/sci/ - Science & Math

I work in a research group in a European University. Each week, in the group meetings we have some organic chemistry exercice to solve together (a difficult mechanism for a natural product, an unknown reaction...) and this week it's my turn to prepare it and I have run out of ideas. So I am turning to redditers kindness to help me with my problem. Thanks!

Ask a math bachelor anything

or

A math bachelor asks: what have I done with my life?

I've been struggling for a long time with the following problem. Any help would be great and if possible could you show me how you got to the solution?

There are five numbers in an arithmetic sequence. Their sum is 25. The sum of their squares is 285. Find the five numbers.

What is a good way to remember a bunch of math rules in a very short term?

I have a final exam tomorrow and i need to remember all the rules to trig, log and differentiating

i think it would be cool to do this because you could extend it for other organisms, not necessarily just humans. you could gestate extinct mammoths or some shit, assuming they cryo'd that DNA sample they found.

if we got to the point that protein synthesis was understood fully and cellular differentiation could be organized on a macroscopic level, you could develop living organisms that don't exist yet, but could help contribute to the biosphere.

>Be me today
>Be responsible human being
>movement of legs towards person of the learning of numbers, and do the filling of brain with knowledge, and am aware how to fix the question.
>Be awesome

Lets say I found a way to make a bijection between every number of N and R in a Cantor's diagonal argument sort of way.
Is this anything special? Would this mean R is countably infinite? Should I Arxiv it?

>>6923770
>>6924813
All true, all catastrophic.

High school math class is a fucking nightmare. These courses should focus exclusively on inarguably applicable geometry, probability, statistics, and only the most basic algebra/trig. Nobody outside of STEM gives a shit about the quadratic formula or trig identites, nor do they need to. Common core math is saturated with these topics because it is designed to prepare students for calculus, a topic that the vast majority of students will never use once as long as they live. High school math courses serve to traumatize far more students than they inspire. As a high school student I learned to detest math because the instruction was so consistently tedious and punitive, to the point that I actually failed Algebra II and had to re-take it, only to pass with a D by convincing the professor that I was already a lost cause.
As soon as I left high school my natural scientific curiosity brought me to lament my horrible performance in mathematics, since I realized that it was actually the most useful topic of all. Now I'm a year away from my B.S. in applied math with 50/50 A's and B's. I'm still not a great student, and while I have learned to love the subject I know that some of those B's would have been A's if my four years of high school math hadn't been so damned esoteric. I ended up learning all the algebra I was supposed to learn in high school in my freshman Calc I course, and it was comparatively a breeze because it had the exciting context of applications in calculus.

What in the world does this giant "less than" symbol mean? my e&m professor uses it on the chalkboard all the time... I want my stupidity to remain a secret as long as possible so I'm asking here, nicely. Call me a fool but you can't tell me anything about myself that I don't already know.

√(x)=±(x)
〖x〗^2=〖(-x)〗^2
∴x=(-x)???

How on earth does this work? 1 != -1 obviously but according to the relatively low level maths I am basing this on it does. Does anyone care to explain this to me.