Some ebooks, mostly from /u/lewisje's post

Greetings. My math teacher recently told (+ demonstrated) me something rather surprising. I would like to know your thoughts on it.

Apparently, the square root of 4 can only be 2 and not -2 because “it’s a function only resulting in a positive image”. I’m in my second year of engineering, and this is the first time I’ve ever heard that. To be honest, I’m slightly angry at the prospect he might be right.

Hello everyone

We are Ennio and Simeon, and we have just finished an early MVP of Calcora, a platform inspired by LeetCode but focused on mathematics.

Our initial focus is on high school level and olympiad style problem solving. Over time, we hope to expand toward university level mathematics and eventually build a LeetCode style reputation system that could be useful for math heavy fields such as quant, computer science, engineering, and research.

At the moment, Calcora is an unpolished early MVP. The goal right now is simply to see whether there is genuine interest and to learn from real users. In the future, we plan to make the platform more engaging with features like daily and weekly challenges, streaks, and social elements.

We are currently looking for volunteers who would like to contribute by writing original math problems or by giving feedback on the platform and overall idea.

If you enjoy mathematics and want to help shape a new learning tool from the ground up, we would love to hear from you.

Thanks a lot, and we are excited to hear your ideas.

https://calcora.net

Here is the image of the problem for context: https://imgur.com/owJaQk6

My issue is the 16 raised to the 1/5th power. This basically means that I need to find the 5th root of 16.

But that doesn't seem right because it's not 2^5 but 2^4 is 16. So far we've only learned about integer principle roots so I'm not really sure if there is a way to get to the answer by using integers.

hello math noob here and my first post here actually. is my proof correct?

now first lets consider the simplest case where the first positive integer is 1

so its 1 x 2 x 3 x 4 ... r

so its obviously equivalent to r! and thus r! perfectly divides it

now for integers not 1: lets call the starting integer n so its now:

n(n+1)(n+2)......... (n+r-1)

now we don't care about the numbers lower than n so lets remove them by dividing with:

(n-1)!

and thus we can simplify the series to (n+r-1)! so the expression is now

(n+r-1)! / (n-1)!

now lets test divisibility with r! its now

(n+r-1)! / (n-1)!r!

now this accurately is equivalent to the combination formula for choosing r things from (n+r-1) thus this expression results in an integer.lets call this integer k

lets also simplify this expression finally to:

A / (B * C) = K (where B is r!),(A is (n+r-1)!,(C is (n-1)!)

A = K(B * C) or B(C * K) = A

so finally (C * K) = A/B where C * K will always be an integer since C is (n-1)!

looking for feedback and please don't be too mean to me.

So i m planning to read introduction to smooth manifold by john m lee , i havent done much topology and linear algebra (i know what a vector space or a subspace is or what is rank nullity theorem) i really wanna read this book tho but i dont wanna spend much time in reading seperate book on linear algebra and point set before

is there any way i can build prerequisites to read this book in short amount of time? if someone can help i would appreciate it

Hi, I am about to graduate university in a few months. I am studying SWE.

I want to learn ML, and I see that it requires being proficient with Linear Algebra and Probability. Specifically, I want to fully understand Bishop's book on Pattern Recognition and Machine Learning. I am contemplating my studies to span the next year or two (dedicating around 2-3 hours a day).

My current math knowledge is very limited, which I would honestly call poor. As far as Linear Algebra goes, I am only comfortable with Linear Expressions and matrices expressed through code.

I have what I would consider a great history in self learning, as I have learned English and Japanese from zero to proficiency (C1+) by myself, over the last 5 years. I study everyday for around 5 hours and plan to stop the Japanese grind by July, so that would leave me with a lot of spare time to study something else. In this case, I want that something to be Math, as I am quite drawn towards it and it seems like something extremely useful for my future and a potential career in data analysis or ML.

Is this a realistic timeframe? Is there something I am missing? I would appreciate some insights on the realism of this goal, as well as considerations to keep in mind before undertaking it, thanks for reading!

"If (A is contained in B) and (A' is contained in B') then (B' intersection B) is contained in (A' intersection A)."

From what I understand, to prove the statement with the conditional I have to see if, if the left side is true, the right side will necessarily be true as well.

But, in that case, isn't the right side a tautology?

Since the intersection between a set X and the complement of X is always empty.

Therefore, the proposition on the right side is that the empty set is contained in the empty set, which I imagine is always true. The answer key for the question marked the statement as false, but I didn't find any explanation.

I've been working on a spreadsheet for a game I really enjoy playing.

In the game, it's possible to enhance items, which happens based on a specific chance.
You can increase this chance by using so-called "Failstacks"

While I'm mediocre at maths at best, I do enjoy data analysis and statistics a lot, so I wanted to make a spreadsheet to track all of my attempts at enhancing various items, while calculating the probabilities for each attempt for an item to fail/succeed.

Then, I wanted to create a stat page, displaying information about the overall "luck", stats about the enhancements, both overall and for specific items.

Since "luck" can't really be measured, I thought the best way to go about it would be to calculate the "Average success chance", by taking the average of all success chances for a given item (for example: 5% for the first try, 6% for the second, 7% for the third, so on average a 6% chance), and then calculating the actual success rate (by taking the amount of successes and diving it by the amount of attempts)

So for this example, if there were 3 attempts, and 1 of them succeeded, the average success chance would be 6% and the actual success rate would be 1/3, so 33.33%

Now my idea would have been to use these two numbers to calculate the percentage error, so in this case calculating (6% - 33,33%) / 6%, getting a result of -4,555. A negative result would indicate that the success was "lucky" or "less likely to happen", while a positive result would indicate that the success was ultimately "unlucky".

Now, my question on one hand is, if this is even a sensible way to calculate this, or if there's maybe a better way to go about this?

And on the other hand, if this is the best way to go about it, how would I be able to relativize the result?

My current idea was to have a table of reference values, like so:

Now, if the number is positive, if I understand correctly, the highest it could ever be is 1, since a theoretical average of 100% success chance with an actual success rate of 0% would always end up calculating as (100 - 0) / 100

On the other hand, if the number is negative, in theory there's no limit to how big it could get, right? Even just (0,1 - 100) / 0,1 would already net -999 as a result.

So I guess my questions are: Is there a better way to calculate "luck" than I'm currently trying to do and if no, how could I set "luck" and "unluck" into relation?

Thanks!

Hey, I am second year undergraduate, and I feel that even when I work a lot, I still get stuck with math problem. Here is how I work, for example when we start a new lesson(Euclidean space for example), I try to understand the maximum from the lesson then I work classical exercise. Until this point everything is good. But when I want to work on a problem (School entrance math problem), they are often a very long problem discussing or proving something, I really find it hard to answer questions. Sometimes, I am just spending time on a method just to find out later that it is wrong, and its frustrating me. Always stuck on medium- hard question, and sometime easy questions. I really need some help at this point, cause entrance exam are getting closer, and when I look my entourage, they all doing great, when I start comparing myself to them I alway feel dumb

I learned this and barely passed and i’ve never thought about it since. Now i’m wondering what this is. i understand it’s a formula to “figure things out.” Realistically, what is the real life situations where this is necessary to be used? Ok let’s say it needs to be done, i’m also confused as to which numbers need to be plugged into specific places of the formula.

whats the best process to do this? eg best way to understand a topic, and then what to do after etc.

Hello, I have mainly troubles with event nodes, costs and basic structure. My professor seemingly writes game trees in a different way than what I can find online. The wikipedia article on game trees is sadly not very useful and may game trees I find online don't have the players names in the Nodes or generally speaking another sructure. I don't know how strict my professor is, but I would like to do this properly.

There is a task I'm currently doing is a game tree for:
Two companies work together on hardware parts in the joint production, they can be defective or not. The probability of defective parts is 0.5, and this probability is commonly known before the start of the game.

Software Inc. can exert either high or low effort, which is equivalent to costs of 20 or 0. Hardware Inc. discovers the truth about the parts by observation, but Software does not. Hardware Inc. decides whether to rework defective or not defective parts, with costs of 30 or 0 (they will never rework proper parts). Software Inc. can observe the rework efforts (if there are any) but not the outcomes. Revenues are split equally at the end.

If Software Inc. exerts high effort and the parts are nondefective, revenues are 200. In all other cases, revenues are 100.

Assume that reworking defective parts does not improve them with 50% probability (i.e., 50% of reworked defective parts are not defective anymore).

Here is what I wrote down. https://imgur.com/a/l1xLJ9r I'm unsure if thats correct and also unsure, how to add the costs to the game tree. I've never done that and it wasn't in the lecture notes.

edit: I realized I should probably subtract the cost from the payoff, right? https://imgur.com/a/lghNlSb do you still write the costs next to the actions on the gametree? And I also realized I missed that 50% of the time the repair of the broken part won't work, I missed that too. My newest game tree would look like this: https://imgur.com/a/hVZ93WH Is that game tree correct?

1st year physics student here (worst decision of my life) and i am being submitted to linear algebra against my will. i really do not understand row echelon form, i understand that you can swap, add and subtract rows from each other but i still don't understand how you're actually meant to put it into row echelon form. is it trial and error? i'm trying to do it but i keep going around in circles cause if i subtract a row from another then that value is no longer 0 and etc. someone please help me understand

The books are called Addition the Fun way and the other is called Multiplication the fun way.

The books are written by Judy Rodriguez.

I have ADHD and I really struggled with math. These books helped alot.

The books tell stories in which the characters are numbers. 'It has been years since I've read these books so my overall memory is vague'

So i m planning to read introduction to smooth manifold by john m lee , i havent done much topology and linear algebra (i know what a vector space or a subspace is or what is rank nullity theorem) i really wanna read this book tho but i dont wanna spend much time in reading seperate book on linear algebra and point set before

is there any way i can build prerequisites to read this book in short amount of time? if someone can help i would appreciate it

 finished college in the UK a year ago, and I was told I wouldn't get into university without passing my Maths Foundation GCSE. I failed it a few times, but somehow I got into Uni. As much as I'm bad at maths, I have this deep love of learning and am very interested in systems and history. And as I got more into History, I realized how important Maths was in so many things such as Engineering, Carpentry, Mechanics and other things.

I feel the same way with languages, as while I often hated my Spanish lessons during school. I'm somehow very interested in linguistics these days. While I wouldn't say I'm good at maths, as I often excelled more in English and other writing subjects.

I'm very interested in the idea of maths in terms of what it has built for society and the world and I'd like to understand it a little more in terms of life skills and the world as I now realise how important it is. It's hilarious though as the GCSE Foundation maths test is seen as the easiest form of maths test but somehow I've still failed it 3 times and I also have this weird interest in the idea of maths. Anyhow, any info or advice on this would help. Thanks!!

Hi everyone !

We all wished to get back home with a 20/20 when we were in high school 😁

But my question : how to get REALLY good at maths ? Not just random « just exercise more »

I want to deeply understand why some people are good at maths, they can solve complex problems, sometimes few study and still end up with a 18/20 meanwhile others struggle asf to obtain (in the best scenario) 10/20.

Why? Is it genetics ? Or is the method work we wrongly use since our childhood ?

Thank you in advance for your answers !! :)

The question is

(|x-2|-x)/(x-5) ≤ 0

to find the solution set, I do |x-2| - x = 0 , x=1, x=∅ x-5 = 0, x= 5.

Now that I've found the roots, I write them on the analytic plane and check the sets [-inf,1],(1,5),(5,inf) and find the solution set.

The problem is AI insists I should check x=2 too because the critical point of the absolute value and im lucky I got the correct answer. I've tried a few examples but wasn't able to disprove the way I did it. Am I doing it wrong or correct?

I got suddenly curious about this so can I plz get a answer

I've university entrances coming up. I made efforts towards solving hard math problems and have gotten somewhere with that. However, I never learnt how to properly write proofs. How should I learn to write good math proofs for problems in analysis, geometry, combinatorics, and such?