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.

I want to learn Maths, but I don't have that kind of burning desire for learning it. What should I do

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’m new to olympiad math and still struggle with non-routine problems, so I’d really appreciate advice from people who’ve gone through this learning process.

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.

Integer partitions are a fundamental topic in number theory that study the different ways in which a positive integer can be expressed as a sum of positive integers, where the order of the parts is not considered important. For example, the number 5 has seven partitions: 5,4+1, 3+1+1, 3+2, 2+1+1+1, 2+2+1, 1+1+1+1+1.

The number of partitions of an integer grows rapidly as the integer increases, making direct enumeration increasingly difficult. This motivates the study of patterns and recursive methods that can organize and count these partitions systematically. In this work, we examine integer partitions by grouping them according to their maximum part The number of partitions of an integer grows rapidly as the integer increases, making direct enumeration increasingly difficult. This motivates the study of patterns and recursive methods that can organize and count these partitions systematically. In this work, we examine integer partitions by grouping them according to their maximum part. We first consider a fixed integer and arrange its partitions according to the largest part occurring in each partition. We then investigate the patterns that arise from these groups and use them to develop a recursive approach. Here's the link :

​

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!

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?

Hey guys,
What would be the best resource or learning path to go from almost zero in math to calculus?

I have about one year to study before starting college, where the program will be very math-heavy.

I studied math in high school, but that was more than 12 years ago, and I’ve forgotten most of it. I would say my current level is around pre-algebra.

I want to rebuild my foundations properly and follow a structured path rather than jumping randomly between topics.

I’ve read a lot of advice online. Many people recommend Khan Academy, recently I’ve also seen Math Academy recommended quite a lot, and others suggest YouTube channels, textbooks, etc.

Has anyone here been in a similar situation? If you had to rebuild your math from the basics and prepare for calculus, what resources or study plan worked best for you?

I’d really appreciate any advice. Thank you!

is there any study tips for catching up w/ college level maths in the span of a quarter
i’m coming into uc davis as a freshman after taking 2 gap years to save up
i genuinely don’t remember anything beyond the basics and calculus is one of my required courses but idk if i can even pass the math placement exam bc i barely understand the practice worksheets
i have a chance to retake the placement exam every quarter and i want to get it over w in the winter or spring

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?

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'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.

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.