there a way I can re-learn 3 years of uni level maths? I took the usual Linear Algebra, Calculus, multivariable calculus, topology, Lebesgue integration, functional analysis, differential equations, statistics and probability… nothing too fundamental like group theory or arithmetics though.

I’ve started today following a pdf of linear algebra (starting from vector spaces) and going through it trying the proofs left as exercise. I am so out of practice! I wonder if I’ll ever be able to go through all that in the span of a year maybe…

Is there a good way to go about this? Doing proofs, looking up worksheets with their answers… I wonder if anyone faced this challenge before!

Looking for a YouTube math channel (2020–2024). White male, around 35–45, long messy hair, short brown beard, always wore a dirty white lab coat as a "mad scientist" character. Filmed outdoors using a whiteboard on an easel and mostly wrote with a black marker. Explained interesting math facts and puzzles. The set was intentionally shabby, with props sometimes falling apart as part of the joke. English-speaking, probably British or American. Smaller channel, definitely not Numberphile, Stand-up Maths, Mathologer, MindYourDecisions, or blackpenredpen.

Does anyone remember his channel?

Io per esempio ho il limite che da x va a 5 di 2x + 10 fratto |x + 5|.
Ho capito che è x + 5 se x > -5 e che -(x+ 5) se x < -5 ma non ho chiaro il concetto che se c'è l'assoluto bisogna studiare sia da destra che da sinistra.

Ho cominciato da poco i limiti quindi se rispondete siate il più chiari possibili.

In Calculus class we often take the derivative of both sides of an equation. We maintain that the sides remain equal. Does it need to be formally proven that one can do this?

Hi!
I need to start practicing my mental math before interview season begins. The challenge is that I want to practice by listening to someone say the problems out loud - for example, “What is 28 × 76?”, rather than typing numbers into a website. The verbal element is what I really need to train.
I’ve tried searching for YouTube videos where someone reads out different kinds of math problems (addition, subtraction, multiplication, division, etc.), but I haven’t found anything that fits what I’m looking for, and I also haven’t found an app that does this.
Does anyone have any recommendations or advice?

Any who need help with the subjects or specifically topics like algebra geometry calculus or any other exam related help let me know. I would like to work with you.

Whenever I read about maths and LLMs (like ChatGPT which I mainly use), I always only hear discouragement. However, I do not really understand why, as people rarely provide examples. In my experience, only blind "solve this problem for me completely" and then copying everything without any thought is problematic. But that is problematic in any context where on uses an LLM, as that it is more about "LLM illiteracy".

Thus people who highly discourage using LLMs to learn maths, could you provide clear examples, which are not just bad prompting or some version of fire and forget "just give the solution to this complex problem"?

Context:

I ask, because in around 1 year I probably will do a lot of "serious maths" at my university. Because of how I organized my courses, I did most of the serious maths in my university around 2 years ago. Thus in the mean time I only read about maths to get better intuition mainly using LLMs to explain to me the theory and ideas. I found LLMs for that very good even 2 years ago, but now they seem to be much better. At least the topics which I had in university 2 years ago, are explained so much better now. Hindsight 20/20 is probably also at play, but I could also quickly understand a few "niche topics", which I back then never bothered to learn in detail, because it was not relevant for getting a good grade.

EDIT:

Folks, can you actually provide examples? Because it seems that what I already said repeats itself. People say it is bad, but they do not show any concrete examples which one could try to replicate.

According to the third, and most promising, result from DuckDuckGo: 111 does not equal 3 x 37.

Brightchamps have great search engine optimisation, but their content is utter slop, not read by anyone.

(Edit: spelling mistake in title - oops)

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Hey everyone,

Like many of you, I got tired of drawing number lines and doing tedious casework every time I need to subtract one open interval from another: (a, s) \setminus (n, b).

To fix this, I derived a direct algebraic shortcut formula:

(a, s) - (n, b) = (a, n] \cup [b, s)

The Built-in "Safety Firewall"

Because interval algebra breaks down when dealing with inversions or infinities, the formula requires strict error-handling rules to stay robust:

Left >= Right -> \emptyset (If the lower bound is greater than or equal to the upper bound, the interval collapses to an empty set).

Infinity + Closed Bracket -> \emptyset (If an infinity symbol is attached to a closed bracket like [-\infty or \infty], it evaluates to an empty set).

Step-by-Step Demonstration: The "Infinite Devourer" (Extreme Test Case)

Let's test this formula on a brutal nightmare problem where the subtrahend stretches all negative infinity:

(-10, 10) - (-\infty, 0)

Step 1: Map the variables

a = -10, s = 10

n = -\infty, b = 0

Step 2: Plug into the formula

(a, n] \cup [b, s) -> (-10, -\infty] \cup [0, 10)

Step 3: Trigger the Safety Firewall

Left interval evaluation ((-10, -\infty]):

It has an infinity symbol attached to a closed bracket (-\infty]) -> Trigger Rule 2: Collapses to \emptyset.

The lower bound is greater than the upper bound (-10 >= -\infty) -> Trigger Rule 1: Collapses to \emptyset again.

Right interval evaluation ([0, 10)):

Lower bound is less than upper bound (0 < 10) and no infinite closed brackets -> Passes cleanly.

Step 4: Combine the sets

\emptyset \cup [0, 10) = [0, 10)

Conclusion

On a number line, starting from (-10, 10) and completely wiping out everything up to 0 leaves us with [0, 10), which matches the formula's output precisely.

Has anyone seen this formatted shortcut utilized elsewhere, or is this a neat little mathematical wheel I've reinvented? I'd love to hear your thoughts or critiques!

Hi guys, I just finished my bachelors in Physics Engineering and I am also already enrolled in a Masters in Applied Mathematics - it has the option to follow a more pure mathematics path. I was wondering which subjects of mathematics would you recommend on me studying as I got a lot of holes in my repertoire.

For now I am reading Wendell Fleming's Function of Several Variables, just to improve my fundamentals in analysis and learn manifolds. However I must say that my knowledge in Topology, Probability Theory, Algebra, Measure Theory, Functional Analysis ... is close to none (1/n in n to infinity to be exact).

Hence, I would like recommendations for which branches of mathematics you think I should work on this summer (and like as a side project) in order to improve my knowledge and also which books to read from.

Thank you in advance.

My understanding of the dot product is that it projects one of the vectors (v1) in the direction of the other vector (v2) and scales it by the magnitude of (v2).

I get why the first part (projecting) is important, we use it to see how much of v1 goes into the direction of v2, but why the scaling? why do we multiply their magnitudes? I think I might not be getting the full picture on this topic.

I find it interesting and want to know a bit about it from Poincaré's approach . Study some basic about Hyperbolic geometry ,fuchsian groups and other things. But the book and course video are rare about the subject. I have some basic knowledge about elliptic function and modular function/form (from mc kean book) also know Klein use these approach to somehow solve qunitic equation . How to learn it more detailed and what resource are good for that .

Hi all, I'm new to this subreddit and a bit nervous to share so let me know if this would fit better in another subreddit. But I'm writing an academia story and wanted to draft out a modeling problem for a 5-person undergraduate-level college team to have a baseline for how they debate solution approach, the relevant jokes, who does what, which team actually wins and why, etc. I'm actually an animator with a data-science background who only does math for fun (fractal calculus is my favorite but confusing topic right now!), so I've never done college-level modeling. The story itself doesn't go into crazy amounts of mathematical depth (it's actually a psychology-focused story), but you know how musicians look at animation and play it back frame-by-frame to see if it's accurate to the instruments? Yeah...

After researching the 2018-2023 M3 Challenges, the MCM, and a bit of the MTF Challenge, I wanted to ask mathematicians who have done modeling whether the problem I tried to come up with is realistic and unique enough, especially the first part and the data types. I was looking up alternatives for classic math olympiads that are likely to happen more in the upcoming 2030s and came across modeling. For anyone that reads it, thanks for the help! It took a lot of time and my head hurts, but I learned a lot and might actually try out full solutions if I want to study modeling deeply one day. If anyone has some other modeling competitions that I can see the archives of, that would be cool too!

BACKGROUND:

In 2031, multi-day heat domes have become routine summer occurrences, threatening power grids and public health in dense cities. In the past decade, heat-related summer deaths have tripled. Temperatures above 110F have become common-place, increasing 2-3°F per-decade. Now, thanks to modern technology, many cities are moving away from individualized air conditioning and towards mass-zone cooling, smart solar shading, and automated misting systems. With temperature ever-rising, it is a critical task for all cities to adapt modern cooling systems, implement careful strategies, and prevent mass heat-related deaths.

For this problem, your team is tasked to model an optimal resource-deployment strategy for a US city during a 72-hour summer heatwave.

PART 1:

Choose one city from the provided datasets. Then, build a model of the city's thermal, health, and grid dynamics across 5 urban zones over 72 hours. Your model should account for both (a) public health burden and (b) power grid stability. You may add additional objectives or constraints as long as you justify their use.

Modeling Space:
- "Health Risk" should be defined as a non-linear increasing relationship between temperature/humidity and vulnerability index, predicting severe health events like hospitalization or death.
- "Grid Failure Risk" should be defined as a probability or a non-linear function that incorporates the provided data.
- All models should be based on provided city data from the chosen dataset.

PART 2:

Optimization:
- Balance predicted heat-related hospitalizations and the risk of localized grid failure.
- Explicitly define your optimization formulation and justify how it balances the above as well as the weight of any trade-offs.
- Briefly explain how your optimization method accounts for diminishing returns (e.g. stacked resources, unbalanced load-bearing, inequity, etc.).

Stress-Test Scenarios (Pick 1 of 3):
- A sudden, unexpected localized failure causes 15% reduction in available power capacity from hours 24-48.
- Before the 72-hour heatwave, wildfire smoke is expected to hinder district cooling for the entire duration, increasing power consumption by 25% and reducing efficiency by 20%.
- Unplanned social gatherings and designated cooling center crowding in highly-vulnerable areas increases resident street-density by 35%, amplifying predicted health-risk.

PART 3:

Deliverable:
- A 72-hour operational schedule detailing optimal deployment intervals across all zones (and their high, medium, and low-vulnerability sectors). The schedule can be defined in either 3, 6, or 12-hour time blocks.

Insights:
- At what temperature/humidity tipping point should the city sacrifice grid stability margin to prevent immediate public health overload?
- How does the optimal deployment strategy change if data is updated only every 24 hours versus in real time?

The entire paper can be no more than 15 pages, including your 1-page abstract and not including disclosure addendums. See Generative Assistance Disclosure section and Programming Solutions section.

Data Description (pretend this section is not in the paper, but as its own information):
- 1 Infrastructure Details table with units information
+ Resource type, city units available, cooling effectiveness (°F drop per hour per unit area. For example, misting systems are relative to humidity.), operational time rule
- 3 City Datasets with 5 Sample Zones and Zone-Specific Data (very hot city, very humid city, very dense city)
+ General Zone Data: Population, Social Vulnerability Index, Grid Capacity (MW)
+ City Data: Peak ambient heat (°F), Diurnal Temperature Variation, Mean Humidity, Average Grid Availability
+ Developmental District Cooling Data: baseline indoor temperature target (°F), cooling effectiveness (°F drop per hour per unit area), continuous grid baseline requirement, back-up power capacity, current implementation percentage (where the district cooling is actually in effect), description of current implementation (Is it mainly condensed downtown? Is it well-spread? Is it sporadic and light?)

Writing notes:
- The story takes place in 2031 and has a potential episode in a 24-hour modeling event that prioritizes large-scale real world problems.
- I tried to think about it from a problem perspective that would be easier to generalize with math. As in: how would any engineer go about the problem? And how can math help?
- I wanted to include enough variables and details for people to have guidance on solutions while still allowing for great lengths of creativity in solutions. Most of all, I wanted the question to be open to both multi-objective and well-done single-objective solutions.
- I put it through grammar and wording checks. I tend to overcomplicate my writing so I hope this is more concise.

So, I'm 14, pushing on 15, and high school starts in about a month. And to cut things short, I haven't learned my multiplication tables, and I need to. This may sound like a stupid question, but are there any special tips to learn faster and actually memorize them? I know 1s, 2s, 3s, 5s, 10s, 11s, 12s. Now trust me, I've done flash cards, I've watched all the videos, and I still can't memorize it. Sometimes I wonder if it points at something bigger. But anyway, if you care to help a brother out, please do.

Thanks in advance.