## struggling with radical expressions. having a hard time knowing where to start in complicated problems and what would be the order of operations. and factors as well.

I am struggling with radical expressions. having a hard time knowing where to start in complicated problems and what would be the order of operations. and factors as well.

I am trying to solve a radical expression and in one of the steps

3+3(sqr root of 5) factors out to 3(1+((squre root of 5))

why though?????

https://www.symbolab.com/solver/algebra-calculator/simplify%20%5Cfrac%7B%5Csqrt%7B45x%7D%7D%7B3%2B3%5Csqrt%7B5%7D%7D

submitted by /u/ReDHoodY_

## Very extremely large numbers

Somehow I am extremely interested in extremely huge numbers. I know of Graham’s Number (or however it was called) and the Googolplex, but I need more.

I wonder what number would come out if a Googolplex was taken to the power of a Googolplex, the process was repeated a Googleplex to the power of a Googolplex times, and this would be continued a Googolplex to the power of a Googolplex times. Then then would be continued, each step increasing the number by a Googolplex to the power of a Googolplex times the entire step before that. This process would have a Googolplex to the power of a Googolplex steps. Then all those steps would be continued by the number the final step provided at the first calculation times.

I have no idea if a number that big was bigger than Graham’s number, nor how many zeros it has. I’ll just call that number the Hypergoogolplex for now.

submitted by /u/ThatOprissmianGuy

## A couple questions about the range of pi in different metric spaces.

I saw a few articles and papers recently that claimed pi (as in the ratio of the circumference to diameter of a unit circle) can fall anywhere between the familiar value of 3.14159… and 4 depending on the metric used. I get that reasoning when applied to distance functions where it is something like ((x1-x2)n + (y1-y2)n …)1/n, but what about a metric that is similar to the taxicab metric, but on an isometric grid instead of a Cartesian one? It seems to me that pi=3 in that metric. I’m not really at a level to fully understand the math, but why does that seem to be excluded? I am having a hard time figuring out a simple distance formula with it, but I don’t know if that has anything to do with being an outlier or not. If there is, could generalizing that formula yield even more possible values of pi?

submitted by /u/HexNash

## Books Recommendations:

Guys can we make this post a reference to maths books?(if there isn’t one already)

If everyone can write the names of a couple of books in every topic in the comments (as organized as possible), we will have a variety of books and hopefully cover most topics

For example(number theory , topology, algebra , combinatorics, analysis , calculus,…,and any study related ones)

Also if you have books like(men of mathematics, music of primes , the man who only loved numbers,…,and that type)

## Undergraduate projects in numerical analysis

I’ve taken an introductory numerical analysis class this semester covering simple error analysis, interpolation techniques, numerical integration, solution of linear and non-linear systems of equations and eigenvalue problems. This was my first applied mathematics course and I felt like my learning methods were out of place. Doing the exercises and understanding the proofs intuitively, which is what I am used to doing, didn’t really make me feel like I was getting better at this. I began writing my own code for numerical algorithms a while ago and I can already see how this is a better appraoch to studying numerical analysis. I want to take this one step further and apply my knowledge to beginner projects. Is there a book/source I can look at for ideas for such projects? If anyone has other suggestions they would like to make, I would be glad to hear them.

submitted by /u/NoPurposeReally

## I quit my undergraduate studies in engineering to follow my dreams, now I will study Mathematical Physics (BMath)

I always wanted to be a mathematician, but I was scared because although I love math and my grades in high school were high, I though that I would not be good enough, many people from my University have been in IMOs and have won many awards, and I haven’t. But I really love math, and even though i’m not that “smart” I am perseverant with what I love so I will do my best 🙂

submitted by /u/AirPodGoose