I saw someone ask if it is possible to multiply 2 and 2i, and most argued that 2i actually is 2 * i, so 2 * 2i is just 2 * 2 * i=4i. That got me thinking, isn't 2 just 2 * 1 then?

Do people commonly define 2 to be its own entity, and if so, shouldn't 2i just the same be considered its own entity? I am having trouble seeing a qualitative difference between 2 and 2i in terms of being a "thing", and a product of two "things"

So I love maths, like seriously love it, it (along with physics) is what I want to do with my life somehow.

But I don’t know how to learn it! Like I can do all the courses, the exams, whatever, but learning things like the P vs NP problem, Wiles’ proof of Fermat’s last theorem and there are parts and concepts I understand perfectly, but some aspects require so much previous knowledge that I don’t know how to get.

Like, I just sort of want to know how to expand my knowledge in maths to provide a good basis for learning more advanced stuff.

My level is sort of all over the place, you know? Some advanced things I can understand easily and even work with, but then some things that are less challenging in terms of understanding I’m missing something?

Sorry I’m rambling.

How do I study maths?

I'm a newly promoted 10th grader who has recently realised that he is not very good at math, sort of. Basically, I'm quite good at the math taught to us in school, I usually get 95+/100 on exams, but I absolutely suck at olympiad level math. I want to learn the fundamental concepts as I've heard it's important to be good in math. Issue is, I just can't find any good resources/methods to do it. Please give suggestions 🙏. Also, since I'm still in school I've got no money to spend...

Hi everyone, I would like to know any pre-reqs for OTT, specifically if there exist any in the purer side of mathematics.

Question: For what values of p does the series converge? Σ( 1 / (ln(n) * n^(p)))

Note the sum is from n = 1 to infinity.

My reasoning: ln(n) < n for all large n

therefore 1 / ln(n) > 1 / n

which implies that 1 / (ln(n)*n^(p)) > 1 / n^(1+p)

The series on the RHS diverges if 1 + p <= 1, i.e. if p <= 0. Therefore, by comparison the series on the LHS diverges if p <= 0. So conversely, the series converges if p > 0.

I'm 25 years old and last year I started taking classes at a local community college looking to attain an AS. I haven't taken many classes yet (trying to do school and work at the same time) but in every class I've taken up to this point I've gotten excellent grades except for the remedial algebra (balancing equations, systems of equations, fractions, linear equations, ect.) they put me in based on placement testing, which I failed outright.

I never paid attention in math class as a kid (my fault, I'm aware) and so I never learned how to properly do math. I know basic arithmetic, but that's genuinely about the extent of my ability. I can do perfectly fine in every other class but I can't even pass the math class I need to pass to start taking the ACTUAL math classes and I'm totally at a loss. I don't see any other option besides giving up on getting a degree as a whole just for the sake of one subject.

Could anyone tell help me with a walk through how the following simplifies:

4x(x^2-1)^2(x^2+1) + 4x(x^2+1)^2(x^2-1)

To

8x^3(x^4-1)

Thanks.

Hi all,

I’m a geospatial science student in my final year and I have one last maths course to get through. I’m 42, so it’s been a long while since I did maths, so my foundations are sketchy (context).

I did calculus 1 and 2 at the start of my degree (3years ago), and squeaked through with some credits. But this semester I’m trying to survive ordinary differential equations. (The fact I’m here tells how well that is going).

I’m working on an assignment and one question just has me stumped. I’ve been working on it for 2 days straight now and I’ve not made any progress. Hoping someone here might be able to help or point me at a resource that will help (keeping in mind my aforementioned poor background - I’m constantly hunting for stuff in really plain English so I can understand).

My problem is: y’’ - 4y’ + 5 = 2e^(2x)sin(x) to be solved using d-operators.

Super appreciative of any help, I don’t even know what else to try.

Specifically, if I were to input the orders of the of the cyclic subgroups in the direct product form of the group, is it possible to produce the subgroup of permutation matrices that is isomorphic to that abelian group? And how could you do that?

Are there Improvements in could make?

https://imgur.com/a/kxfgm33

getting correct values but reversed +/- signs. what am i missing here?

https://imgur.com/a/QV3BdRs

What's the easiest way to solve problems like this? If 15 grams of fat is 19% of the daily recommended value, how much is 100%? I divided 100 by 19 to get 5.263 then multiplied that by 15 to get 78.947

Did I do that correctly and get it right? Thanks!

The function f is defined by f(x) = ax^2 + bx + c, where a, b, and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than 1, which of the following could be the value of a + b?

Options: A) -6 B)-3 C)4 D)5

I have data set: a1 a2 b1 b2 c1 c2 d1 d2. So n=8 & I need r=4. Here's the catch, objects with the same letters can't be in the same combination.

For example, a combination of: a1 b1 c1 d1 is fine but a1 a2 b1 c1 is not acceptable.

Would I just use the combination non-repetitive formula and divide the output by 2?

Thank you in advance!

I am trying to use the data below to make a chart with a line of best fit using this site https://statscharts.com/scatter/scatterchart although i am unsure how to do it correctly. Would someone be able to show me. . This is the data I need to put in the chart https://ibb.co/ZSV4YTn temp change was over 5min

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Trying to progress in my path of learning abstract math.... I have a conceptual question about denumerable sets and how one would go about proving it is denumerable.

For context, Im a 1st year engineering student that’s currently taking a differential calculus class. I passed my previous pre-calculus classes with ease, but for some reason I just fail most of my tests in differential calculus. I frequently do practice problems and I have a good understanding on the concepts of equations. But I still fail my test.

When doing practice problems I think my skills are fine, I solve most of the problems on the first or second try. But when it comes to actual tests I somehow forget something minor like putting a square on a variable or even straight out forgetting to differentiate the whole equation. It’s just so frustrating seeing how minor my mistakes were and how I could’ve easily solved the problem. And I try to double check my solutions every time but in the heat of the moment while keeping the time constraints of the tests in mind, I just don’t notice my mistakes.

Is there any tips that you guys can give me? Midterm exams are coming and I really need to get a high score or I will likely fail this course.

Thank you in advance <3

I enjoy doing maths, and want to solve problems. I don't want to do lots of arithmetic, I want to prove things. I don't know where to find problems that I can solve recreationally, because everything seems to be either incredibly difficult unsolved problems, or pages and pages of arithmetic and memorizing algorithms, which would be useful if it helped me prove things. If this question has already been answered, you can send me a link to the answered post and close this question, because I understand answering questions takes time and effort.

I just failed my second midterm and need over 82 percent on my final to pass the course. And at this point, I basically do not know shit about this course. I feel so stressed out and need to focus like crazy for the rest of the time. Just wondering if anyone have had the same experience to tell me how to manage that.

the ratio of 1:9 can be expressed as 1/9 is it not?

then if an amount of apple is 1/10 of the amount of pears, why is then the ratio of apple to pears 1:9, why is it not 1:10?

A line segment and a (filled) square has the same cardinality, right? So there should be a bijection between the two?

Thank you very much for answering!

Hi,

I'm trying to prove that the ratio Z = X/Y of any rotationally invariant vector (X, Y) will display a Cauchy distribution.

I think I have to start by doing the integral from minus infinity to infinity of f(x² + y²) to find a condition of f. (like is it uniformly distributed? I read that somewhere)

If anyone is good in stats and could help me figure it out, it would be very appreciated. Thanks :)

I'm wanting to make another attempt at understanding math. There have been many, but I keep hitting a wall, and I need to solve that problem before I reach for my math books again.

I'm going to offer an explanation. I'll try not to be too verbose.

---------------------------------------------------------------

I grew up moving around a lot. I might well attend three or four schools across three cities in two states within a single grade. Back then there were no national standards, and it caused me some major problems.

Imagine this. A kid is in school A. They're finishing up fractions, with decimals next on the list when they move to school B. School B is just starting fractions, so they are suddenly a math genius, having already learned this. They coast for a while, knowing all of the answers. Then they transfer to school C. School C is finishing up fractions, having taught decimals earlier. Good enough. The kid finishes the year, graduates, and moves on to the next grade (and/or school.) See the problem? This hypothetical kid never learned decimals. They skipped it between schools. And it's likely that the kid never realized that they'd missed a topic completely.

Then, a year or two later, a class starts doing advanced work with fractions, knowing that the students all already know decimals, and our hypothetical kid is completely and totally lost. This kid, who is praised for being so intelligent, is suddenly unable to even begin to grasp what's going on. The teachers aren't willing to help them figure it out, and so this formerly great student is now getting Fs. It's humiliating, and the kid ends up ashamed, feeling like a failure.

Now, continue that process for a decade. The kid ends up with so many holes in their knowledge of math that it's just become a confusing mess.

This was just illustrative of my education, not an actual example (in truth it wasn't missing whole subjects, it was missing parts of them, various operations and processes.) But the effect was still the same. By the time I was in high school, I had grown to despise math. It was almost guaranteed failure and humiliation. I took three years of algebra in high school. Three years of algebra 1, that is. I never did pass it.

College ended up being an even worse mess. I failed four classes my first semester because they assumed a certain level of math that I didn't know (I hate you, hydrocarbons. You too, molarity.)

-----------------------------------------------------------------

So, now I'm 50. My lack of an understanding of math has kept me out of so many interests and opportunities that I can't count them. I've tried several times over the years to learn, to open those options back up for myself. I know the resources. I know that I need to start from the beginning, as my foundation is decidedly lacking.

The problem is that my formative years were spent hating math, fearing math, and avoiding math. Which is sad, because my thought process is such that I think I could excel at math, and even enjoy it (I love working with orderly systems and with theory, and the math I do understand I understand, if you follow what I'm saying.)

Because of that, whenever I start to study math, my jaw clenches, my shoulders and neck tighten up, and my stress level spikes through the roof. My inner child screams, "Math is pain!", and even though I know that it's nonsense, working with math is still a miserable experience for me.

Has anyone else dealt with something like this? Anyone have any tips for working through/around it?

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Could one of you explain how the first equation is derived from the triangular element?

Link: https://imgur.com/gallery/dlN8sMh

This is the question, and I cannot figure it out. Any and all help is appreciated!!

A hearing test gradually raises the nose a listener is subjected to. If the test starts with an intensity of 10⁻¹⁴W/m2, and the intensity is increased by 15% every 20 seconds, what will the average rate of change be, in dB per minute, when the dB level reaches the level of a whisper, 30dB?

I’ve got a test on April 9th, about 4 days from now, mostly Trig.

We study straight from the textbook, Precalculus: Mathematics for Calculus 8th Edition by James Stewart

It’s formatted Concept -> Example, then an Exercise page at the end of the unit.

I ask, because I’m very much a perfectionist when it comes to notes, and I know I’ll take too long to properly study 15 units worth of content in 4 days, especially since I can’t focus for some reason.

I do have access to a calculator that lets me make note documents so if I need to make notes on there then bring it to the test, I can.

Also, the units in question are going to be:

5.1 The Unit Circle

5.2 Trigonometric Functions of Real Numbers

5.3 Trigonometric Graphs

5.4 More Trigonometric Graphs

6.1 Angle Measure

6.2 Trigonometry of Right Triangles

6.3 Trigonometric Functions of Angles

6.4 Inverse Trigonometric Functions and Right Triangles

6.5 The Law of Sines

6.6 The Law of Cosines

7.1 Trigonometric Identities

7.2 Addition and Subtraction Formulas

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

7.4 Basic Trigonometric Equations

7.5 More Trigonometric Equations

Also, just as a note, my Prof doesn’t necessarily go through All of an entire unit, he highlights specific sections to study, but is also the type to be very unorganized and unpredictable when it comes to tests

Greetings all,

I am a master's student in computer science and full-time software reverse engineer. Through my work, coursework and independent exploration I've taken a liking to theoretical computer science. That said, I do not have a particularly strong mathematical background and would like some guidance on what I ought to study to help me understand my areas of interest. I've found that my lack of a strong mathematical foundation holds me back more than anything else. And unfortunately, pursuing the required mathematical background falls squarely on my shoulders. I can't really leverage my company to pursue a math degree like I can computer science, and the program that I am in is heavily applied.

Potential areas of interest in theoretical computer science that I would like to be able to explore more deeply, or at least have the suitable background to dabble in should I so choose: program analysis, formal verification, cryptography, type theory, programming languages & compilers, computability theory, complexity theory, and so on and so forth.

I know that I am asking a lot, and that I will not actually be able to pursue everything that I have listed, but I would at least like to have the mathematical foundations required to narrow down what I'd actually like to spend my time on when on the surface all of these things are incredibly fascinating.

Assume the following background: theory of computation, two semesters of calculus, linear algebra, discrete math, probability & statistics, introductory proof-writing. Edit: Can't edit the title, but strictly speaking it should probably say undergraduate mathematics, as I imagine I'm missing background at both levels.

I don't expect anyone to lay everything out neatly for me, but I don't currently even know the keywords that I should be using to effectively search for resources.

I recently changed my major to applied mathematics. Is 4 300 level math classes with spanish in one semester too much?

The classes are:
Spanish 1.
Mathematical Statistics
Methods of Differential Equations
Methods of Numerical Analysis
Discrete Models of Financial Mathematics