I loved math in school. I majored in math in college. I taught middle school and high school math for six years, including geometry for at least three, before changing careers 15 years ago. A trapezoid always, ALWAYS had exactly one pair of parallel sides.

Tonight, my 7yo was doing an online math quiz, and a rhombus was classified as a trapezoid. Lo and behold, trapezoids now have AT LEAST one pair of parallel sides. So previously trapezoids were defined in opposition to parallelograms, and now parallelograms are a subset of trapezoids. Honestly, this feels about as destabilizing as when Pluto was demoted to dwarf planet status.

The internet tells me this was a common core change in the 2010’s. It also tells me that until the early 1900s, all the shapes we think of as “special parallelograms” were defined as not being parallelograms. So I guess there’s precedent for this kind of change. But also, I’ve seen a LOT of online math resources today still defining a trapezoid as having “exactly one” pair of parallel sides. Maybe those resources are written by people my age who are clinging to the past?

My question is for the geometry teachers who were teaching during this change. How long did it take you to stop thinking of parallelograms as not-really-trapezoids? Did that transition actually make sense to you, or do you still secretly have a trapezoid bucket in your head that’s fully separate from the parallelogram bucket?

In my first year of University as a Mathematics major, I’m looking for advice on finding a good popular mathematics book.

For any quadratic formula ax² ± bx ± c = 0

You can solve it the long way (quadratic formula) and you can solve it the simple way (factoring).

My issue is with the factoring method.

Assuming that [a] = 1, you're now left to dealing with factoring for [b] and [c]

Let's assume that factor 1 is [i] and factor 2 is [n]

So to solve it, it has to be presented like this:

(x ± i) • (x ± n)

Now the last piece of the puzzle are two constraints:

1) i ± n = ± b

2) i • n = ± c

The above is my issue. If I want to figure out the above, is there a logical and consistent way to always get the right factoring?

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The way I see it, you can either:

(A) intuitively figure it out — which involves fully memorizing the multiplication table.

or

(B) brute force it through trial and error by making an array of all possible multiplication factors of [c] and then sum all the individual factors and pick the one that gets you [b]

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Is the above (A) or (B) truly the only way to solve it by factoring? Or is there another simple method that I'm missing?

A bit about me. Finance and math background, CFA Level III, Treasury funding experience, and I know ML well enough to build and ship models. I'm retired (FIRE) and have time on my hands. I love teaching and explaining things.

I'm thinking of building a math learning app and I want to make sure it actually solves real problems rather than just being another flashcard clone.

For those of you learning math (or ML): what's the one concept that, no matter how many times you read about it, still doesn't click?

Or, more broadly: what's the most frustrating part of your learning process right now? (e.g., getting stuck on a problem with no feedback, losing motivation, not knowing what to study next, etc.)

Just trying to figure out where I can be most helpful. Not selling anything, no app to promote, just genuinely curious.

I would also like to know what this type of calculation is called.

I want to know if I will be okay if I take abstract algebra before real analysis.

My university allows me to take abstract algebra before real analysis. If I take real analysis first, due to scheduling issues, I would have to wait 1 extra semester. I don't want to do that, but I also don't want to get absolutely demolished, or be at a significant disadvantage.

Description of my university's real analysis class:

"Sets and functions. Induction. Axiomatic introduction of the real numbers. Sequences and series. Continuity and properties of continuous functions. Differentiation. Riemann integral."

Description of my university's abstract algebra class:

Groups and their homomorphisms; commutative rings and modules; fields and vector spaces; subgroups and quotient groups, permutation groups; modules, submodules, quotient modules; polynomials rings and their ideals, modules over polynomial rings.

I also have inattentive ADHD which makes things harder. Is there any math genius here who can message me privately and explain to me how they study math, or what is their way of understanding new topics? I'm so overwhelmed and I need to pass to go to uni. (I know this is probably basic, easy stuff, but I hate the Quadratic formula... and completing the square so badly).

I used to really like angles, geometry, and inequalities because it felt like a puzzle. But I honestly don't understand this random stuff. I feel the intense need to know why we do every formula in order to be able to solve them, which leaves me frustrated because teachers teach how to solve it, not why we're doing it. Does anyone... get what I mean?

Hello. I'm a 30+ adult & I would like to relearn math from scratch. I used to struggle with it when I was in school & something happened recently (too personal to share) that ignited the idea of me relearning math. I'm serious about this. How can I approach this? How and where do I start? And what advice can you give me to be able to stay consistent in learning? Any resources are welcome too. Thank you all in advance.

As a kid I slept through almost every class and used my nights to teach myself other things. I ended up skipping a lot of school and building my professional career from a young age. I'm very happy with that path and have no regrets.

The one important thing I skipped along the way was math.

Lately I'm in a lot of settings where numbers come up constantly, and where things like percentages have to be worked out quickly, mid-conversation. I can't answer fast enough, and it's starting to bother me.

If you believed someone could learn math quickly, what roadmap would you suggest?

I know I could ask an AI and get a pile of suggestions. I'd end up going through whichever resource is best at "AI SEO", which may not even suit me. Many of you may think this is a pointless post for that reason, but that's exactly why I'm asking. I'd rather hear from people with real experience.

Thanks in advance!

I’m honestly just looking for advice on whether I should just take the WD and drop this class or if it’s feasible to actually get around a 75 in this class without a scale/curve. I got a 15% on my first midterm which is worth 20% of my grade, which was 100% my fault because I procrastinated. I still have 1 more 20% midterm, a 40% final, and 20% worth of assignments. Any advice is appreciated i’m willing to put in the work i’d just like to hear if anyones had any success turning around their mark and what you’ve done?

Starting mech eng soon. First-semester Mathematical Analysis I covers functions, series (ratio/root tests, Taylor/Maclaurin, nth-root, etc.), limits, and derivatives (no integrals). It’s quite different from the usual Calc 1 track, so I’m unsure what to prep.

My algebra is mediocre—not terrible, but not solid. I don’t have time to grind prealgebra → Algebra 1/2 → Precalc + Trig properly. A lot of Algebra 1/2 feels irrelevant to the course beyond a few key skills.
What should I actually focus on? Is there specific algebra/trig topics that matter most for this course?

Edit: Is Just-in-Time learning a good approach here—working through lots of problems and only drilling the specific algebra gaps that actually block me when I get stuck? It seems more efficient and better at exposing real weaknesses than trying to relearn everything upfront.

Hi I am Shreyas I have a problem in maths in my lower grades I have problem in maths till 10th in 10th I got 55 in maths out of 100 so I have now problem in high school because I want to pursue computer science i genuinely like computer science but computer science is not complete subject in our India education system the thing is that we have to pursue whole science subject with bifocals that is language,cs,IT that's it

But I want CS so I want to take maths without maths i didn't get computer science so I want to take it in 11th means in 1st year of high school I got literally 29 out of 100 my parents scold me so much i try to them figure out that I was week in maths

By the way I want to tell one thing that I was in military hostel from since 13 years and that university professors are not that much good but one of the Sir is good but one sir is not good he just read textbook and go that was my algebra sir after 10th I leave that school and in Mumbai i join in college

So back to story I want to improve maths calculus literally fears me and coming days I have my board and university entrance exam so please help me if you help me i literally thank you 😭

Thankyou

Im in my early twenties, during highschool I struggled immensly with math, not being able to graduate with even a pre calculus course under my belt and failing the easier math courses multiple times before finally succeeding barely, I want to pursue post seco dary education, one of the Universities I really want to go to is very competitive to get into. I want to give myself to be accepted by the university and others so I plan and retaking my highschool math courses at an adult learning center/school soon and aiming to get the highest marks possible. In the meantime before i enroll at the adult learning center I want to study math at home/with a tutor to make my ability to get high marks while taking my highschool courses as high as possible. I want to buy workbooks/textbooks that use my provinces corriculum for the appropriate grades, how much time per day should I spend working on these books/with a tutor?

Fairly straightforward- does anyone here have any recommendations of what I can do to essentially "teach myself" math again from the ground up (online resources or anything that could also be of use to me)? I want to spend the rest of my semester studying and improving rather than continue to let this problem go on. I considered Khan Academy for a sort of "gamified" structure but I read on other forms that it's very unhelpful beyond 10th grade mathematics. I'm not looking for a way to "gamify" my education, I was only saying that in terms of finding something with structure- I was also considering tutoring... but for now just things that I can begin at this moment in time.

Background information:
I'm constantly struggling with my math classes: I had to retake pre-calculus I twice before I passed with a C and I'm currently going to drop pre-calculus II because my grade is too far gone to save. What made it worse was the regretful decision of leaning onto Chat GPT as a form of "tutoring" / cheating (something I'm trying to stop).

A major problem I've had all my life is my ADHD, I would constantly use it as a crutch throughout high school... but as an adult I'm honestly sick of it; my best friend with similar "problems" as me has a 4.0 GPA while I'm barely scraping by at around 3.0 simply because of my lack of knowledge in math (it used to be 1.6 before I created a better study routine and after this semester it's bound to get lower than a 3).

It isn't like I cant pass a class- last semester I almost got all As while taking 6 online courses, but that's also because none of them required me to write a+bi in terms of r, (cos(theta) + sin(theta)i) lol.

My goal in life has always been to become an engineer or something music related (I'd like to design instruments or make sound equipment for studios), however I let my insecurities knock me down and lost sight of my priorities since high school up until now (currently taking general education at community before I transfer credits to a university to pursue a bachelor).

If I can boost my GPA up from a 1.6 to a 3.0, I believe that I can do the same with my struggles in math because I'm dedicated to do the work.

Thank you to whoever took the time to read all of this, and whatever response is much appreciated!

Pre Calc student here, I hard a hard time on this problem last quiz I took and was wondering if anybody could help explain what to do in a case like this. Thanks!

problem: 4^x-6(2^x)=16 solve for x.

Im really not good at math and physics but have them at university in the first year. My question is, are there any tips on how to get good at math or is it mostly just doing exercises after exercises each day? Or are there any specific learning techniques for it? I’m already trying to do some exercises each day but Im really bad at visualizing the problems and knowing how to find the right formula for the specific question. I know it might sound stupid but it’s a genuine question. Thanks in advance! 🫶

Like in the title, the most math I know right now is 10th grade things and some 11th since I'm ahead. I sometimes read proofs for better understanding on certain topics and also do programming and I am more and more realizing I don't have any idea on how logic works. For example I was reading something about parabolas, saw the `->` sign and just came upon material implication on Wikipedia and I just saw all these terms that I had no idea on 😭

What's a good introductory course to logic, for mathematics and computer science. I feel that I may be lacking a lot of foundations so really introductory but still rigorous. I came onto 2 things

ForAllX's open logic project and mathematical logic 6th edition by Elliott Mendelson, would you recommend those or something else?

I’m currently in school to get a bachelors in electrical engineering and minor possibly in materials science. The college I want to go to actually doesn’t take these classes under their engineering program because they have them wrapped into one class along with engineering analysis. I figured if I take these 2 extra classes along with some classes that would transfer then I would be in then with the math part of the class and could focus more on the theory. Is it worth it? Or are these topics that can be learned along side what I assume are applied applications problems in the engineering analysis class?

I've been having this problem for a while now, especially in math, and I'm honestly struggling to figure out what's going wrong.

Whenever I have an upcoming math test, I spend a lot of time studying. I go through the homework questions, practice different problems, and make sure I understand the concepts. I also use ChatGPT to help explain things, but instead of just asking for answers, I have it explain the logic behind the math, why certain methods work, and how to approach questions step by step.

The thing is, I genuinely feel like I understand what I'm learning.

For example, I recently studied a lot for a math cumulative exam. I went through the material, practiced the questions, and made sure I understood what I was doing. When I actually wrote the exam, I felt pretty confident. The questions didn't seem particularly difficult, and I even had time to go back and check my answers.

I walked out thinking I had done pretty well.

Then I got my mark back, and it was 55%.

I was genuinely shocked. I wasn't expecting a perfect score, but I definitely wasn't expecting something that low. I was so confident in how I performed that I initially wondered whether there had been a marking mistake.

What's even more confusing is that this doesn't happen nearly as often in my other subjects.

I've experienced something similar in chemistry before, but recently my chemistry marks have been improving. Physics, on the other hand, has always been different. Whenever I studied for physics, I usually performed about as well as I expected. I could understand the concepts, apply them to questions, and get decent marks.

But for some reason, math is completely different.

I'm starting to wonder whether there's something wrong with how I'm studying. Maybe I'm understanding the explanations but not developing the ability to solve unfamiliar problems independently. Maybe I'm making small mistakes that I don't notice, even when checking my work. Or maybe I'm just not preparing for the types of questions that appear on tests.

The most frustrating part is that I don't walk out of these tests feeling confused or unprepared. I walk out feeling like I actually did well, only to find out that I didn't.

I don't mind putting in the work. I'm willing to spend hours studying and practicing if that's what it takes. But I want to make sure I'm studying effectively instead of repeating the same mistakes.

Has anyone else experienced something similar?

If so, what ended up being the problem, and how did you fix it? Is there something I should change about how I study, practice, or check my answers?

I'd really appreciate any advice, especially from people who have struggled with this and eventually figured out what was going wrong.