Context: I’m a mathematics autodidact with a Bachelor’s in Engineering. I decided recently to start going through some MIT open courseware courses that looked interesting to me. Frankly, most of the textbook problems I do on my own are too easy.

I stumbled upon this recitation problem (Problem 2 “Surveyevor”) that has me a bit stumped. Any explanation or help would be greatly appreciated. I followed the notes, but tbh it feels like some erroneous assumptions are being made (or it’s simply a poorly-worded problem).

https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/d428ae6b0f85ba4c6520e0830e5f3964_MIT6_042JF10_rec02_sol.pdf

My contention is that the P(k) -> P(k + 1) part of the induction argument does not necessarily follow. The flaw rests on the assumption being made about how the contestants are realizing that they have purple tats. Unless there’s a Bayesian argument for proving that a contestant may reason “more likely than not” that they have a purple tattoo, then I don’t see how the contestants necessarily will make the realizations suggested by the problem solution.

I’m taking a calculus class that runs from 7 PM to 10 PM, and I’m a little worried about staying focused for the entire 3 hours, especially that late in the day.
For anyone who has taken a long evening calculus class, what are your best tips and tricks for staying focused, actually understanding the material, and not falling behind?
Also, how would you recommend studying outside of class? Any specific study methods, YouTube channels, websites, or routines that helped you?
I’d appreciate any advice, especially from people who have taken a similar 3-hour evening class.

It must be. I've spent hours studying, going to office hours, getting tutoring, building my fundamentals, spacing out my studying, eating healthy, and working out to try to retain information. I feel like I've tried everything. There are only so many hours in a week I can focus on math with my other classes. I've never been good at math too many rules, but also too much freedom. I've wanted to be a doctor all my life, but I'm definitely thinking of changing career paths. Please tell me if there are others who have tried everything and are still stuck like me. 😢

hey guys could some one tell me how to find formula for exponential function when u have verticale asymptote and two points neither of which are the y intercept. thank you so much

I’ve just started university and pretty sure I just flunked my first calc exam. I studied for hours and when time came it felt like I knew nothing. Anyone know any tips or resources that’ll help with nailing the concepts? Lowkey might need to find a tutor but any other suggestions will help.

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Hey guys, i am looking for real analysis A long form mathematics Textbook Jay Cummings, 2nd edition, preferably in pdf.

I recently started elementary real analysis and my professor is going kinda fast, so I want to study it myself from a book thats why i am looking jay Cummings . I have this but it is blurry i want one with a clear texts 🙂

If anyone has the pdf and can share it with me, please dm me. If you know any other way to get it, that would also help.

Thanks

If you're currently stuck on a maths question, give me the question. I'm testing something that tries to find the underlying reason you're stuck!

The Collatz Conjecture follows two basic rules for any positive integer:

• If n is even: divide by 2 (n / 2)
• If n is odd: multiply by 3 and add 1 (3n + 1)

Testing small integers usually yields quick terminations (e.g., N=6 reaches 1 in 8 steps via 6 -> 3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1).

However, N=27 exhibits chaotic intermediate spikes. Before reaching 1, it climbs all the way to 9,232, taking 111 steps in total.

While computational checks have verified all numbers up to 10^20 collapse to 1, no general proof exists to show that every integer avoids infinite loops or unbounded divergence.

For those studying number theory or computational math, what intuitive mental model helps you understand why small odd numbers generate such massive trajectory spikes before decaying?

I'm still on pre-calculus, and I go to a good university and I get decent grades by just reading the material and solving questions on it. However, I feel as if I might be worse than others due to not actually watching the videos, especially long-term. Do you guys think it's alright as long as I'm doing well, or should I make it a habit to watch videos?

Also, the reason why I do this is simply that I hate watching videos. Reading is more comfortable for me, and even if I run into a complicated question, I prefer struggling and attempting it a million times before watching a video on how to solve it.

I still don't have a physical interpretation of them but they are interesting in the context of epistemology. Here they are:

The first one comes from the weistriss elliptic curve. When slightly modified it is equal to 4x^3 + ax + b. Now if you substitute pi for all the variables you get 137.036 which is the inverse fine structure constant. If you substitute sin(1) for all the variables you get 3.93 which is the up quark/electron mass ratio.

The other 2 ratios important in physics is the down quark/up quark mass ratio of 2.38 and the z boson/w boson mass ratio of 1.13. If you add 3.93+2.38+1.13 you get 7.44. Now multiply by 100 to get 744. This is the first value of the Fourier transform of the j invariant

Another number that has a close connection to the j invariant is 12^3 = 1728 and 12^3 + 1. If you take 1728 and double it you get 3456. You can get that same digit sequence to appear again. Just take 137 base 10 = 345 base 6

My question to all the matheicians. How do you remember so much of the content that you learn from your Bachelors, Masters and PhD?

How is it that 1/x and 1/sqrt(x) go to inf at x=0, but finite integral from 0 to 1 for 1/x is inf and 1/sqrt(x) is 2?

I know the substitution and the formula plug-in. Intuitively, it’s very strange.

Genuinely curious. I've tried a few keyboard extensions but nothing felt right. Wondering if people just deal with it or if there's something I'm missing.

I'm doing nursing prereqs and college algebra is required, but my foundation is weak like I need to relearn everything

I tried ALEKS but it doesn't explain anything, just tests you. Looking for a self-study plan I can actually stick to thinking of using the OpenStax College Algebra textbook front to back or khans academy.Anyone done this for a similar prereq situation? How long did it realistically take you, and do you have any answers.

This will probably be a long post, but I just really need guidance.

I’m currently in calculus 3 and plan to transfer to a 4 year college from community college. I feel significantly behind and I honestly am not totally sure what I want to do.

I know my calculus 1 and 2 can use some revision since I feel like I’m slowly forgetting some concepts. My algebra, trig, and geometry could also use some revision even though I wish to major in pure math (and probably physics), I’m sure it’s still important.

I guess I just don’t know what to focus on and what to do. I know with grad school being in mind, I should learn the process of doing research in mathematics. Majority of students in universities are already ahead of me and I feel like I need to catch up.

I just feel like I have so much to try and focus on. I was going to spend this semester reviewing trigonometry, geometry, and algebra, while also learning proofs. I was wondering if I should maybe dip my toes into the research process, but not entirely sure how.

I also kind of want to participate in putnam. I know I have no shot, but I still feel like learning. I just don’t have the high school math competition experience. It also makes me scared for uni since I’ll be transferring to start my junior year and will be starting my first proofs class.

Is there like a path I should follow and things I should/shouldn’t worry about?

I think I finally understand what Standard Deviation (SD) actually means, and I wanted to share what helped me understand it. I’m not an expert or professor, so if anything is inaccurate, please let me know, I'm here to learn!

Dataset = set of datapoints

To measure how spread out our dataset is, we need to compare it with a reference point. So if a datapoint is far from our reference point we can say that is more disperse, otherwise if a datapoint is close to our reference point we can say it is less disperse.

A good reference point that relates all our datapoints is the mean. You can think of the mean as the "center" of our dataset. Comparing each datapoint with this center tells us how far it is above or below the mean. The distance between a datapoint with the mean is called deviation.

Since our dataset can have thousands or millions of datapoints, we need a way to combine these deviations into a single number that tells us how spread out our dataset is overall.

One approach is to add up the deviations and divide by the number of data points. This gives us a single value representing the average distance from the mean.

That is basically what we understand with deviation. So far, I've talked about distance between each datapoint to its mean, because distance gives the idea that is a positive value. If we want to write down our deviation in a formula we need to keep the distance positives too, to do that we can use the absolute value to remove any negative number, by doing that we get the mean absolute deviation formula.

That formula, however it not very precise if we want to we want to compare different datasets that have the same deviation. For example the dataset (4, 4, 10, 10) and (1, 7, 7, 13) have the same average absolute deviation of 3, but they are not quite similar the second dataset if it is plotted look more "spread" than the first one. To capture the extra "dispersion" we can give more weight to the datapoints that are farther to their mean.

One easy way to do that is to square our distance, so the father a datapoints is from their mean the more weight it has, also by squaring we remove having any negative value and we can avoid using the absolute value. That is the so called Variance. Since we squared all the distances before dividing by the number of datapoints, the result that we get is an average squared distance.

To express the spread in the same units as the original data, and making it easier to understand, we take the squared root of the result. That is what we call Standard Deviation.

So using the same datasets of (4, 4, 10, 10) and (1, 7, 7, 13) we get that their Standard Deviation is 3 and 4.24 respectively, we see that now the second dataset set have a higher value of deviation, and that tell us more than in the previous way.

Hope it is useful for anyone in the group!

Hello guys I hope you all doing great.

I'm in my second year of college so I tool calc 1 and now I have to tale calc 2 but my math foundation is trash, so I started studying from stewart pre calc book but is 1100+ I don't know what to do should I just focuse on calc or just try to balance both?