NOTE: I will not accept an answer because a lot of answers are really good and if anyone want to post under this question later then they are most welcome to post as comment or answer because it will certainly help many people. Thanks to all that contributed.
I have completed my master's in mathematics a couple of years ago and due to very strong personal and professional reasons I couldn't get admitted to grad school despite having a good academic background.
To some extent, research questions are really research themes, and these can definitely be found in journals. Just open a journal (e.g. Algebra and Number Theory) and read an article or review. Sometimes picked at random it can be interesting to read to the end, and you're left with many ideas for new developments, and often direct open questions stated at the end of the paper.
Attacking the "open problems" (as they are called) in number theory (e.g. Riemann etc) straight away may not be fruitful as they can be very difficult if attacked directly from first principles, though this is tenacious and can teach you a lot about the problem. Though to some extent almost no one is just attacking them. Even Wiles was working on something else when he realized he could therein work to prove Fermat's final theorem as a consequence of what he'd seen. He was working on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory, which had surrounding workers publishing about it (from what I understand).
But there are plenty of research themes in number theory (and otherwise) which are currently being worked on (e.g. probabilistic number theory, etc), and I suppose one would look at research articles in journals of number theory to see what those are. What are other students in number theory working on? What did they publish? Even take a recent PhD thesis of interest and ask "what can be done to develop these results", or "why are these results not interesting"?
Knowing all the research themes is quite difficult, but one learns about them in conferences etc, sometimes presented by experts, but more often presented by PhD students just learning the ropes of the area, each are useful to listen to. Each is a window into a research area one could pick up and get into, like an investment or stock, which hopefully pays off in the long run.
Go to a good math library, pick up a few books (perhaps even randomly) in number theory and start reading them until you find one book which you really like. I am (almost) sure that you will ask yourself plenty of questions when studying deeply some interesting mathematics. At the beginning, many of these questions are already solved (and perhaps not hard) but questions help advancing. At some point, some of your questions will have no known answer. With some luck, one of these questions is interesting and solvable. (Books can of course be replaced by attendance of lectures, discussions with collegues etc.)
How do I limit the number of levels that the tree command goes through in Windows? I need to output the results to a text file for work, but because by default the tree command lists every single directory under the one you ran the command in, the output I'm getting is over 44,000 lines long, which isn't helpful at all for my work. How do I restrict it to listing just the first couple levels?
Timing: On average, you should allow approximately 90 seconds for each multiple choice question. You may need more or less time, depending on the question and how well you understand the topic.
The best way to study for the CFA Level I Exam is to follow the CFA program curriculum and give yourself enough time to learn the material in your ideal learning style. Here are some resources candidates have listed as being most helpful for their exam preparation:
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This phrase refers to the Census Bureau poverty thresholds, although it is included in the legislative section of the 1981 Omnibus Budget Reconciliation Act (OBRA) that requires the Secretary of Health and Human Services to update the poverty guidelines annually. The thresholds are mentioned in this legislative section because they are the starting point from which the poverty guidelines are calculated. (The legislative section is section 673(2) of OBRA-1981 or of the Community Services Block Grant Act; the U.S. Code citation is 42 U.S.C. 9902(2) .)
Since 2006, the poverty guidelines have been published in late January (except for 2010). The Federal Registration notices published since 1982 may be viewed by visiting the Prior HHS Poverty Guidelines and Federal Register References page.
The only way to get an official update of a chart showing percentage multiples of the poverty guidelines is to contact the organization or office that prepared it. While ASPE calculates the poverty guidelines each year, ASPE does not calculate or prepare any official charts showing percentage multiples of the poverty guidelines even though such charts may indicate the HHS poverty guidelines as the source. However, ASPE provides a spreadsheet tool to assist organizations in creating these charts. Be aware, however, that the rounding rules for these calculations, as well as procedures for calculating monthly income, are determined by the federal, state, and local program offices that use the poverty guidelines for eligibility purposes. Therefore, the numbers in these spreadsheets could differ somewhat from what is used by other federal, state, or other organizations.
Chart showing different multiples of the poverty guidelines for 2024 (XLSX)
Chart showing different multiples of the poverty guidelines for 2024 (PDF)
Chart showing different multiples of the poverty guidelines for prior years (XLSX)
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The only way to get an update of a sliding fee scale is to contact the organization or office that prepared it. While ASPE calculates the poverty guidelines each year, ASPE does not calculate or prepare any sliding fee scales even though such scales may indicate the HHS poverty guidelines as the source.
The HHS poverty guidelines, or percentage multiples of them (such as 125 percent, 150 percent, or 185 percent), are used as an eligibility criterion by a number of federal programs, including those listed below. For examples of major means-tested programs that do not use the poverty guidelines, see the end of this response.
Some state and local governments have chosen to use the federal poverty guidelines in some of their own programs and activities. Examples include financial guidelines for child support enforcement and determination of legal indigence for court purposes. Some private companies (such as utilities, telephone companies, and pharmaceutical companies) and some charitable agencies also use the guidelines in setting eligibility for their services to low-income persons.
There is no simple answer to these questions. When determining program eligibility, some agencies compare before-tax income to the poverty guidelines, while other agencies compare after-tax income. Likewise, eligibility can be dependent on gross income, net income, or some other measure of income. Federal, state, and local program offices that use the poverty guidelines for eligibility purposes may define income in different ways. To find out the specific definition of income (before-tax, after-tax, etc.) used by a particular program or activity, one must consult the office or organization that administers that program.
No. ASPE does not project price changes for the current year; instead, we issue guidelines based on price changes through the most recent completed year. Accordingly, the 2024 poverty guidelines, issued in January 2024, reflect actual price changes through calendar year 2022
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Fatal/Critical: Overall application or system failure that should be investigated immediately. Yes, wake up the SysAdmin. Since we prefer our SysAdmins alert and well-rested, this severity should be used very infrequently. If it's happening daily and that's not a BFD, it has lost its meaning. Typically, a Fatal error only occurs once in the process lifetime, so if the log file is tied to the process, this is typically the last message in the log.
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