Hello,

I'm having trouble putting a few theories into practice.

I don't know where to begin when approaching two questions (both involving basic algebra)

Question 1: Write (y−4)⋅(y+4)⋅(y+5) in the form ay^3+by^2+cy+d.

I'm unsure if the answer here is y^3 + 4y^2 - 4y^2 -16y -80

= y^3 - 16y - 80 with the two others cancelling each other out

Question 2: Write 3/x + 8/x^2 + 9/x^3 as a single fraction:

I need some help understanding what to do when faced with problems like these.

Suppose, I have to prove that the given three statement: a), b) and c) are equivalent. Then does it suffice to prove the following: a) is equivalent to b) And a) is equivalent to c)?

https://www.academia.edu/105787552/On_the_Unprovability_of_the_Riemann_Hypothesis

https://www.academia.edu/105760672/On_A_Potential_Computational_Approach_To_Falsifying_the_Riemann_Hypothesis

Its probably just bullshit, so roast me all you want.

Hello, I'm working on proving something. My proof is done, as long as I can say that, for events E1, E2, ..., Ek, it is always true that P(E1 or E2 or ... or Ek) <= P(E1) + P(E2) + ... + P(Ek). ("P" means probability.) But proving that part is looking messy.

Thinking about it, it seems pretty obvious that it's true. Think about something like a venn diagram. The area of the union of a bunch of disks is at most the sum of the areas of each of the disks.

But when I try to prove it, I end up constructing a complicated inclusion-exclusion expression that I don't see how to simplify.

I'm pretty sure there's an easier way to do it. Can anyone tell me what it is or at least give me a hint?

Hey Everyone,

I'm currently working on a Discrete Math problem related to Graph Theory, and I could really use your expertise and insights to crack it! This question is part of my Master's level assignment, and I'm stumped on how to approach it.

Assignment Question

Consider a graph G with n vertices, where n is a positive integer greater than 2. Each vertex of G is labeled with a distinct positive integer from 1 to n. There is an edge between two vertices if and only if their labels have a common divisor greater than 1. I'm tasked with proving that G is a connected graph.

I've tried exploring the concept of Greatest Common Divisor (GCD) to establish connectivity, but I'm not entirely sure how to structure the proof.

If you have any ideas, insights, or suggestions on how to approach this problem, I'd be incredibly grateful for your input. I'm open to various approaches and techniques to prove the connectivity of this labeled graph.

Any help or pointers you could provide would be fantastic! Whether it's a high-level strategy or a detailed step-by-step solution, I'm eager to learn from your expertise.

Thank you in advance for taking the time to read and respond. Looking forward to engaging with the brilliant minds of this community! Let's tackle this assignment together!

https://www.academia.edu/104899336/The_Uncertainty_Principle_for_Entropy_Rank_and_Complexity_Implications_for_the_P_vs_NP_Problem

Abstract: This theoretical paper introduces a novel uncertainty principle that explores the relationship between entropy rank and complexity to shed light on the P vs. NP problem, a fundamental challenge in computational theory. The principle, expressed as ΔHΔC≥kBTln2, establishes a mathematical connection between the entropy rank (ΔH)and the complexity (ΔC) of a given problem. Entropy rank measures the problem's uncertainty, quantified by the Shannon entropy of its solution space, while complexity gauges the problem's difficulty based on the number of steps required for its solution. This paper investigates the potential of the new uncertainty principle as a tool for proving P≠NP, considering the implications of high entropy ranks for NP-complete problems. However, the possibility that the principle might be incorrect and that P=NP is also discussed, emphasizing the need for further research to ascertain its validity and its impact on the P vs. NP problem.

Hello everyone! I have simple question.

I know that Aleph-0 is an countable infinity and that Aleph-1 is an uncountable infinity.

I know that set of Real numbers, R has a cardinality of Aleph-1.

I know that R^R has a cardinality of Aleph-2.

Does R^R^R have a cardinality of Aleph-3?

The reason I ask this is because, I know that in the case of problems like x^y^z, it is the same thing x^yz. So wouldn't R^R^R be the same as R^R since R*R = R? Or does the nature of uncountable infinity make this rule different?

I have a rather interesting problem for my birthday and I think that the underlying mathematics might be slightly more complicated than I originally thought.

I am doing a taskmaster style event which will include 12 events and I have 12 guests.

The games themselves are taskmaster style events (UK TV show) and because of practical reasons, I can only have 6 players on each event at once.

I have used the Social Golfer problem to organise who plays what game so that each player plays exactly 6 games. I have also made a small ammendment to the algorithm that I used so that married couples have 3 games together and 3 games not together. As such, I have constructed this matrix where the rows can not be changed but the order of them can be.

The columns are the players and the rows are the games. So for example, the player in column 1, let's call her Kelly (because that's her name) is playing in games: 2, 4, 5, 6, 8, 12.

The issue that I am having here is that she is playing in three games in a row with no break. What is the minimum I can get this value for all players? Is it possible so that no player has 3 games in a row? What should I even look up for this? A key distinction between this and standard round robins is that the teams consist of the same players in different orientations so my rows or game configurations are like ordered groups.

Any help would be greatly appreciated, thank you.

My guess : when ppl found that they need math for math. But when?

Recently I am reading Atiyah MacDonald's 'Introduction to Commutative Algebra'. Now I am having fun when I am reading the theory but I am also finding the exercise problems tough to think about. In one exercise there are almost 30 problems but I have done only 5-6 by myself completely for others I had to take help from the solution manual. I feel like I am not learning the topic well in this way. But completely thinking by myself for all problems takes too much time and in the end, I may fail the course or do badly in semester exams.

How do you do the exercises of such Advance Math Books ?

What is the statistical likelihood of knowing a person who is one degree of separation away from me, living in a city with a population of 25,000 in Lexington, SC, given that I live in Los Angeles, CA?

Is there either publicly available code to generate a description of the full list of finite families of uniform polyhedra including the degenerate cases or is there place where such description file(s) can be downloaded?

Preferably, the descriptions would be lists of faces encoded as ordered lists of vertices, but anything consistent would work.

Hello,

I just got accepted into a PhD program to study profinite groups. I got hold of a book called Profinite Groups by Luis Ribes and Pavel Zalesskii to start learning the basics over the summer before I start the PhD.

My problem is that I don't know where to find exercises. Does anyone know of a good source of exercises on this topic?

​

PS: There might be exercises in this book, but I am getting access to this chapter by chapter, so if there actually are exercises at the end of the book or something I won't have access to them for months, which is not great for learning a subject.

​

Thanks in advance.

Goldbachs conjecture states that every even number greater than 2 can be expressed as the sum of 2 prime integers. Here is a proof

Every prime number >3 can be written as 6n+1 or 6n-1 for some natural number n.

​

Addition of 2 prime numbers can be in the form of:

​

(i)(6n+1) + (6k+1)

​

(ii)(6n-1) + (6k-1)

​

(iii)(6n+1) + (6k-1)

​

Case i) the resultant number is 6n+6k+2 or 2(3n+3k+1) and 3n+3k+1=1(mod 3)

​

Case ii)the result number is 6n+6k-2 or 2(3n+3k-1) and 3n+3k-1=-1(mod 3) or 2(mod 3)

​

Case iii) the resultant number is 6n+6k or 2(3n+3k) and 3n+3k=0(mod 3)

​

Now, any natural ,let x, number can be expressed as one of the following:

​

x=3q (0 mod 3)

x=3q+1(1 mod 3)

x=3q+2(2 mod 3)

​

Therefore we can see that the sum of 2 primes (>3) will always be in the form of 2x for some natural number x.

​

Therefore every positive integer can be expressed as the sum of 2 odd primes.

i’m wanting to do a dip in math after being interested in pure mathematics for a few months, but in order to do that i need to do a calculus class but i was wondering if there are any other basics i’d really need to know

For whoever did WMA11/01, how was the exam??

https://www.academia.edu/101393275/On_the_Question_of_the_Falsifiability_of_the_Riemann_Hypothesis_

It would appear false, but I may have made a mistake.

Any and all constructive feedback is most appreciated.

Edit: I've updated my statement in an attempt to take the feedback being given into consideration, thank you for your patience with me.

Edit: I think a better way to put it is that RH may be a special case, though I understand that is a boldly obnoxious statement I mean no ill will, and simply wish for constructive feedback.

https://www.academia.edu/101102489/A_conjecture_on_initial_conditions_of_Non_Deterministic_polynomial_problems_

https://www.academia.edu/101123143/Theorem_on_initial_conditions_of_Non_Deterministic_polynomial_problems_and_their_solutions_in_polynomial_time_

https://www.academia.edu/101144624/On_the_Computability_of_Problems_

I need someone to check to see if there is or (hopefully) isn’t a massive mistake that was missed.