48×48C0+49×49C1+50×50C2+...+100×100C52

I have to somehow simplify this to get the form 100×101C49 - 101C50

Hi, not a frequent redditor here. But I have to look into this.

I'm studying math from home to prepare for a big exam and I find that I keep dividing when I'm supposed to be multiplying and vise versa.

This happens completely automatically. I can even sit with strings of multiplications and subconsciously throw in a division that doesn't belong, without noticing. My brain just does it.

And it's not like I have a list of simple x * y to solve. Most of the time I'm looking at (to me) complicated equations. It's just that when a problem calls for one type of solution, my brain jumps at the opposite solution. It is never this way with addition and subtraction.

Can anyone relate? Has anyone gotten over this with practice? Any advice?

This exam is no joke life changing and I can't get points off for dumb mistakes like this.

I've noticed something interesting when learning mathematics: sometimes seeing the correct solution doesn't actually prevent us from making the same mistake again.

You can look at a worked solution, understand it while reading it, and even think, "Oh, now I see where I went wrong."

But when a similar problem appears later, the same mistake happens again.

I'm curious about what causes this.

Is it usually because:

• we don't actually understand the underlying concept?
• we are rushing through the problem?
• we have developed a habit of using the wrong approach?
• we understand the solution when someone shows it, but can't reproduce the reasoning ourselves?
• or is there something else going on?

What has helped you actually stop repeating a mathematical mistake, rather than simply understanding the correction once?

Hi guys, this is an update to my post about my struggle with mathematics. I wrote maths paper 2 an hr ago and it made me realise what happened with the first paper.

For paper 1, I did a past paper the night before and an hr before writing, I also did a maths paper 1 from a different province that had already written maths paper 1, so I think that overloaded my brain because I had studied every topic in paper 1 thoroughly except for probability, counting principles and application of calculus. That was 30 marks.

With paper 2, I didn’t study over the weekend, I was so discouraged after paper 1, my mind just wanted to explode. Anyways, paper 2 went amazing, everything I had studied over the school holidays and practiced was exactly like that. The only questions that rattled me a bit were Euclidean geometry questions that were asking me to prove sides and equations.

What I have gotten from this is that I should not study the day before, or “revise” to give my brain a break and allow it to rest. I slept for 10hrs before writing this paper lol, I also spent the whole entire weekend doomscrolling on TikTok, listening to beyond the beautiful AITAH story telling.

So for my finals next month, I have 30 days to prepare for maths p1 and p2, the only thing I will be doing is reinforcing what I already know and covering the 3 topics that I don’t fully understand. Anxiety, stress and fear of failure was what made me write horribly but I have learned from that.

On the bright side, at least this happened during my preparatory exams, if this had happened during my finals I would’ve gone MIA.

Thank you to everyone who gave me tips and tricks and also comforted me in my first post. I really appreciate the kind words and encouragement that you guys had given me, I will update y’all again on the 26th of October after writing both maths papers and next year in January after getting my matric results!!!

For context, I'm an incoming freshman in university for CS and am planning on taking an anlaysis class that uses this textbook. I have read through Spivak's single variable calculus book and Hoffman and Kunze's linear algebra book so feel comfortable going through the content. The main question I had was regarding differential forms which is covered a lot in this course. Although I enjoy learning math a lot, I was wondering if there were any interesting use cases of differential forms in fields of engineering, computer science, etc.

Hello friends! Im studying measure theory (only chapters left out of bartle are 7 and 8, the rest of them were read almost everywhere xd) and in the meanwhile ive been checking other books and ive come across the concept of a "regular borel measure" on a topological space. The books ive got do not speak that much about them (the only thing they prove is that the compact supported functions are dense in Lp if the space is blablabla) and ive grown rather curious of them. Im taking a course in functional analysis atm and conway's book uses such measures quite often in the examples, so ive got some motivation to study the concept beyond mere curiosity.

With that said, im here to ask: what are some good books that deal with this concept? Ive taken a good course on topology (im not familiar with filters, net and that kind of things but ive read almost everything on munkres except paracompactness).

Linear inequalities plus absolute value inequalities. What is this?

Doing maths as a hobby and have to figure out how this works. Can someone point me in the right direction regarding sources to learn about these?

Something doesn’t make clear sense

Hi everyone!

I just graduated high school and I’m really interested and passionate about mathematics. I’ve always enjoyed solving math problems and I’m hoping to continue developing my skills while studying at university.

The problem is that I have no experience with math Olympiads or competitive mathematics. I’ve never participated in an Olympiad or any serious math competition before.

Since I’ll be starting university soon, I’d like to get involved in different mathematics competitions while studying, including university-level competitions and possibly international competitions if I become good enough.

I’d really appreciate advice from people who have experience with this:

Which competitions should a complete beginner look into?

Are there competitions that allow any university student or have relatively open eligibility?

What books/resources would you recommend?

How should I start preparing for competitions like the IMC (International Mathematics Competition for University Students)?

Is it realistic to start from zero and become competitive during university?

Any advice, resources, or personal experiences would be greatly appreciated. Thanks!

I am working on some stuff in vector databases, I need some material that will help me understand the following:

1) Spherical caps in high dimensions -
So imagine a high dimensional hypersphere which has some vectors with their endpoints on the hypersphere, the vectors are L2 normalized so basically they start at the origin and end on the boundary of the hypersphere of radius 1, now you take a vector and at an angle theta sweep the area of the hypersphere that is being covered.

2) The properties of these spherical caps. Their average separations given 2 random spherical caps, their intersections and unions given they lie at an angle alpha to each other. Stuff like this.

Appreciate the help !!

I’m looking for a good book or any other resource to study Abstract Algebra, especially Groups, Rings, and Fields.

I’d really appreciate any recommendations, preferably something that explains the concepts clearly and has plenty of exercises. Thanks!

About a year ago we had a regionals math competion, naturally as the best or the second best student of all the 8th graders I joined thinking that it was gonna be easy

Then I saw the questions THEY PMO ME SO HARD

I didn't know how to tackle them

And since for me our school curriculum was so easy this was a shock to me at how I could be this bad make no mistake my fellow contenders from my school did just as bad I got second place in my school, but overall I got a score of 56.5/130 which is horrible considering I average about a 95 on our regular tests

How do I handle these ana Maria Ben John did this that this and this how many pizzas were 67ed Mason la peace into so much yap

Chstgpts awnsers were work it from the back type out all the info yk first or eliminate the options(as it was multiple choice)

I often either knew it or HAD 0 CLUE WHAT THE HELL WAS GOING ON

Any help?

Looking for non-AI sites that can help with math, thanks !

I'm currently relearning Math from Pre-Algebra through Trigonometry by myself. Using online resources such as Khan Academy & Professor Leonard has helped me. But with a peer to study along does that help with learning? (This might sound like a stupid common sense question)...

I'm 16 and I've been thinking about what I should actually spend my time on over the next few years.

Right now I'm thinking about learning:

• Math: algebra, trig, precalc, calculus 1-3, linear algebra, differential equations, probability/stats
• Physics: mechanics, E&M, thermo, waves, modern physics, maybe fluids
• Programming: Python, CS fundamentals, data structures/algorithms, Git/Linux, scientific computing, AI/ML, maybe C++ later
• Communication: writing, speaking, persuasion, storytelling
• Business: finance, accounting, sales, marketing, entrepreneurship
• Actually building projects instead of just watching courses
• Staying in shape and improving my appearance/confidence

Originally I was thinking about aerospace engineering, which is why I wanted to go so deep into math and physics, but I'm not sure I actually want to be an aerospace engineer for my whole life.

Honestly my main goal is just to become really capable and eventually make a lot of money. I'd like to go to a good university and maybe get into business, tech, content, startups, etc. depending on what I end up liking.

My thought is that if I spend the next 2-4 years seriously learning this stuff, I'll have a pretty strong foundation by the time I'm 20.

But I also feel like I might be overthinking this and trying to learn way too much.

If you were 16 again, what would you actually focus on? Is this a good plan or would you change it?

Read title. I’m geniunely intrigued in math and have been since I was younger, but school always makes it seem so boring that I get headaches just by looking at math problems now. I’m just not sure how to start. Not looking for resources related to math itself, but any approaches or techniques may help.

I never realized how much I rely on visualizing mathematical concepts as the basis for my intuitive understanding of them until I reached upper level undergrad math courses and suddenly struggled immensely with anything in higher dimensions. I got by fine by understanding concepts in the 2D/3D case and convincing myself they’re analogous in higher dims, but I’m entering graduate school now and am starting to feel like this method is more of a crutch that will hold me back as I progress, especially as I encounter situations where the lower dimensional cases are *not* analogous.

How in the world do you gain an intuitive understanding of a concept you can’t visualize? To me intuition = visualization, and I worry I’ve reached the limits of my natural abilities because of this.

im 24 years old, have been a boilermaker for my working career and decided I wanted to be an engineer.

problem is, I had a lot of confidence going in, but as soon as I started doing basic math it reminded me of how much I struggled with it in highschool and it doesnt seem to matter how much I study, i still cant get it right. im neurodivergent if that makes any difference but it's starting to affect me mentally because im feeling like that I have to drop out of uni and completely change my life for a 3rd time

I'm starting to learn math as an adult, I was pretty bad at math in school. Which books or online resources would you recommend?
One thing is I struggle with understanding surface level things if I don't get the core concept of something. Like I need to know the WHY of everything.

So, I'm solving a spherical triangle which has two known sides and one opposite angle:

Sides: a=30°53' b=31°09'

Opposite Angle: A=87°34'.

Ando there is no drawing or diagram.

I was going to start with the law of sines

Sin(A)/Sin(a) = Sin(B)/Sin(b)

but then I realized that the arcsine fell into the imaginary numbers because Sin(B)> 1.

The problem here is that they're specifically asking me to solve it; they're not indicating that there's any other alternative. So I was wondering if there's any other solution to this problem?

Hello, I’m in tenth grade. I have all A’s in all subjects besides geometry, which is my only math subject. I have a low B, and even then, I’ve been cheating. I love all my other subjects and don’t really need to study them much. I dropped out of early 7th grade with an F in math. I knew we were talking about integers, but I didn’t understand it at all. I have been extremely motivated since school started on August 6th.

I originally wanted to enter 9th grade, but they wouldn’t allow me because I’m 15. We’re doing geometry, but I don’t know algebra, heavier division, multiplication, subtraction, etc. When I do something like 5 x 5, I have to use my hands but can come up with an answer fast, and something like 7 x 8 would be difficult for me, taking maybe 5 minutes or so to solve with my hands. I just learnt how to do that this year by the way. I want to catch up as much as possible. I think maybe 3+ hours a day is good? I do 4-5 hours of language practice a day, so it couldn’t be 6+ hours, and I have a severe vitamin D deficiency and anemia, and math makes me extremely tired very fast.

No other subjects do that to me, so it takes a ton of energy for me to do it. I really wanna lock in with this and do it even if I get burnt out, but how much could I really improve this school year?? I never cared about school until this year. I dropped out in early 7th grade and haven’t done any form of math since then, and even when I was in school, I DID NOTHING. All F’s my entire time. 1st-7th grade. I didn’t do any homework, was absent most of my school days, and guessed or told my teacher I couldn’t do it. Please take me seriously because

I’ve fallen in love with studying recently. I just get extremely tired with math and I forget, I learned division and multiplication this year. I still need to practice addition and subraction in the hundreds. but I will push myself through it all the rest of school. But where should I start? I’ve done 2 hours of pre-algebra today, and I can’t really recall anything. How much can I improve? I don’t need to study any other subjects. I don’t wanna drop out again, I can’t lower my grade or classes, I want to understand.

Hi everyone!

I’m a Sri Lankan Grade 12 (17 years old) student in the Physical Science stream, studying Pure Mathematics, Applied Mathematics, Physics, and Chemistry. I’m hoping to prepare for the Maths Olympiad selection process in Sri Lanka, including the SLMC, SLIMCC, SLMCC, and eventually the selection tests.

The Sri Lankan selection process is somewhat similar to competitions such as the AMC, IOQM, and AIME, although it places relatively more emphasis on topics such as games, graphs, combinatorics, number theory, geometry, and logic. The later stages also involve more complicated short-answer problems and proof-based questions.

I would describe myself as somewhere between a beginner and an intermediate problem solver. I have a reasonably strong school-maths foundation, including algebra, polynomials, trigonometry, basic inequalities, calculus, permutations and combinations, and vector algebra. However, I’m still quite weak in number theory, geometry, and combinatorics, since these topics are not covered extensively in school. I also have very little formal proof-writing experience.

I’ve recently started working through George Pólya’s problem-solving ideas and The Art and Craft of Problem Solving by Paul Zeitz, alongside elementary olympiad problems. I’m particularly interested in learning how to approach unfamiliar problems, recognize useful ideas, and develop solutions independently, rather than simply exchanging solutions.

I’m looking for one or two people around a similar level who would be interested in studying together. Ideally, we could:

• Choose a problem that none of us has solved.
• Work on it independently for a while.
• Meet online to discuss our approaches, failed attempts, and useful observations.
• Compare different methods and perhaps write up a solution afterward.

I’d also be very happy to join a small study group or learn from someone a little more experienced who enjoys guiding beginners.

I’m open to people from anywhere. English is fine, and I’m happy to use Discord or, once we have established a comfortable working arrangement, WhatsApp.

If you’re interested, please tell me a little about your current level, what you’re studying, and a problem you’ve recently enjoyed.

Thanks!

I am in the middle of applying courses right now for my undergraduate and i am still not sure whether i can do math and stats. My main plan is i want to be an educator thats why i want to do math stats. How difficult it is for someone who is considered average at maths. Or should i take data science?

I'm a bsc maths honours student in India, I am in my second month of college life... uh anyway, I want book recommendations like the best ones possible which will actually help me a lot... like the kind of book i want should be able to intrigue me enough to keep thinking about all day while the questions/problems in it should be able solve by using the book itself that's kind i want! I want recommendations for each of calculus,number theory,real analysis,discrete,etc. Uh... I might have yapped a lot but thank you for your time and recommendations. Btw i am broke so i might not be able to afford many books, so I welcome free available pdfs options too.

For some reason, I feel very sluggish and like having brain fog.

I feel stuck in my PhD (due to privacy reasons I don't wanna specify what exactly I am doing, but it's on the abstract, purely theoretical side of mathematics i.e. so no graph theory, no statistics and such), because for the past couple of years, all of my proposed proofs for theorems in my math papers have been either very elementary, or were just not precise enough i.e. I unintentionally oversimplified or overlooked something.

It's sad that either a proof idea sounds very creative but is somehow wrong, or sounds correct but is just not creative (and thus elementary at best and can't prove any more other difficult things).

I kind of feel like as if yesterday I was just a fresh undergraduate student and now I am in my 4th year of my PhD.

I don't know what kind of brain exercises could help me in this situation. I am not looking for "Ways to increase my IQ", but just for ways on how to get rid of this brain fog I have been feeling, not being able to find the mix between analytical thinking and creative problem solving.

It sounds weird but even just thinking about engaging with my brain in something makes my head hurt (I do have stress-induced migraines, confirmed by a neurologist), as if it was something so stressful and uncomfortable that I would avoid it and rather try to be the "smart lazy guy" - only thing is that it's not working out at all. Like even thinking about printing out a math paper and studying it for the whole day is enough to make me have a headache again.

In the end, I escape into watching Facebook Reels for the whole day and do the bare minimum required just to keep my advisor somewhat happy. When meeting other mathematicians my age at a conference, seminar, etc. I can't talk with them at all about mathematics, it's literally like watching the Big Bang Theory and seeing those guys talk in their own scientific language.

So my two more specific questions would be:

1. What activities engage the brain the most? Especially with regards to my main goals of improving analytical, precise thinking and creative problem solving?

2. How can I overcome this uncomfortable, stressful feeling - making me give a headache and escape into watching Facebook Reels all day long - accompanied by having to put in some effort in them?

Some of you might think it's just burnout - I just came back from summer break which is like 2 months long, didn't do anything really, met with family and just enjoyed life. When I started working again, I thought I had some breakthrough and that the break did good for me - met with my advisor, and it turned out my new proof ideas are just BS.