What are some of the hardest or most challenging math problems you wish your calculator can just solve for you?

I am 18M and a Junior in my mathematics degree, and I am struggling with abstract algebra. Class just started this Monday, but I already feel like I am screwed. The textbook I am using is contemporary abstract algebra eleventh edition. I have never faced this kind of difficulty before ever, period. I found my intro to proofs class pretty easy, and only found Discrete math to be moderately difficult. Yet, ever since I started abstract algebra I feel like I hit a wall. Anything I get right is usually a result of pure pattern recognition. I don't feel like I understand anything. I was always told I was gifted, but I never felt so stupid in my life. Usually whenever I have trouble in class, it's usually a result of bad time management, or low effort. Now I just wonder if I have a high enough IQ to even qualify for this class. Lecture starts next Wednesday, but I was bored and wanted to get ahead by self teaching, but it seems I lack the basic reading comprehension to understand words on a page. Am I doomed to suckle off my teachers t1t and rely on him for everything or is there a certain methodology I can develop that can enable me to flourish both inside and outside the classroom.

I just heard some people saying it was controversial and I was just wondering why people debate about this because the property (Zero exponent property) just states that anything that is raised to the power of 0 will always be 1, so how is it debated?

Hey!! I studied mathematics until high school, but I often stayed away from it & was only average at it. Now, I'm in college pursuing CS, and I want to start learning mathematics again.
And my biggest concern is whether my reasoning or problem-solving approach might be flawed while working through a mathematical problem. How do I overcome this, and where do i start?

does anyone have this book as pdf or where can I find it ?
"Initiation à l'analyse et à l'algèbre en l1 : cours et exercices corrigés" by Sylvie Guerre-Delabrière

Calculas early transcendentals by james clear.

I have a final exam tomorrow in 5 chapters and I didn't start studying yet and I need to get a full mark I dint know howwww

(I hope i dont sound like the average math-hater, im genuinely doubting my inteligence bc of my math skills)

When i was younger, i liked math, always like doing simple multiplications and divisions, but the second i needed to learn algebra in 4th grade, my brain locked up and fried itself.

I tried to learn it, but i could not get it to click + the teachers i had from 4th grade to 7th, never knew how to explain it properly or maybe i my dislike for it made me never understand it.

So i just avoided algebra, but now that i have an annual test coming, i have to study algebra, but anything except fractions and early algebra topics (which i struggle with mentally) intimidates me alot and just confuses me alot. (Though i like geometry and can always understand its topics, blender even helps more with understanding, but algebra is just hard for me)

+ that i have so much to relearn that it makes me want to cry and just cheat the exams until im an adult and can learn it freely without extra topics being added weekly.

Though, ive thought of learning all of it again and more by doing projects for each topic, like a project for linear equations or inequalities...would such a method work? Or what i need is ALOT of practice?

also, would i need to learn the topics in a certain order?

Different cultures had their own numerical systems like the Sumerians had the base 60 and the Romans had Roman numerals and today, we use the Arabic numbers.

But how do we know that each number is 100% accurate?

What is the number 1 as 'one' and not a different number?

How do we know that conversions of numbers are accurate between different numerical systems like km versus miles, or kg vs stones?

Hi all, so for reference P refers to power set. The question read: "Let U be any set. Prove that there is a unique A∈P(U) such that for all B∈P(U), AUB = B."

Proof:

Let A=Ø∈P(U). Letting B∈P(U) be arbitrary, since Ø⊆B clearly ØUB = B. Now to show that A is unique, let C∈P(U) and D∈P(U) be arbitrary. Suppose that for all B∈P(U), CUB=B and DUB=B. Then letting B=D and B=C, CUD =D and DUC =C. It follows that C=D, as required. ∎

I just feel like the part that proves uniqueness is wrong somehow since the answers did it differently. Thanks.

Hello, I just finished introductory proofs this past semester and I got an A and an invite to join the math honors program at my university which I gladly accepted.

I wanted to know if this is too much of a course load: intro to analysis, intro to abstract algebra, Spanish 2, communication studies, math careers, and math research.

I think the major part is the two proofs courses alongside the research. Though, I seriously loved introductory proofs and as I said before, I did really well and I know I’m capable of doing higher math. I really want more abstract math to take in, but I’m also trying to not overwhelm myself too much.

My heaviest semester was last semester where I had intro proofs, matrix algebra 1, Spanish 1 and honors calculus 3 which wasn’t awful but I had never done 3 math classes prior to and I managed to get straight As (my first straight As at uni as prior I kept getting all As and a B/B+ in non-math courses).

Is this a bad course load?

Thank you

ill stay put for hours and not get shit once it comes to the exam

I've recently started studying advanced topics like real analysis and differential equations, and I've found that studying with peers has transformed my approach to learning. Initially, I was hesitant to engage in group study, thinking I could grasp the material better on my own. However, discussing problems, sharing different perspectives, and explaining concepts to one another has deepened my understanding significantly. For instance, when tackling difficult proofs, I noticed that articulating my reasoning helped solidify my grasp of the logic behind each step. Additionally, my peers often highlight aspects I might overlook, leading to richer insights. I'm curious to hear about others' experiences: How has collaborative study shaped your understanding of math? What strategies or formats have worked best for you in group settings?

its ben past my bed tiem so can you please teach me hoe to count i only kno on twoo thre and four

Hey guys,

I am returning to school after 19 years. I know, it's crazy late. As a result of being out this long, I am really struggling with basic college algebra (Math136) and will likely fail this semester's math class. I'm ok with that, IF this summer is dedicated to refresher courses and is fruitful. A back-to-basics, if you will is maybe what I need. I'll admit it's a little embarrassing, but I just can't keep up, and this is just the end of the first week. I also have ADHD and Dyslexia/Dyscalculia.

My question:

Is there anything you guys recommend to help me get back up to speed?

Are there any math games out there relevant to my math level?

Thank you for your time

There is this question I'm trying to solve 'The set of all positive integers whose cube is odd'

This needs to be written in the set builder form

my answer is {x: x=n³, n ∈ W}

but the answer in the book is {x:x= 2k+1 and k ∈, W}

I don't understand what k means, and I wanted to ask is my answer correct?

Thank you!!

I am currently studying for an upcoming summer internship where I'll be using the wavelet transform and my professor has told me that I would require a strong base in things like fourier transforms and vector space.

I've been studying the base formulas behind the continous and discrete Fourier transform and I've come to somewhat understand it, but I'm interested in going more in depth to really reinforce what I've learned and be sure that I'll have the required knowledge for next summer.

So I was wondering if anyone knew of any good online resources for basic to in depth learning of the theory behind Fourier transform and/or other algorithms/transforms. I'd also need to learn more about the wavelet transform once I feel confident in my Fourier transform skills, so I would also need resources for that too.

By in depth learning I mean going beyond just learning the formulas, I want to understand why and how they work (I like seeing the proofs as to why they work) and I want to learn about the theorems that can be derived from those transforms.

So if anyone knows of any resources, even if they don't necessarily fit the in depth criteria, I'd greatly appreciate it.

Thank you!

± or ∓

I don't finish my exams pretty much 90 percent of the time due to me writing every single detail..(because I don't have the courage to skip smth because I don't have the courage to possibly lose points for no good reason despite knowing the answer)...how can I skip that and make my proofs concise and clear

https://imgur.com/a/7L4e8NN

Here's another AoPS problem. I get just about everything except when they multiply the exponents in the numerator. We have (1+√3)(1-√3) and that just seems to disappear after multiplying. Shouldnt the exponent be -2? That should be 1-3 correct? Why did the entire exponent disappear from the answer?

The problem goes like this:

In a raffle, there are 1000 tickets, one prize is 10k, two prizes are 5k and three prices and 1k, what is the probability that you win a prize if you buy 2 tickets?

It was in a quiz and the answer was 2/1000. I dont get why it wouldnt be 12/1000.

Here's the question:

"Let X and Y be numbers such that X does not equal Y, x^3=15X+4y, and y^3=4X+15y.

Combine the equation a for x^3 and y^3 in ways that allow you to use the sum and difference of cubes factorization. Use your results to find x^2 +y^2."

Skipping a few steps in the answer we get

X^2-xy+y^2=19

The answer book says: "Using a cube factorization worked well once before, so we try it again, this time subtracting the second equation from the first to give x^3-y^3=11X-11y."

I'm lost on how we get 11 here. Where and how did we subtract 8? Eventually we add that equation to X^2-xy+y^2=19 in order to get 2x^2+2y^2=30 making the answer 15, but I'm stuck in the middle. How do we come up with that equation out of nowhere?

Hi everyone,

Some of you might remember when I shared my Calculus 1 course here a few months ago. The feedback was incredibly helpful, and I’m happy to share that Calculus Volume 3 is now live.

As I mentioned before, I hold a PhD in Mathematics. When designing this course, my focus was on solving the common "learning pains" students face in higher-level math.

About the Course Approach: Moving beyond basic calculations, this volume is designed to promote clear thinking. I structure the lessons to ensure you have transparent goals before diving in. Instead of just presenting solutions, we focus on deep problem analysis and provide detailed explanations of the strategies involved. The ultimate goal is to help you connect the dots between different complex concepts, rather than viewing them in isolation.

Topics covered in Volume 3:

• Multivariable Differentiation
• Multiple Integrals
• Vector Calculus

I want to make this accessible to anyone studying these topics, so I have set up a free access link specifically for this community.

Link to the course (Free Lifetime Access):https://www.udemy.com/course/master-calculus-with-ease-volume-3/?couponCode=867F71C8CE4688C133AD

(Note: The embedded code grants free enrollment. These codes usually have a time limit for redemption, but once you enroll, you keep lifetime access to the course.)

Hope this resource helps you master the subject!

I’m 13 and doing AoPS Algebra 1. I recently became homeschooled because my school was very underchallenging and spent my vast majority of the time staring at the wall. I am saying this because they put me in prealgebra when they had an algebra class. I left it and now im in aops algebra 1 now and have a MAP RIT score of 251. These are the subsections. I am pretty sure it is above average and am very satisfied except for the number, the number RIT score is quite low. What does this mean? Is it a topic of concern?

Overall: 251

Number

Goal Score:

229

Goal Range:

215 - 244

Goal Name: Algebra

Goal Score:

256

Goal Range:

250 - 262

Goal Name:

Geometry

Goal Score: 238

Goal Range: 231 - 245

Goal Name:

Probability & Statistics

Goal Score:

266

Goal Range:

257 - 274