I am reviewing fractions at the moment for the GRE. I am practicing problems but I am confused on when or why you would convert an improper fraction into a mixed number.

Are there rules to when you do this?

I am attempting to solve 2 1/5 - 1, as an example.

Thank you 🩷

Most algebra courses I've seen use general abstract algebra books which are somewhat encyclopaediac like dummit and foote. However I've seen Armstrong's Groups and symmetry used quite often for introductory group theory.

I'd be grateful if anyone recommend any standalone books covering just a particular object, specifically on modules, rings, fields and galois theory that can be read by a novice.

Hey there, I am entering in my 1st year of bachelors. Can anyone please share math contest and competitions in which all students can participate irrespective of their nationality.

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!

I've been wondering how many hands and arms on average do people worldwide (or just Australia) have. I was looking at research papers and one said that on average people have 1.998 hands, and another paper stated on average that people have 1.99765 arms. This seemed weird to me and i was wondering if this was just a rounding issue. Would anyone be kind enough to help me out with the math?

As I’m going through my studies, I find myself having to write more and more of the greek alphabet. It started off easy with ones like alpha, beta, theta, all very straightforward to write. Then I get hit with letters like xi, zeta, or chi which I either have to compromise by writing illegible scribbles or spend multiple attempts to get them right. Anybody else have this issue or any tips?

I’ve been reading a book by the name ‘Can You Outsmart an Economist?’ by Steven Landsburg which is proving to be an extremely gripping read. The book teaches you about economic and mathematical theory through puzzles and the specific chapter I’ll be referring to is a ‘quiz’ where you may or may not receive ‘irrationality points’ based on your answers. It’s very fun.

After completing the quiz, I got a single irrationality point and since I believe, understand and agree with everything else Landsburg has said (so far) I want to know what others think since I am confident I’m wrong but not sure how. The explanation in the book was sufficient enough to help me understand Landsburg’s argument but not enough to help me grasp why mine is ‘irrational’.

The question is this: There is an urn with 30 red balls and 60 blue balls. Some unknown fraction of the blue balls are light blue and the other are dark blue. You will put your hand in the urn and pull out a ball at random. Would you rather:

Q1A) Receive $1k if you pull out a red ball? Q1B) Receive $1k if you pull out a light blue ball?

And then…

Q2A) Receive $1k if you pull out a red or dark-blue ball? Q2B) Receive $1k if you pull out any blue ball?

My answers were A and then B. Landsburg argues that you are irrational if your answers to the two questions are different (I.e. A then B as opposed to A and then A or B and then B). Upon reading his argument, I understand: Q2 is identical to Q1 other than the fact that pulling a dark-blue ball rewards you independently of your choice, as opposed to being a loss independent of your choice. That is to say, the dark-blue balls always reward independently of your choice and are the only change from Q1 to Q2 so Landsburg argues the questions are the same: just asking you to pick between red and light-blue, and therefore if you are willing to bet on a potential 2/3 chance over a guaranteed 1/3 chance you should be willing to do so again since the question ‘has not changed’.

However, I currently argue that although maybe not maximally efficient, my answers had reasoning. In Q1 I opted for a 30/90 chance over ?/90 chance. In Q2 I opted for a guaranteed 60/90 chance over a (30+?)/90. In both questions, I essentially opted for an ‘extra’ 30 balls over an ‘extra’ unknown. That seems consistent and rational. For me the difference is Murphy’s Law. If I pick option 1B there’s a chance I could win with 0/90 (or 1/90 if we assume there is at least one of each ball type), and if I pick option 2A there’s a chance I could I could win with 30/90 (or 31/90…), both of which are worse than their guaranteed counterpart.

Was it truly irrational of me? If so I humbly await a further in-depth explanation of my mistaken argument. Thank you.

Edit: Landsburg’s Explanation:

Remember that you’re drawing from an urn with thirty red balls and sixty blue balls. Some of the blue balls are light blue and some are dark blue, but I haven’t told you how many. Now I want you to reach into that urn and draw a ball. If that ball is dark blue, I’m going to give you the envelope I’m holding. If it doesn’t come up dark blue, which would you prefer?

A. To win $1,000 if the ball is red B. To win $1,000 if the ball is light blue C. A and B sound equally good

A rational person can answer this question without knowing what’s in the envelope. After all, you either will or will not draw a dark blue ball. If you do, your choice won’t matter anyway. And if you don’t, it doesn’t matter what’s in the envelope. So there’s no circumstance where the contents of the envelope should affect your choice. Now let me reveal that the envelope is empty. That makes this choice identical to question 8. Oh, wait—I was mistaken. Actually, the envelope contains $1,000. That makes this choice identical to question 9.

Did changing the contents of the envelope change your answer? In other words, did you give different answers to questions 8 and 9? If so, you earned both an irrationality point and an invitation to lunch. I’d very much like to sit down with you and offer a deal: We’ll draw a ball from that urn. If (like many people) you chose 8A over 8B and 9B over 9A, we can make these trades: I’ll give you the prize from 8A, and all I ask in return is the prize from 8B. To sweeten the pot, I’ll give you 9B, and all I ask in return is the prize from 9A. As you can see, no matter what ball we draw, we’ll give each other $1,000 and break even.”

Hey all,

suppose i have a spline p(s) in R^n of degree>2 and ||p‘(s)|| nonzero. Is one of the two conditions sufficient for the normal bundle of this curve to fill R^n? p(s) is periodic i.e. p(s) = p(s+d) p(s) goes to infinity lim s->inf ||p(s)|| = inf I struggle with finding related resources that don‘t seem like a huge effort to go through (as i am an engineer). Any hints for papers/book/proof schemes would be greatly appreciated.

I hope this falls under the rule #1 of

All posts and comments should be directly related to [...other math topics or...] the community of mathematics.

I keep having arguments with my mom. She's incredibly kind and outgoing, but she doesn't understand how to accomplish things in a successful way. We had an argument recently about how she can arrange a part of her garden using asymmetrical pieces.

I just couldn't communicate to her how much harder it is going to be for her to fit together asymmetrical pieces to find a suitable shape than it would be if she used symmetrical pieces.

I ended up giving up and just told her to draw it out on paper first and iterate a lot until she has a model she can reproduce.

But I run into this situation often with people outside of my career; certain ideas require building up a large understanding of fundamental components and I just can't summarize all that to get my point across before they get sick of listening to me.

It is something I'm working on (I love teaching) but I find my frustration outpacing my patience a lot... especially with family.

How do you manage?

Sorry if this is a silly question, but if your field of study had a logo, what do you think would it be?

I’m not mathematically mature enough to say much about this myself, but I think an integral would do reasonably well as the logo of Calculus - it is relatively simple and very recognizable.

I am looking for an alternative to D&F -- one that is a bit more selective with detail, and is gentler with module theory?

I love the sections on group theory, and the sections on rings is also readable (at least when I read the corresponding discussion in Artin as a supplement), but then the module section is where it became really difficult for me. I've read the section (10.4) on the construction of the tensor product four or five times now, and I still can't understand his "essay" justifying the need for the tensor product for "extension of scalars" to a larger ring and what could go wrong if you do it naively. After that, it goes into exact sequences, etc., and I feel like I don't understand the point of any of these constructions anymore. I guess I shouldn't blame a book for me being too dumb to understand it, but it seems like the level of abstraction noticeably went up at around chapter 10.

The other irritating thing is that Dummit and Foote bury a lot of essential information in the examples in a smaller font size. There are a lot of them, and it's a bit tedious to go through all of the carefully on a first pass. However, some of these examples are in fact critical (at least for me) for understanding the intuition and nuance behind an idea/definition, but it's formatted in a way that's easy to miss, almost like an afterthought.

Any suggestions? Artin is my favorite algebra book so far in style and content. I didn't appreciate how good it is when I was taking abstract algebra in college, but (re)learning algebra from it has been a pleasure. I guess I'm asking, what book comes naturally after Artin? Ash's Basic Abstract Algebra is nice, but it's written too much like an outline/lecture notes than a book.

Hi, I have a question: what is the difference between wolfram alpha app (on windows for 3$) and wolfram alpha pro on website (which cost 52$ a year), I mean It must be better for that price but I don't see any advantages over the app.

Like I get they didn’t have a symbol but the idea that couldn’t convince of not having something falls flat to me, they had quadratics and trig not to mention some optics and other cool stuff. for the sake of the discussion say you’re a Roman money lender

Dude owes you 100 dinari but he’s a buddy so you’re not concerned about interest Pays it back 10 per week.

And you’ve got a slate and stylus. Every week you do your tally first 100-10=90 Next week 90-10=80 At the end of it you’ve got 10-10= what

What does that look like. Leave it blank?

I've always taken it for granted that L^1 or L^2 functions that are periodic can be represented as a Fourier series, but functions on all of R^n require an integral representation. Is there some intuition as to why this is?

I bought the first two for myself and I wanted to complete the set but for some reason the third volume is unavailable whereever I look. Why this volume specifically? Anyone have any clue?

This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.

Please consider including a brief introduction about your background and the context of your question.

Helpful subreddits include /r/GradSchool, /r/AskAcademia, /r/Jobs, and /r/CareerGuidance.

If you wish to discuss the math you've been thinking about, you should post in the most recent What Are You Working On? thread.

If I have a random matrix-valued stochastic process A(t), does it make sense to consider the SDE

dX(t) = A(t) X(t)dt ?

Here's my full question, crossposting here for more visibility.

https://math.stackexchange.com/questions/4947581/stochastic-differential-equations-with-only-time-integrals

for me it's alice in wonderland

Being exposed to generalized special functions, the MacRobert-E, hypergeometric, Meijer-G and Fox-H functions seem to be jacks of all trades, but where do we draw the line? Which function includes a wider domain and, possibly, other functions within it? Also more importantly, how do we numerically compute all of these (say in a general-purpose language like C, python or Julia)?

Hello I am a 2nd year student and Im taking Applied Physics right now. And I was just wondering what Math or Physics courses you took that was the hardest for you and if ever you had the chance would you take it again? Or no?

Thank you very much I am just curious enjoy your day :))

Hey everyone,

I'm starting my math master's degree soon, and I've got Real Analysis and Mathematical Statistics in my first semester. I've heard these classes can be pretty tough, so I want to get a head start on studying.

I've already bought these books to prep and help study for the GRE:

• Thomas' Calculus: Early Transcendentals (15th Edition) by Joel R. Hass, Christopher E. Heil
• Elementary Linear Algebra, Applications Version by Howard Anton
• Proofs: A Long-form Mathematics Textbook by Jay Cummings

I'm also planning to purchase:

• Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings
• Mathematical Statistics with Applications by Dennis D. Wackerly

I haven't delved deeply into any of these books yet while prepping for the GRE. I'm planning to skip around and focus only on the topics that will come up during those two difficult courses. So my question is: which topics and chapters should I focus on in these books? And is there another book I should look into getting?

Thanks!

So me and my friends are kinda fed up with carrying large log books and diaries for notes, which just pile on and on, and are subjected to the entropic forces of the universe, being especially vulnerable to the deadly combination that is cat on the table + coffee near the notes.

We were planning to tex notes together, like a github repository common for all of us. The idea was that, people write down the lecture notes (the theorems, proofs, examples and stuff) in the tex file pertaining to a subject, in more or less the same order as the lecture / book, but the added benefit would be that, if we have different proofs, both proofs go in the tex file (more proofs, the merrier), multiple interpretations, and if we find cool stuff in the side, that goes in too. So one guy learning something cool is like 7 other guys learning something cool. Effectively we would be learning ~ 7 times we would on our own.

Our semester starts in about 10 days, so that's how long we have before we start doing this.

My qualm is, is this practical? Does this actually work? It sounds solid in principle, but are there any growing pains potentially I have to worry about? has anyone done this? I am somewhat new to this github business to be honest, and I am not able to see the (im)practicality of it all. Any suggestions to maximize our learning would be much appreciated.

Hi

I’m in my 20s and I’m relearning math from elementary school to high-school. I’m doing a lot of arithmetic and algebra right now to prepare myself for college algebra in the fall. I passed my math classes in high school by memorizing the formulas they gave you. When the same problem was slightly altered and I couldn’t identify it, I didn’t know how to answer it. It was much easier to memorize problems than understand them. It worked. I mean I passed with A’s in my math classes up to college algebra and statistics. Now I’m going back to actually learn it. And damn is it hard. Understanding takes a lot more effort than brute memorization. It’s very difficult and I struggle a lot. Math has always been my fear. Sure I passed in the past but actually learning the material scared me. I was brought up thinking I’m “not a math person” and I’ll never be good at math in school. When I see math in paper I read or even math for calculating calories and protein, I shut down. I gave up. I’m done giving up. And I’m looking for inspiration, it helps me to keep going to know there’s people out there like me who overcame their math fears and poor ness at math and do well at it now.

So, please tell me below your story. Were you a failure at math in primary and secondary school or good at hiding your lack of understanding, and now as an adult, you went back and relearned math and actually understand it? I just want to hear your stories.

Hello! sorry if its a weird question, I recently bought a university textbook for an engineering program at a prestigious university and realized that I study quite slowly. The book is for Calculus 1 and linear geometry/algebra. In 3.5 hours, I studied 4 pages (I made about 3 pages of notes plus a formula sheet. I should note that I am sure I know the material perfectly, from top to bottom. However, I can't tell if I'm taking too long or if it's normal). When I study, I don't watch the time; generally, I never get bored studying mathematics, so I don't even realize how much time passes. On average, I study two hours, then I take a break, which, to be honest, is definitely too long (about an hour or more) and i repeat this cycle from early afternoon until late at night, so I study about 5+ hours daily. I can't tell if it's normal to take so long to learn just four pages. For me, taking a long time wouldn't be a problem, but I'm afraid I won't be able to keep up with others. Thank you very much, and sorry if I made any grammatical errors English is not my first language.

We have Eisenstein integer and Gaussian integer, which actually make uniform tiling on a coordinate plane. But there is also, infinite amount of so called k-uniform tilings, which have more than one distinct polygons, but still being lattice. Does it make sense to use those tilings as form of complex integers, and if so, how it is formalized?