I am an Electrical Engineering undergrad at one of the better engineering schools in the US. Now I have some background I want to explain, and I'll try to keep it brief. Back during high school I was taking classes at a community college, and easily completed all of the requisite courses for transferring into a STEM program. The problem at the time was that I had no idea what I wanted to do. So I left academia and went on my own route for a good couple of years. I never thought I would look back.  Fast forward to the future. I am married and have three children. My wife and I decided that I should look into all those credits from community college. Fortunately, there is no 'expiration date' on lower division math courses, physics, etc. So I was able to transfer, and ended up where I am now.  When I got here, I was already (at least) 30. Having been in the work force and bringing up a family, I was used to pushing myself and getting things done. So it seemed natural that being in college was difficult. It was not the courses, however, that caused problems. For example, my first math course in 10 years was vector calculus, and I completely aced that course, receiving near perfect scores on the exams. Rather, the university is optimized for the student who is just barely in his 20's, the "traditional" student.   I am a "non-traditional" student, and have come up against institutional barriers. This makes sense, since there are tens of thousands of undergrads around here, but only a handful of them have dependents. But still, not fair. Without mincing words, some professors have said that when you have kids, your life is over. Obviously some of these professors never had kids. How to make people understand that when you start a family, life does not end!!! Also, the looks on the faces of those 20-year-olds when I tell them my age, and my situation. (Most people think I'm in my early 20's - I look young.)  My focus in Electrical Engineering for grad school would be in communications. I love math. I am a big fan of our pure math department, and although I am up against a unit limit, I have taken some first year graduate level courses in pure (not applied) math. I am also interested in RF/microwave circuits, in particular MEMS devices. I have research experience, letters of rec, and an okay GPA (3.5). I'm in a summer research program right now, doing MMIC work. I know how to code, I can use version control systems on group projects, and do everything in latex.  I would like some candid advice on whether or not I should apply to grad school. On the one hand, I believe that being a parent necessitates organization, focus, and communication (the latter, with the wife :-) ). These qualities, it seems, are a good fit for grad school. Having a partner can also be advantageous in that I won't have to go through it all alone, and I know that some grad students struggle with this. On the other hand, well, some might say that I should just go find a job and have my family.  My children are young now, and we have lived at housing for students with family. It has been a great environment for all of us. But I also feel like if after graduation I found a job, then they might not want to come back, after having lived in "the real world". I would also like to hear what other grad students have to say, whether or not you have children or a spouse/partner.  tl;dr I am in my mid thirties, finishing up an engineering degree, have wife and kids, want some advice on grad school yea or nay.
The essential gist of my question relates to what the real, unvarnished realities are of graduate, post-graduate, research, fellowship, and professorship attainment - when you aren't a single person with no pressing demands other than feeding yourself.   [EDIT: I am humbled by the incredibly helpful and thoughtful responses so far, all of which are +1 from me. I'll leave the question open a few more days before clicking 'accept' on any one, but you all have my gratitude and I hope others will benefit anywhere near as much as I have. ]  What I don't know is what succeeding in this path truly requires in time committment and family support.   Right now I can handle a 12-14 credit course schedule with 3.7-4.0 GPA (in the top 5-10% for college and program, dean's list, etc), work part-time, and still have time to be home and not have a burn-out/breakdown - and the academics are the easy part by far! I could do more, but I need to work more too.   What I really need to know is how sharply different is the time/dedication curve of graduate work and above. I realize each step is a filter that removes most of the entrants (most people don't get a degree, most who do don't attend/finish graduate school, most who do don't seek a PhD,  most who do don't seek/gain professorship...and on and on). But I don't know how severe the stepping is - I'm not talking "tenured professor at MIT or bust" - I realize that bar is many orders of magnitude higher.  Background Details: As an "adult, returning" undergraduate student with a (disabled) wife and kids, I'm halfway through a bachelor degree now. I've located a field of study (in a focus of Industrial Engineering) that has made me very interested in altering my life path to include seeking a Masters and maybe even a PhD/professorship (my father was a professor, so its not a purely novel concept to me). I've met and spoken with my advisor and 2 other professors with experience in related fields, and all is encouraging; I have a graduate school in mind, I've received lots of great advice on preparing for school (on this forum and in person), I test well (no GRE fears remain), good grades/class rank, good prospects for future strong referal letters, etc - a comparitively charmed existence for which I am very grateful! I just have to investigate whether I can make it through with an intact, cared for family!  Any guidance you could provide me, and other aspiring "non-traditional" students alike, would be appreciated immensely - thank you!
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For a given $0&lt;r&lt;1$ and $|z_1|,|z_2|\leq r$, $z_1\neq z_2$ then,   $$\left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|\leq \frac{1}{(1-r)^2}.$$  My attempt is: part a  of the question asks to prove $$\left|\sum_k^\infty a_nz^n\right|\leq \frac{ |z^k|}{1-|z|}.$$   So, \begin{eqnarray*}  \left|\frac{f(z_2)-f(z_1)}{z_2-z_1}\right|&amp;=&amp; \frac{|\sum_1^\infty a_nz_2^n-\sum_1^\infty a_nz_1^n|}{|z_2-z_1|}\\  &amp;\leq&amp; \frac{\frac{ |z_1 |}{1-|z_1|}+\frac{ |z _2|}{1-|z_2|}}{|z_2-z_1|}\\  &amp;\leq&amp;\frac{1}{(1-r)^2} \frac{   |z_2| ({1-|z_1|})+  |z _1| (1-|z_2|) }{|z_2-z_1|}\\ \end{eqnarray*} But could not prove that the last term is controlled by 1. How do you apply a QgsExpression to a Label ?   I can do it in QGIS with this simple expression  concat('N:' ,round(Value,0),'\n','Yield:' ,round(Value 2,0))  N: 65   Yield: 40  How do I do it in PyQGIS ? 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