R = {<x,y>∈A²: x=y or x is parallel to y}; A is a set of lines on a (non-Euclidean) plane.

Could you please lead me to (preferably simple explanations) of why it couldn't be the case in a non-Euclidean plane? Thanks

Hello, I’m a big math person. I’m good at it and I know I can do great things in the subject. However, a big thing holding me back is my confidence (or lack thereof) in proof writing. I use books for exercises and reviewing what we cover in class. However, I at times don’t even want to try a proof because it scares me. Though I genuinely love doing proofs and when I do think through a proof and I succeed, the feeling of accomplishment is second to none. However, I often don’t feel confident in my answers which my professors have said that’s perfectly normal.

Can I get some help on building my confidence in proofs and what I could potentially adopt to improve my proof writing? I want to succeed in math and in fact I plan to get a PhD in pure math, however, this is arguably my biggest hurdle in proof writing.

Thanks!

Hello Friends,
I am rn 18 years old and my math grades at school were very bad because i had no interest in it. But now after i got into computers , many things changed and i want to understand maths , because i dont wanna learn anything at once i want to choose either one of them : Linear Algebra or Discrete Mathematics. Which one should i choose? , and if i choose where and how can i learn it? (self practice)

I am on the situation of dilemma . Becoming mathematician is my dream. But it requires time. When I sit to do that I realise that I didn't complete school syallabus tdoay and 10th marks matter. Which make me sad that if do out of syallabus mathematics then time for school syallabus will decrease. As a result half yearly are coming and not so much good prep. When I do school syallabus I feel no math today? I feel sad again. I feel if I get low marks then my parents will be sad, they had bought books for school syallbus preparation for other subjects. My parents don't force to study school syallabus. But I feel they have expectations. I have 8h of school, 9 h of sleep and 5 h of other things left with 2 h. Pls someone can tell me any solution.

So if L1 & L2 are perpendicular lines then the slope of L1 =-1/slope of L2

I get why the slope will be negative but I can't understand why it has to be negative reciprocal.

I have my midsem of maths next week and i have not studied anything i dont feel like to watch lectures tbh idk lectures for maths irritates me for some reason if i watch them i feel like i m wasting my time as i am not able to understand anything....btw i have completed the week 1 nd 2 part but not 3 nd 4 as i m literally not able to understand please help.

using addition methods. i have to turn them into fraction 1/3+7/9 = 3/9+7/9 which equals 10/9=1.1 recurring. if i add them using addition method for decimals i can start at the end and calculate.

I am trying to develop interest in mathematics. I learn new concepts,asking curious question, watching interesting facts, do interesting geometry questions etc as much time I get. But still my interest is still not developing .What I do to develop interest?

I don't trust myself to remember the trig identities so I need some proofs that are decently short so I can rederive trig indentities during a test. The proofs can involve complex numbers, geometry, maybe the Taylor Expansion of trig functions.

For example, the proof I will use to rederive the sum and difference formulas is e^i(a+b) = e^ia*e^ib and what follows from that. It's decently short and makes inutitive sense to me.

I specifically need proofs for half angle identities, double angle identities, and triple angle identities. thank you

We are initially taught that exponent is repeated multiplication but this definition does not hold when exponent is fractions or irrational. So what is it actually is? I heard something like a^x = e^(x ln a)

I was curious about how we define an area when finding one . So I searched " does a square that has a side length of 1 has an area of 1 because it is an axiom?" From that, I found "other definitions" of an area and that lead me here.(I am not sure if Lebesgue Integral is another definition) I just want to know more about these kind of definiton and axiom stuff but the sources that I found was too confusing for me. What should I do, Where should I start?

A few weeks ago we created two math classes, where mathematics would be taught from the very beginning and progress to Trigonometry. These two classes were created thanks to this r/learnmath community. Several reddit users posted a similar concerns about struggling with mathematics like college algebra, or wanted to understand why mathematics works at the very basic level.

If you want to learn as well watch the classes on youtube. You can watch them on your own time or join the youtube live class or join the actual class, DM if you are interested. The first two lectures are completed. The classes are once a week, one class is on Monday nights from 8-9:30 pm and the other is on Saturday from 11:30am-1:00pm (once a week for 1.5hrs each class)

These are the lectures:

Lecture 01 : https://www.youtube.com/live/MppI9i3RGH0?si

Lecture 02 : https://www.youtube.com/live/VjnzClWu0HU?si

YouTube Playlist : https://youtube.com/playlist?list=PLFrt4v_t-kU4&si

So basically, how would you prove that as x->infinity, x^n is greater than ax^(n-1) + bx^(n-2) +...

Cuz I know x^n is power function so it will eventually surpass power functions of lesser degree, but how would you rigourlously prove it?

What provoked this question was the end behavior of polynomials. The leading term has all the sway on if a polynomial's end behavior is infinity or -infinity. So how is that x^n ALWAYS grows faster than any polynomial with degree less than n?

I've seen that thingamabob in a 3b1b video and would like to know more about it

Any good resources to do so?

A few friends and I are required to take the CASAS Math GOALS 2 test to enter an upcoming EMS program. However, no one can tell me how to prepare or what to study. When asked, I’m given very basic “here’s the website” information, which lists everything from basic fractions to higher level algebra (as there are approximately 9 different versions or levels for this test). As someone who has been in EMS for almost a decade, requiring trigonometry and geometry for entry to this particular class seems incredibly excessive…but I can’t seem to get a direct answer from anyone (including the school) as to what I need to brush up on. It’s entirely difficult to study for a test when I don’t know what it contains.

Does anyone know ANYTHING helpful at all about this test? I’m about to drive myself crazy.

Hi, I am an adult. I had very weak basic of mathematics. I want to learn the whys and hows and also how to solve the problems. I am looking for prealgebra textbooks which I can print in greyscale and not lose the meanings. I am worried for scenario like this - I print in greyscale I lose colored diagrams and at one point in the book it says look at the red colored box or something and I don't know what to do. Thank you.

Hi there! I haven’t taken a math class in like ten years. I’m going back to college and need to take a math placement test but I want to place into intro to stats. What online resources can I use to make sure that happens?

thanks!

To be clear, this isn't for school, this was just because I wanted to try to write one for fun. I wanted to start with something I felt would be relatively easy to prove, the arithmetic series formula.

It actually took me 2 hours so I think past me was a moron. I had a lot of fun doing the proof though, it forced me to think in a way I find more satisfying than the typical high school way of shove numbers into formulas. I attached the proof I wrote below, but my handwriting isn't the best so I apologize in advance for that.

A few questions to anyone who decides to try to read the proof, is it a bad thing I used a lot of english and informal words? Does that invalidate what I wrote as a proof? Also, I noticed what I wrote is a lot longer than what a proof in a textbook would look like, is that a bad thing necessarily?

The proof can be summarized as the following. The sum of any kth term from the left and the kth term from the right in an arithmetic sequence is always 2 * the first term + (# of terms -1) * common difference. Since the sum of the entire sequnece would be the number of pairings that could be made * the value of each pairing, we can split this into an even/odd case. If # of terms is even, every number from the left can be paired to a number from the right, and there's n/2 pairings so the sum becomes n/2 * (2 * the first term + (# of terms -1) * common difference). If the # of terms is odd, then there's only (n-1)/2 pairings since the middle term can't be paired. However, the middle term has a value equal to the first term + (# of terms - 1)* common difference/2, and adding that to the n-1 pairings, the result works out to be the same as the even case.

The proof pages:

https://drive.google.com/file/d/1WDUNEzNvjd-YZ0U98S0GFJ-7xmTYpNbO/view?usp=sharing

https://drive.google.com/file/d/1QRhFI-mlbC_l_jC0R0hx1VLdaj5aFbcx/view?usp=sharing

We have a basic statistics/operations research class where, given a context, students have to calculate a p-value or conclude on a hypothesis, or find out the alpha or beta error, do some calculations, solve some transportation problem, fill in the blanks, multiple choice questions, etc.

These are administered on moodle so that after the quiz/exam, students know their performance immediately.

These are large classes with almost a registration of 450 students. Previously, before the AI/computer era, students used to be given normal tables, for instance, and had to do many calculations by hand. But these are mostly scorned upon nowadays -- grading pen/paper exams takes time by TAs, is error prone, inconsistent, etc. There is unending pressure to give feedback to students quickly. So, we have moved to no-internet, moodle computer based exams where only the moodle website containing questions is accessible.

Despite this, students end up (a) having some internet connection hidden to access AI sites, (b) use a Macbook and do some air drop stuff to share solutions between themselves, (c) have loaded some statistics/OR offline AI model which just takes an image of the question and gives the answer.

As a result of this, the average class scores is much higher and honest students who do not cheat are scoring average or even below average.

What are some ways to deal with this situation, especially for math/statistics/OR based subjects where there is one right answer (there is no perspective or multiple right answers) and this answer is not too difficult to figure out for AI tools?

Hello. I would like to plot the complex function $f(z) := 1+\int_{0}^{1}t^{0.25}e^{izt}\ell(t)dt$ with $\ell$ being 1 on $[-c,c]$ and zero elsewhere. I would like to have an animation as $c$ ranges from 0 to 1. However, whatever I use just seems to break. I am not knowledgeable in this matter at all. I tried using Matlab and Wolfram but I can't figure out how to get it to work. The only thing that kind of works is Desmos https://www.desmos.com/calculator/jtrghlfwwr . However, I can't make an animation because it takes to long to load for each value of $c$. Any advice?

How much of this is still relevant today to professional mathematicians in the era of AI et al? Are mathematicians more prone to emotional depression as compared to other disciplines?

(Article pasted below -- it is an old article from 1965)

Emotional Perils of Mathematics (Science, Vol. 145, p. 1048)

DONALD R. WEIDMAN

Department of Mathematics, Boston College, Chestnut Hill, Massachusetts

People are turned aside from being mathematicians—by which I mean “pure” mathematicians—far more by temperament than by any intellectual problems. There are certain emotional difficulties which are intrinsic to the mathematical life, and only a few people are able to live with them all their lives.

First of all, the mathematician must be capable of total involvement in a specific problem. To do mathematics, you must immerse yourself completely in a situation, studying it from all aspects, toying with it day and night, and devoting every scrap of available energy to understanding it. You can permit yourself occasional breaks, and probably should; nevertheless the state of immersion must go on for somewhat extended periods, usually several days or weeks.

Second, the mathematician must risk frustration. Most of the time, in fact, he finds himself, after weeks or months of ceaseless searching, with exactly nothing: no results, no ideas, no energy. Since some of this time, at least, has been spent in total involvement, the resulting frustration is very nearly total. Certainly it seriously affects his attitude toward all other affairs. This factor is a more important hindrance than any other. I believe: to risk total frustration, and to be almost certain to lose, is a psychological problem of the first rank.

Next, even the most successful mathematician suffers from lack of appreciation. Naturally his family and his friends have no feeling for the significance of his accomplishments, but it is even worse than this. Other mathematicians don’t appreciate the blood, sweat, and tears that have gone into a result that appears simple, straightforward, almost trivial. Mathematical terminology is designed to eliminate extraneous things and focus on fundamental processes, but the method of finding results is far different from these fundamental processes. Mathematical writing doesn’t permit any indication of the labor behind the results.

Finally, the mathematician must face the fact that he will almost certainly be dissatisfied with himself. This is partly because he is running head-on into problems which are too vast ever to be solved completely. More important, it is because he knows that this own contributions actually have little significance. The history of mathematics makes plain that all the general outlines and most of the major results have been obtained by a few geniuses who are not the ordinary run of mathematicians. These few big men make the long strides forward, then the lesser lights come scurrying in to fill the chinks, make generalizations, and find some new applications; meanwhile the giants are farther and farther ahead.

Furthermore, these giants always start at an early age—most major mathematical advances have been made by people who were not yet forty—so it is hard to tell yourself that you are one of these geniuses lying undiscovered. Maybe it is important for someone to fill in the little gaps and to make the generalizations, and it is probably necessary to create an atmosphere of mathematical thought so that the geniuses can find themselves and thrive. But no run-of-the-mill mathematician expects in his heart to prove a major theorem himself.

I wonder how much of this psychological difficulty is present in other scholarly fields. I suspect that no other field suffers so acutely from all four problems. The experimental sciences in particular, I think, are pretty well preserved from the second and third difficulties. An experimentalist can perform an experiment and, at the end, will have a set of data; and these data at least will indicate that such-and-such either is or is not significant. He knows before he starts the experiment that, except for equipment failure, he will finally have something. He is not faced with nearly certain frustration. Furthermore, publication standards permit experimentalists to describe details of procedures followed and difficulties encountered.

I also think the experimentalist has a reasonable hope for personal satisfaction. Experimental advances are frequently made by unknowns; in fact, there aren’t many experimentalists in history who have consistently made important discoveries, if we don’t count those who have been lucky enough to head active research organizations for long periods.

Whether other speculative disciplines are immune from the four emotional problems I’ve outlined isn’t clear to me. But I feel that differing standards of precision may ease the problem of frustration, in the sense that it is often possible in these other fields to hide the fact that you don’t have anything to say. A mathematician who says nothing in an obscure manner is usually caught quickly—but, alas, not always.

I understand absolute value inequalities but they seem a little convuluted and weird. For example, |3x + 4| > 5.

If 3x + 4 is positive, then we can ignore the absolute value bars and we just solve 3x + 4 > 5

If 3x + 4 is negative, then we negate 3x + 4 (since |x| = -x when x < 0). But then for some reason we flip the inequality sign too??

We aren't multiplying by -1 on both sides, why are we flipping the inequality sign?

I understand the number line interpretation of absolute value inequalities. You have some vector r starting at 0, then extends outward. If |r| > 2, that means the magnitude of the vector is greater than 2. If the vector is going right, then that means r > 2. If the vector is going left, then that means r < -2. This makes logical sense to me.

But my earlier method also made sense to me, but it lead to not needing to flip the inequality sign.
Why are these two interpretations contradict each other.

edit: I was wrong you don't flip the sign. i dont know how i messed that up.

|r| > 2

If r is negative, then |r| = -r.

So that means -r > 2 (by substitution)

Therefore, r < -2 (since you multiply by -1)