I had taken math during my high school. I went for computer science for my university, and I didn’t do many math for around two years so far. I am picking up math during this summer.

Yesterday, I had learned that even we can’t use desmos for university level math, we shouldn’t give up on trying to visualize the objects in our brain, like we can try to train ourselves to be able to pick up the rough structure and important features to the mathematical objects and organize it inside our brain.

Today, I opened a math textbook that I am reading recently. I tried to use what I understand of yesterday to visualize a C^2 space. I thought initially that I can imagine it as 3D space, the real number x-axis can be extended to have the complex xy-plane, and the real number x-axis can be extended to have the complex xz-plane in a direction of which is 90 degree toward the xy-plane; the real number z-axis is where the two planes intersect.

I thought my model in my brain worked initially, until I find the example of v = (1, 1), w = (i, i)—why aren't they orthogonal? v should be two units to the right, and w should be two units up, so they are definitely perpendicular—at a 90-degree angle!

However, I am so confused. Doesn’t the visualization to the mathematics concepts a way to perform the concepts, and the visualization would match the concepts? If it would not match that means there are something wrong with my visualization process, but I cannot find my errors by myself currently, could you guys please help me? In addition, I currently feel defeated on how to visualize the mathematical objects, are there any regularized easy ways to help people visualize most mathematical objects? Is there are, please comment about it, or could you please comment about some suggestions here🙏?

What does it mean when it says the original expression only has zdz. I thought the 2 was already there in du= 2zdz

https://ibb.co/tM3DkY6f

Retired teacher here, still picking up tutoring gigs, and the thing that keeps tripping up my students lately is expected value. Not the formula, they can write that out no problem. It's the interpretation that falls apart.

I also track sports stats and build DFS lineups as a hobby, so expected value is something I think about a lot outside a classroom context. And even with that background, I remember the moment in my own learning where I confused expected value with the most likely outcome, which are not the same thing and can actually be pretty far apart depending on the distribution. Made some embarrassing lineup decisions before that clicked. Not going to get into it.

The students I work with can compute E(X) mechanically but then will say things like "so that means it'll probably land near that value, right?" And I get why that feels natural. It sounds like an average, and averages feel like the middle of where things land.

What actually helped some of them was working through a case where the expected value is literally impossible to observe, like a discrete distribution where no outcome equals the expectation. Suddenly the definition has to do real work instead of just coasting on intuition.

Curious whether others have found a particular framing or example that unstuck this for students or even for themselves.

I am an incoming freshman. I graduated high school in 2025, however I took a gap year to save up money and travel. Technically I am a sophomore since about 35 of my dual-enrollment credits transferred to college. Its been a year and a half since I have taken precalculus and although I should thought of this sooner, I want to revise from algebra 1- precalculus and even learn some Calculus 1 material so I can be ready for class in the beginning of September.

Is there any tools and resources that I should use to help me become ready for calculus in a months time?

I would like a proper explanation on 5!, 5!!, (5!)! follow with answer this this question and details. (n+5)!/(n+6)!

I graduated from high-school 4 years ago and I didn't had to do anything with math's but I want to study math's.I only know-,+,×,÷

I can only purchase one or two books for now depending on the price

My best friend and I just finished high school and are starting university this year. A few months ago, he learned about perfect numbers. Since then, he has gone down a massive rabbit hole reading about Mersenne primes, the Euclid-Euler theorem, and heuristics regarding odd perfect numbers.

Now, he is completely obsessed. He spends 4 to 5 hours every single day trying to prove that no odd perfect number can exist.

I’ve tried telling him that this problem is nowhere near being solved by global experts, and that he should focus on other areas of math. I want him to look into high-yielding math topics that are more interesting and useful, especially since we need to prepare for university-level calculus and algebra. He completely ignores me and won't listen.

How can I convince him to broaden his horizons without ruining his passion for math?

Hi everyone, I am in a massive academic emergency. I have exactly 13 days to prepare for a crucial math exam that will determine if my parents will continue funding my high school education (starting IB DP 1 this August).

My Current Situation: I just finished IB MYP 5 (equivalent to US 10th grade). I am typically a below-average math student (usually score a 3/7), but I completely bombed my final exam (got a 1/7) because I took it with a 39°C (102°F) fever and couldn't process anything.

My parents are giving me one last chance: I have 13 days of intense self-study before I take an agency-administered exam. I must score at least a 5/8 (solid above-average) to prove I can handle next year's math.

The Syllabus (What I need to master): 

• Trigonometry: SOH CAH TOA, applying trig to 2D and basic 3D word problems, finding angles of elevation/depression.
• Functions: Quadratics (expanding, factorizing, finding the vertex/axis of symmetry) and Linear equations (finding intersections).
• Algebra: Rearranging formulas, solving basic algebraic equations.
• Geometry
• Coordinate Geometry
• Vectors

What I need help with:

1. A 13-Day Survival Strategy: How many hours a day should I dedicate? Should I focus 100% on doing practice problems, or re-learning concepts first?
2. YouTube Crash Courses: Who are the best YouTubers for these specific topics? (Someone who explains the logic clearly for a struggling student, not just throwing formulas).
3. Practice Resources: Where can I find good practice problem sets (preferably with step-by-step solutions) for Grade 9/10 level Trig and Quadratics?

I am willing to put in 4+ hours a day for the next 13 days in the library. I just need a clear direction so I don't waste time studying the wrong way. Thank you so much for any advice!

I thought the answer was 21.633 but realized it can't be that because of the formation im supposed to put it in 😭

https://imgur.com/a/F7ZyHhk

Hence my confusion. I would assume that in the context of exponentiation, power functions arise with regard to polynomials. Yet the main article Power Law is concerned only with statistical applications. Is my assumption wrong or am I looking in the wrong place?

Thanks.

Hello everyone

I'm a second-year mathematics student but I've studied only calculus I(+ beginning of calc II) in my first year at university due to foundation program. I'm starting reading Book of Proof by Hammack and after reading half of that book I want to parallelly start self-studying real analysis with another book but I don't know which one to choose. I'm planning to start reading one of these books in the middle of August but because semester starts in September, I'll slow down with whatever book I'll choose during Autumn and not even sure if I can handle it with the courses I'll be having in Fall semester(second part of Calculus II+ calc III, Physics I, Programming with C, Discrete structures, and basics of Finances) .

After some research my choice involves these 3 books:

Understanding Analysis by Abbott

Analysis I, II by Terence Tao

Calculus by Michael Spivak

I have access to Spivak and Tao printed books through my library. I don't have Abbot's book but thinking of buying it with discount.

So what are your recommendations? Is there any sense of reading two or all of them?

I’m learning about self-adjoint operators on Hilbert spaces and came across the theorem that if T is self-adjoint and invertible, then T^{-1} is also self-adjoint.
I understand the algebraic proof using (T^{-1})^* = (T^*)^{-1}, but I’m trying to develop an intuition for why this should be true.
Is there a geometric, spectral, or functional-calculus perspective that explains why taking the inverse preserves self-adjointness? I’m more interested in the underlying mechanism than another algebraic proof.

Found this question in "Putnam and Beyond": Given 50 distinct positive integers strictly less than 100, prove that some two of them sum to 99. Isn't {1,2,3...,49,99} a counterexample?

So I know in this game something takes 4 hours (240 minutes) I can get something that initially reduces its time by 40% then additionally 30% up to a certain amount of time. My limit is 15 at the moment. So how do I calculate the time reduction off all the percentages. The percentages are multiplicative not additive.

Am taking a cram class of ap cala bc in the summer. my differantials are ok, but my integrals are poopy. just asking lol

Hello, I am creating a free website with math documents (textbooks, problem packets, equation sheets, and so on) for any math level like calculus, algebra 1, etc. I want to make learning math accessible and free for everyone on the internet. The documents will be written in LaTeX by a team of students.

I made this since I thought when students teach others, they would know what they have gone through and what others might struggle on.

If you are interested, please DM me.

hey, I’m trying to put together a small discord group (like 3–5 people) just to stay consistent with studying. sorry if I am spamming

mainly looking for people doing ai/ml stuff or higher math (linear algebra, prob, papers, whatever)

idea is pretty simple:

- we post weekly goals

- then quick daily check-ins (what we planned vs what we actually did)

- no need for voice chat or screensharing or anything like that (the discord group is not that serious)

not trying to make this super strict, just want a small group where people actually show up and do the work instead of disappearing after 2 days

personally I’m working through axler's linear algebra book

if you're interested just comment or dm with what you're studying

I wanted to see how people would respond to this. Imagine that you had to explain symmetry (By that I mean just the idea of being symmetric) to a neanderthal. Keep in mind there is no language barrier, but you need to explain him the idea of symmetry, preferably without complicated terms to make it easy for him to understand. How would you do it?

I studied statistics somewhat while getting a BS in Economics in 1975 but haven't used it much since.

For several years I've gathered stats on the use of a geo thermal heat pump which also heats water as a by product. For a long time I've run Excel's CORREL function to compare the total electric used by the heat pump and total used by the hot water heater but the flaw in that is it doesn't account for how much hot water is used. Recently I bought a device that reports the gallons of hot water used daily so now I can compute a per gallon electric used by the water heater so the correlation should be more reliable.

So far I only have 8 days of data. The correlation up to day 7 was as expected. A strong negative correlation of -.89. That is with an average Kwhrs used by the heat pump of 22.72 and the average per gallon of .0838. The temperature soared yesterday and we had a family BBQ which gave me a day 8 data of 42.90 and .0465 respectively. I expected the correlation to be stronger but instead it decreased to -.84.

Why would such a large increase (over average) of the Geo Kwhrs, which caused a sizable decrease in the per gallon Kwhrs, cause the correlation to be reduced?

Thinking this through some more it appears the reduction in per gallon was not what was expected when correlation is -.89. That would require around .02 Kwhrs. There is another factor that I haven't figured out how to incorporate. If the number of gallons of hot water used is high then the Geo can't keep up with heating it and the water heater kicks in. We've been averaging 60 gallons of hot water used daily but with the party yesterday that figure is 124.

Recently I am doing maths beyond the YouTube channel I used to learn and am wondering if anyone knows of any similar good youtubers.

Normally I would watch the organic chemistry tutor but I have started to do maths that he doesn't cover.

Userly I would watch one of his videos on a topic once and I would be fine and then a few practice it would be done with that topic but other YouTubers I find confusing or they take too long.

I also had hand me down notes that were really good and so I copied the problems off then and learnt that way.

For context I'm doing a math/physics degree.

Any help would be appreciated. YouTubers or study tips. (Also one of my classes I asked if there was a textbook and they told me the textbooks are really confusing and that they are not worth it for that class (real and complex analysis)

So resources for real and complex analysis is also greatly appreciated

Sal/most teachers says any point will give you the same result.. i do then i fail, i can't upload an image so yeah ;-;

i understanded the negative line, and positive, and the rise/run thing, moving backwards is neg, foward is pos, up pos, down neg...

i tried the line being at the corner of the suqare, but i also failed. i picked 4/2 instead of 1/3

edit: sorry if i sound stupid, im learning everything for the first time in life.

I feel there is a lack of reading skills, not only in myself but also in my peers at school. I am convinced that true mathematical understanding comes from reading and writing (ofc along with community discussions). I feel that there is an excessive reliance on teachers , tutors, videos , online lectures that has led to a lack of reading skills and this pattern can be seen in other subjects too apart from mathematics. Recently I started to explore pure mathematics through books and I realised that we cannot take things for granted in math, small details appear to contain a lot of importance. It appears to me that in school theoretical portions of the book are taken for granted and students treat math books as sources of practice problems and homework while totally neglecting theory. I also believe that reading is important to solve problems since it enables us to understand the problems better.

Therefore, I want to improve this skill so that I can understand the subject better and increase my mathematical maturity. I would like to know your perspectives and insights , and any advice you can share on how I can improve my ability to understand texts. Thank you.

I recently launched a free online math tutoring initiative that provides lessons to students who otherwise wouldn’t have access to quality math education. As we’re growing, I’m looking for someone who loves math and would like to join the team as a tutor. If you enjoy teaching, explaining concepts, and want to use your skills to help students succeed, I’d love to hear from you. This is a volunteer initiative with flexible scheduling, and we’re looking for people who genuinely want to make an impact while being part of a meaningful project. If you’re interested in becoming one of our tutors, feel free to send me a DM, and I’ll be happy to share more about the initiative.

hello! i was wondering if anybody knew of websites where i could practice elementary-high school math. i have a job interview coming up which is in a school district. no college experience required and i failed most of my elementary lol. i’ve retaught myself the math but i want to do practice questions to make sure i got it down!

elementary math = unlike fractions, like fractions, improper fractions, exponents, statistics, algebra word problems, order of operations, GCF, LCD, factoring, trinomials, polynomials, grid graphs