Vene

It's been done. This has been known about for 100 years.
 

*bolded for emphasis*
 
It can actually be really hard to notice implicit bias when you're not the target of it. But, talk to most any woman and you'll hear plenty of stories.

Speaking in generalities here:
 
When a male student flirts with a female TA, he's doing it because he is attracted to her. She is an object of his desire. Emphasis on her being an object.
 
When a female student flirts with a male TA, it's because he's in a position of authority and she wants favor. It is not because she desires him, instead she is trying to use her body as currency.
 
There is a world of difference between these two events.

Yes to sleep. I made it a rule to get a good night's sleep during undergrad and to always get a full night's before an exam. I don't believe in all-nighters, I think they do more harm than good.

I know you're frustrated, but this is a tantrum. On paper, you're honestly a good candidate. On paper, you're actually a stronger candidate than I was. (3.5 GPA, BA from an open enrollment regional state university, 161V/161Q/3.5AW, 1 semester senior research project, 1 year as a formulation chemist, applied for 5 programs, got 2 interviews, 1 acceptance) Getting 6 interviews should be enough so that even by dumb luck you'll get an admit. Graduate programs aren't going to the expense to bringing you there to jerk you around. To put it bluntly, you fucked up. The simplest explanation is that during the interview process you said or did something that raised alarms. One post-interview rejection is bad luck, 6 is a pattern.

Your GPA is decent, not great, but high enough to get you past most cutoffs (don't listen to Fun_Cookie). You have good research experience, which will help a lot especially if you get strong LORs. I don't think anybody cares that you didn't stick with a single lab in undergrad, it's the best time to explore different fields to see what it is you want to do. You are looking at prestigious schools, which does mean you're going to face a bit of an uphill battle. If I was in your shoes, I'd hedge my bets and try for a few of the schools on your dream list as well as funded MS programs at lower tier universities because a good record during a MS does help. I would definitely talk to professors you did research under at the Ivy universities, assuming you are interested in the program and what they do.

So, aliens?

Even though there's been some feedback already, I'll add my two cents.
 
Interviews are as much them evaluating you as it is you evaluating them. A university wants the best students so they're going to be selective, but at the same time they want to attract those particular students to come to their school and not another one. You don't exactly want to slack off and assume you're going to get in, but you're certainly on the short list at this point.
 
I can add that your academic credentials do meet their standards, so you don't have to worry so much about them anymore. The goal is to connect with professors and grad students and convince them you are the type of person they'd like to spend the next few years around.
 
Oh, and good luck.

As someone who went straight through from undergrad to PhD I am a huge huge HUGE advocate of taking a few years to do something besides school. Even for students who really really want it and think they are 95% sure they want a PhD. But especially for a student who is ambivalent and really rates financial stability as being a top priority. Graduate school stipends do NOT confer financial stability. It looks that way from the outside, but there are all kinds of caveats. My first stipend was around $32,000 in New York, which sounds like it should be enough to live on, particularly since I was sharing an apartment with another graduate student. It was - just barely. Had I had some kind of crisis or emergency I would've been wiped out. I had friends who did not have summer support and had to run around to try to get that. There's conference travel for presenting, which often takes a bite out of your income (even if your department says they support students, it's often not enough to cover all the expenses for one trip. And often they reimburse you.) There are additional things you need to get that your stipend will have to stretch to cover.
And $32,000 is an extremely generous stipend for a graduate program. I know the anthropology stipends were less even at my same university, and they are quite a bit less at other universities in other locales - even expensive ones. (I think CUNY was paying out around $18,000.)
Let me put it this way...I spent 6 years in my PhD program. I don't regret it, and I have an awesome job (in industry) that I could've only gotten with a PhD in the field I finished in. But people still ask me 1) if it was worth it and 2) if I would do it all over again, and I still don't know how to answer either of those questions (my degree was conferred a year and two days ago). Nothing even particularly bad happened to me during my PhD program - I was funded all the way through at above-average levels, got a couple of papers published, lived in a great city, got married, had good friends...but it's just a really long slog to do particularly if you would be equally happy doing something that didn't require a PhD at all. I had no idea of the kinds of jobs I could do without a PhD; I had no idea that I could get involved with research-related jobs even with a master's degree, and very little actual idea of what a PhD-holding person who wasn't a professor actually did on a day-to-day basis (because I didn't want to go into academia).
So your professors are just trying to encourage you to explore a little bit before you spend 6-8 years earning a degree that you potentially don't need to do what you want: to see if there are any other jobs you really love, figure out all that life stuff that was referenced above and really make concrete decisions about career and research that are filtered through experience.
Also...be easier on those cousins of yours. Sometimes moving back home IS a smart choice. I feel like we're way too hard on our generation; there's no switch that flips at college graduation/age 21-22 that magically helps you find a job that can support you at levels high enough to pay rent everywhere and allow you to save. Being under 30 and broke isn't all that uncommon - and honestly, if you go to graduate school living on a grad stipend, you will probably be 24 and broke, too! I was! It takes time to start earning more money, put enough in savings to be a cushion and build your life up. That doesn't mean you'll be starving, though.
  

So eloquent.
http://www.everydayshouldbesaturday.com/2015/9/8/9249681/broke

Like I said, you need to be more specific. 
Both $64k and $120k can be perfectly accurate, depending on field and experience. 
The vast majority of professional chemists belong to ACS, and as I said, their salary/employment estimates usually jive pretty well with what the Bureau of Labor reports for this subsection of professionals. 
For people I know that went to work with BS degrees (getting a professional job with a Chem BA (non ACS certified) is very hard), $60k+ starting was what I saw (Low CoL South/Midwest), with a fairly quick salary rise after a few years of training. 
But someone doing analytical QA at a water testing center (for instance) is going to get paid a lot less than someone doing pharma QA in the northeast. 
An "average salary for a PhD Chemist" is about as useless of a number for someone entering the field as I can think of. Your work experience before and during the PhD will matter, as will your specific skill set, where you're applying, and what industry you're going into. 
Also, if you're using ACS sources, you should probably use the most up-to-date (2014) vs the older (2012). Trends are also more important than numbers. Even as the sample isn't perfect (hint: no sample is) the relative proportion is constant, and ACS data over time is very good for seeing salary trends. 
https://www.acs.org/content/dam/acsorg/careers/salaries/cen-salary-article.pdf is the 2014 report.
I also particularly like Chemjobber's blog, and he has a good breakdown of some salient points from the report (http://chemjobber.blogspot.com/2014/09/the-full-2014-acs-salary-survey-is-out.html). 
Response rate in 2014 was 23%, down from 35%in 2012. You can quibble with who is or isn't an ACS member, but a 35% response rate is damn good for any survey.

My husband, originally a math major, also "hated stats" the first time he took statistics and probability. He decided to give it another go and changed his major to stats after that. The major reason, according to him, is he loved the varied applications of statistics. He wasn't a huge fan of the sort of abstract nature of his math major before that; he really wanted to do more applied, practical work, and stats was the way for him.
However, there are many other areas of math that can be applied besides statistics. I think statistics is probably important for most applied mathematicians to know in some sense, but there are applied mathematicians that don't use much if any statistics on a regular basis.
Also, let's walk it back a bit. If you don't know what you want to do, why are you hoping to get a PhD in math? Math is a pretty abstract/theoretical field - there are more applied portions of it, of course, but the kind of math people study in graduate school generally isn't. Even in applied fields, a PhD is often not the degree you want if you really want to "do" something. My PhD is in public health - which sounds very applied, until I realized into the program that it mostly encourages doing research, and not the on-the-ground kind of public health work people think of when they think of public health. A PhD is a research degree; if you don't want a career as a researcher (or aren't sure that you do), then you shouldn't get a PhD in math. Most of what you want to do can probably be achieved with a BA or MA in math, applied math, statistics, or some related field.
Here are some applied areas you can enter:
Epidemiology (math + public health)
Biostatistics (statistics + health/medicine)
Bioinformatics (statistics/math + health/medicine/biomedical science + computer science)
Meteorology/atmospheric science (math + atmospheric science)
Quantitative psychology (math/statistics + psychology)
Mathematician position in the federal government (do a search for "mathematician" on USAJOBS)
Medical physics (more physics than math, but still)
Check out this website on careers in math.
Also, "making the world a better place" is a broadly interpreted statement and a lot of traditional jobs (including in big corporations in finance and accounting) involve work that makes the world a better place or at least some necessary function for humanity. For example, some finance jobs may involve helping to improve the economies of developing nations, or developing a microfinance program for low-income laborers, or providing support and financing to nonprofit organizations. Nonprofits, NGOs, governments, hospitals and clinics need people in their finance and accounting departments just like large corporations do. And pharmaceutical companies (where many biostatisticians work) create drugs that help millions; there are some non-profit pharmaceutical companies, and even many of the for-profit ones do pro bono work.
On the flip side, make sure that you avoid romanticizing nonprofit or helping professions kind of work, because a lot of it is very different from what you might expect. For example, in medicine, a lot of healthcare provision and research organizations these days are very large corporations, and their primary goal might be to make money. A lot of academic and nonprofit medical research is directed by the winds of NIH funding, which is competitive and makes the atmosphere different from what you might otherwise expect. Some non-profits are poorly run and their employees not well compensated for their work (and I don't mean "I can't buy a yacht" well-compensated; I mean "I'm struggling to pay my rent this month").

You include the transcript. Some of my credits were done at a community college and I absolutely was required to include those. In fact, my degree granting institution just listed it as generic "x credits at Y college" on the official transcript (I was given a copy that I opened upon graduating) so those grades may well be essential.

Patents absolutely count as research. They're less common for academics than journal articles, but they're still fantastic additions to an application.

Just as a follow up: I took the full time offer, and then waited to give 2 weeks notice. I was glad to have waited, since I've been able to build relationships with my coworkers and a good work rep, so when it came time to talk to my managers, they were very kind and supportive about the whole thing. The income wasn't a huge factor for me, but I have learned a lot in the past few months and ultimately, the experience was a good one.
 
Thanks for all the advice

I had to resurrect this board. This quote hasn't quite enraged me but certainly has motivated me to comment. Attitudes like this frequently put girls off weightlifting. My undergrad university was very sports focused as was top 2 in the country for most sports, and a Team GB training base, so we had a lot of pro athletes train in our gym. I'm a S&C coach, PT and am hoping to do my PhD in sports injury prevention and rehabilitation...and I'm female. I also have never competed as a weightlifter, but can hold my own in our gym. The first few times I went into the weights section, I went with the guy I was training. Yup. I was training this 6ft 250lb guy with olympic lifts, and showing him correct form  but the amount of guys there who made out like they had an issue with me was amazing. I told myself that they were just jealous I had good technique   I love the weights section, I deadlift double my bodyweight, bench my weight, squat my weight and a half and have encouraged all my friends who have shown an interest in the gym to accompany me and see that the guys who look, for the most part, are the ones with the problem!
 
With regards to the original theme of fitness - we put so much focus on what we should be doing with exercise these days. When we were kids, we'd run around, kick a ball, do cartwheels, play tag...all of this was exercise but it was PLAY. As adults, we lose this sense of fun and make exercise a chore. Find something you enjoy, go with friends, go by yourself, but most importantly - have fun! I frequently blast my music and have a dance around the kitchen. If I'm annoyed I'll run in circles in my garden if I can't get out on the road. If I've got a spare hour, I'll go for a swim. If my friends are here I'll go for a walk. Moving should be FUN, and should be something we look forward to, rather than "build into our schedule". If we can make playtime fit into the adult world (sex anyone?) we would be so much fitter as a nation. /end rant

To add to this, I think it's good to have a pitch for specialists (people who you're likely to cite in your papers), non-specialists with the same degree (people who would work in the same department as you or have the same job title, but don't work on your exact topic), and non-specialists who have minimal familiarity with the field (neighbors, HR, administration).
 
So, for my work, I think I'd want to be able to explain what I do quickly to somebody else working on thyroids, where I can ignore a lot of background information. I'd want to be able to explain it to another biologist, where I could assume that they know cell biology and biochemistry. And I'd want to be able to explain it to the HR rep that is sitting in for an interview, who likely has only the roughest idea of what a thyroid does.

To add to this, I think it's good to have a pitch for specialists (people who you're likely to cite in your papers), non-specialists with the same degree (people who would work in the same department as you or have the same job title, but don't work on your exact topic), and non-specialists who have minimal familiarity with the field (neighbors, HR, administration).
 
So, for my work, I think I'd want to be able to explain what I do quickly to somebody else working on thyroids, where I can ignore a lot of background information. I'd want to be able to explain it to another biologist, where I could assume that they know cell biology and biochemistry. And I'd want to be able to explain it to the HR rep that is sitting in for an interview, who likely has only the roughest idea of what a thyroid does.

Update: they offered me the job and it came with a tuition waiver and stipend 

Everyone seems to be quite competitive. However, it is hard to tell sometimes just looking on paper because research/personality fit is major component to consider (that's why many universities have interviews!).
For example, my PI gets a lot of requests from straight A students to volunteer in his lab. It looks great on paper, but then he finds out that they aren't fit to do research or coursework is so high a priority that they just quit. He's also told me that ~20 graduate applicants wanted to be in his lab this year, and I imagine some of them were much more competitive than I was. What set me apart is that I made a connection with the PI, volunteered in his lab for a summer, and showed him that I was very well suited to do research, even if I did not get straight A's or come from a prestigious university (I was from an unknown liberal arts school).
The point being, looking at the stats/numbers doesn't say much about your motivation to do research, how involved you were with the projects (were you doing data collection, literature searches, or were you leading your own projects?), and how your interests and goals match with a PI. You're more or less applying to join a lab, not necessarily towards a program (this doesn't necessarily apply to those doing rotations, though you will eventually choose a lab). Your LoRs and SoP will be the main venue for showing that you are competent and motivated to do research. If you haven't started writing a draft of your SoP, I would do it soon. I remember making many dramatic changes to my SoP before it was fit to submit to graduate schools.
Finally, I would suggest at least trying to make a connection with your top choice PI's. If you have a chance to have a phone or face-to-face conversation, that's even better.
 
So, there's my little speech on grad school applications. If anyone on this thread wants me to take a look at their SoP, shoot me a PM.    

Gram, your writing score is fine. It is the absolute least important aspect of your application and I'd be surprised if adcoms even so much as glance at it.

Why does being from a particular family make somebody qualified for anything? The applicant might be for some other reason, but that's not the same as saying your father did a postdoc here 10 years ago.

It's a nonsensical point, that's the problem. That a parent of mine when to same school has about as much relevance as when I last had a haircut.

Did I say that? I said that giving preference to legacies, over a more deserving student (and I dare you to tell me that doesn't happen) just perpetuates privilege. I'm saying that legacy status helps elevate students based on factors that have nothing to do with the student (which is true). If you can't get in on your own merits, and need legacy status to sneak in to a school, you are taking a spot from a student who deserves it more, and are, in fact, a bad person. (And that isn't even getting into the racial and economic disparities tied up in legacy issues).

The thing is, the AW section has nothing to do with scientific writing. It's useless for us. The value of the quantitative section makes sense as we should be able to do math. The value of the verbal section makes sense as it has many questions on logical reasoning.