Guidance and resources For a PhD hopeful.

[Gil]

There are books that talk about what its like to be a Chef or a Scientist, etc, but we haven't found any that talk about being a graduate student.

However, I have a kid who thinks that he might like to obtain a PhD, but we haven't found any resources for kids re: college/graduate programs. Surely there is something out there, but I can't find it. I'm thinking there has to be a book, probably aimed at teens, that explains about post-secondary life. I'm hoping that there is a book that kind of lays out what all the (standard) post-secondary options are. Can anyone point me in the right direction?

So far, he's sent off for brochures from various universities with graduate schools, has written to a graduate academic advisor (no response), has searched for a book via Google/Amazon and our local librarians (no luck) and he hopes to have an opportunity to ask questions at a thesis defense this year or next. Since I try and take them to a few public thesis defenses each year, we expect to attend a few this year.

Currently, Pal is interested in what it would be like to earn a PhD in Pure Mathematics, but I'd like to help him consider the idea of doing a PhD in any field.

Ideas?

[4KookieKids]

I have a PhD in pure mathematics and I'm always happy to answer anything I can, but I have never heard of a book about what grad school is like. In particular, the grad schools I visited before deciding where to attend were SO vastly different in their expectations of students (much more so than undergrad programs), that I'm not sure how helpful a book would be. It was eye opening to visit prospective schools and go out to eat with grad students and just listen as they talked - you could tell a lot about the departmental culture based on a single meal. :)  I finished grad school in 2010, so I may quickly be becoming dated, though! lol.

[Gil]

He's looked at websites for several math PhD programs and they seem to describe having 8 upper-division math courses as the required foundation for beginning a PhD in mathematics: Does that sound about right to you?

Quote

... 2 full years of lower-division work (covering calculus, linear algebra, differential equations, and multivariable calculus)... followed by 8 courses including real analysis, complex analysis, abstract algebra, and linear algebra. These courses may include some mathematically based courses offered by other departments...

 

He doesn't aspire to any particular school and has said he wants to just go to a "normal university", meaning he doesn't want to go to a Big Name school. He looked at the PhD programs at several of our state universities, but I expect/hope that this will change as he grows. 

Currently he has no particular branch/area of math he's interested in above all others. But as his teacher I can tell you that he has very strong interest in and talent for geometry, he did well in our home grown Intro to Real Analysis class despite having me as a teacher. He's done really well with pretty much every sub-topic of algebra and calculus that touches on geometry or graphs. He has really enjoyed chapters/lessons on graph theory in the past.

Even though I'm not a mathematician, and being his father I'm obviously biased, I really do consider him to have fantastic intuition for some things in math. But mostly his interests for undergrad are leaning very heavily toward a BS degree that is drawing or video-game focused. But because he would like to have the option to pursue a PhD in mathematics, he's open to taking math classes beyond his major requirements to that end.

When I asked him what he hopes to get out of a college degree/experience, he said that he wants to "seriously play with all the subjects that I love" and to "get even better at them".

 

[Frances]

Once he is in high school, he might be able to do research at a university. Then he would be able to talk to grad students and professors about their different experiences. There are also online forums for those applying and those in grad school, but I’m not sure you’d want him reading them without you. And recent memoirs by individuals with PhDs might provide some insight. But ultimately, the experience is going to be so variable, even within a program 

the programs were similar in only the broadest ways. Some combination of coursework, research, teaching, exams, and writing a dissertation.

Edited March 4, 2019 by Frances

[8filltheheart]

Your quoted list is the basic core list of math courses for a BS in math. Every math major is more than likely going to have taken those courses regardless of where they attend for UG. He doesn't need to get so far ahead of himself. I agree with @4KookieKids. Different grad depts are going to have very different cultures. My ds went through the grad app process last yr and that was one of the things he noted.

UG is a great time for exploring options. Research will be necessary for grad school admissions and he can use different research projects to help him sort through what he wants to pursue. Math is a huge category, just like physics. My physics grad student did 2 different major research projects on his home campus and 2 REUS in different fields. Those research experiences and his additional courses helped him decide the filed he wanted to pursue. (His chosen field i s theoretical cosmology.)

You might find that as he gets older that he might shift gears, too. My ds thought he wanted to pursue math until he took physics in 8th grade. Physics never left his 1st place favorite after that, but he does have double UG degrees in math and physics.

[lewelma]

Something to consider given your kids' acceleration, is the ability to take courses without formal prereqs.  My ds is taking the 4th class in the sequence of combinatorics this term, with only his homeschooling/self-study as the 3 prereq courses.  If he had to take all three of those classes first, he would be bored out of his mind. My impression (though I'm sure that this is university dependent) is that larger universities are more strict on formal prereqs. 

Also, big time generalizing here (and I'm sure 8 can clarify), big name schools have more financial aid money. And given your kids' academic level and my impression of your financial means, your kids could get a full ride to "Big Name" universities to study maths. So those schools could be cheaper than a "normal university." However, when we were looking at universities, the math departments were very very different when it came to mentoring, which I think is a huge piece of the puzzle when picking where you want to go. For example, even though U of M, Ann Arbor is very large, they have a very good mentoring culture in the math department. 

 

[regentrude]

I am not entirely clear on what you hope to find in the book you are looking for. Graduate programs vary widely. Does he have any specific questions? Part of grad school is like undergrad- just fewer, but harder, classes and more freedom. The other part is research and either RA or TA work. But how exactly that will look like depends on the department and advisor.

[4KookieKids]

Yes, those basics you mentioned are pretty foundational to most undergrad degrees, though not all are four year long classes. Depending on where you go to grad school, though, many expect more (and not just big name schools). Some schools are more willing to work with students from lower end UG programs, so long as they show potential (e.g., excellent GRE subject scores and fabulous recommendations can sometimes off-set having had only a semester of abstract algebra and a semester of linear algebra, for example). I found that GRE subject test  and Putnam scores were more of a "thing" than I expected them to be when applying to grad school. I guess I didn't expect them to carry the weight that they did.

I went to a relatively small UG school, and the teachers bent over backwards to help me get into the classes I wanted in to. So after I did a year of UG algebra, they let me take the grad level algebra course there. But it was a small enough school, that their grad level algebra course was only slightly more extensive than the UG algebra course at the grad school I ended up at. So I came out with an impressive looking resume, especially since I graduated in three years, but it wasn't nearly as impressive as it looked! lol. 

As for money -- you just have to make it through UG, and (at least where I live) state schools have very generous financial aid / merit scholarships (some of the more generous in the country, I think, since an ACT of 32 gets you completely free tuition, I think?). But, I think the rule of thumb with math is that grad school shouldn't cost you money: most offer you a "standard" package where you teach a course or two each semester in exchange for them covering all tuition, health insurance, and a monthly stipend. Here's where some grad school culture comes in again: I have a friend who went to school in Cali where the stipend was barely enough to cover renting a room with 8 other guys in a house, and he was pumped about it. Where I ended up going, the stipend was enough to live comfortably in a nice 2 BR apartment with just one other roommate (and a number of my classmates had their own apt without a roommate). 

With his interest in geometry, I wonder if he's ever pursued algebraic geometry and/or algebraic topology? He's need to have a good foundation in algebra first (the kind commonly called modern or abstract), but there are some really cool topic there that have pretty cool applications that young folks might like (like algebraic curves being used as a public key system in cryptography that is an alternative to the ubiquitous RSA system). 

Also, DEFINITELY don't underestimate getting him involved in research young! There are some pretty awesome research programs out there, even for undergrads just getting started (e.g.,  the Director's summer program at the NSA), and I feel like THE biggest thing that grad schools want to see is that students understand what research actually is and are interested in doing it. I don't know how the age thing would work with summer programs, but I definitely think a local UG dept would be able to work with you on coming up with a research plan and mentor, even if he's not an UG student, yet.

Edited January 28, 2019 by 4KookieKids

[8filltheheart]

My ds did research under 18. The U was ok with on-campus circumstances but denied him access to travel to Kitt Peak (where his research mentor was traveling for a major part of his research.)

FWIW,  my ds is at a "big name school" (Berkeley is considered one of the top schools for the field he is pursuing) and he is receiving enough of a stipend that he is living in a nice 2 bedroom apt with 1 roommate. He TA'd last semester. This semester he is head GSI (managing the TAs.) I think he said the TAing roles are for the 1st 2 yrs and 3rd yrs+ are RAs. His stipend covers full health, tuition, plus living stipend. 

 

[4KookieKids]

7 hours ago, square_25 said:

 

I was a contest kid, so I'll note that I'm biased ;-). 

 

I was not a contest kid, so hopefully we can present a well-rounded picture. 🙂 
Seriously, though - my transcripts were rarely requested if I happened to mention my putnam ranking. I did a total of two putnams and that was my *only* experience with any sort of math contest.

[Gil]

Thanks everyone!

re: Research
I'm working on getting The Boys in touch with mentors. Sadly we are reaching the limits of the education that I can provide them working solo. Even though it pains me to change, since I'm young and set in my ways, we're changing things around significantly.

On ‎1‎/‎27‎/‎2019 at 8:13 PM, regentrude said:

I am not entirely clear on what you hope to find in the book you are looking for. Graduate programs vary widely. Does he have any specific questions? Part of grad school is like undergrad- just fewer, but harder, classes and more freedom. The other part is research and either RA or TA work. But how exactly that will look like depends on the department and advisor.

A lot of the commentary online about grad school and especially a phD can be self-depreciating or negative. There are tons of blogs, forums, instances of people stating how miserable life is for grad students or how unending graduate studies are. Or how it's so difficult to be married/a parent and a grad school student. Or how it ruins you financially, etc. Since he's curious about graduate school, that's not the sort of stuff that I what I want him reading/hearing while he's exploring it out of genuine personal interest. If he decides against graduate school, I want it to be based on what he thinks he wants or doesn't want.

He's mostly just really curious about graduate school. He doesn't know what being a student in a graduate program would entail, or what graduate school is like. We some times go to public thesis defenses and most of them have been extremely technical, over his head and pretty boring but a couple of them were really cool, but since the audience has to leave after the public part, we don't get to ask questions.

So "graduate programs vary widely" is super true, it is unsatisfactory for his curiosity. I found an article on Noodle.com that lists books that might be leaning in the right direction for general information, though they aren't targeted to youth. I will probably order a couple of them so they will be on hand for inspiration, guidance, reference etc, if and when he wants it.

re: Prereqs for a phD
I know that he is going to grow and change and mature, yada yada yada, so I'm counting on it working itself out with time, but currently he has interests in a few different fields and pursuing a lot of math at the UG level is a low priority, currently. But he's talked about becoming a math professor  since he was 6ish, and his longest-standing dream is to be a college math professor. That's still his current dream, so I would like him to be aware of the reality of the matter so that he can make informed decisions in his future.

re: Contests.
Pal usually does exceptionally well in math contests but isn't passionate about them. His brother is the competitor interested in competitions for the sake of competing (and winning). The social aspect of these competitions have been very hit or miss.

[regentrude]

8 hours ago, Gil said:

He's mostly just really curious about graduate school. He doesn't know what being a student in a graduate program would entail, or what graduate school is like. We some times go to public thesis defenses and most of them have been extremely technical, over his head and pretty boring but a couple of them were really cool, but since the audience has to leave after the public part, we don't get to ask questions.

Does he know what being an undergraduate entails? 'cause it's not that much different - harder, fewer classes, more freedom, plus research.

[4KookieKids]

12 hours ago, Gil said:

 

A lot of the commentary online about grad school and especially a phD can be self-depreciating or negative. There are tons of blogs, forums, instances of people stating how miserable life is for grad students or how unending graduate studies are. Or how it's so difficult to be married/a parent and a grad school student. Or how it ruins you financially, etc. Since he's curious about graduate school, that's not the sort of stuff that I what I want him reading/hearing while he's exploring it out of genuine personal interest. If he decides against graduate school, I want it to be based on what he thinks he wants or doesn't want.

Unfortunately, talking with some grad schools and grad students it the same. I visited grad schools where the grad culture really was, "Well, life stinks, we're dirt poor, we work a ton, faculty don't value us, I'm not publishing as fast as anyone wants me to be, but - that's grad school, right? At least we're old enough to go out drinking now to temporarily forget how much my life stinks." (followed by feeble chuckles.) Needless to say, I did not pursue those programs. 

So make sure whatever mentors you find don't have those same feelings or expectations! 🙂 You want him being assured that grad school is really great! Super fun to work on hard math with others who *also* find it fun! Research is super fun because who doesn't like coming up with new math that no one has ever figured out?! You get to do math for ALL your classes and don't have to take dumb gen-ed's (though you may still have to take math classes that aren't your favorite, of course...)! And you get paid to do it, to boot. 🙂 Grad school really is great!

[quark]

Hi Gil,

I have not read all the responses yet so this might be repetitive. Here's a book that we explored a while back when kiddo was still considering options:

How to Study as a Mathematics Major - https://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316

I also really like this section from the Princeton Companion to Mathematics (an oh-so-drool-worthy compendium for aspiring mathematicians):

Advice to a Young Mathematician - http://assets.press.princeton.edu/chapters/gowers/gowers_VIII_6.pdf

I also suggest looking for advice on Quora and Math Stack Exchange.

 

PS: I realize these are not math graduate student resources, but I think first understanding what it is like to create/study math for a living (or living to create/study math, as my kiddo would say) might be a good approach.

PPS: Kiddo is not yet in grad school but is taking grad math classes and says the following (true at least at Berkeley):

• Classes are more challenging than undergrad level.
• Homework seems to be less important.
• Exams are usually take home. Which is not really helpful as the problem sets are extremely challenging.
• You may get taught by even cooler profs vs undergrad classes (one of kiddo's profs is a Fields medalist).
• Some of these grad level profs may not love teaching though (which is the same for undergrad) - their true passion being research.

 

Edited January 31, 2019 by quark

[Xahm]

I don't know if this is any help, but my cousin dropped out of a math PhD program. She liked the classes and loved the undergrad teaching she did, but as she advanced in the program, her advisor wanted her to do less teaching and more research. She hated the research end of things, or at least she hated her advisor's project that she was required to work on. She now works developing curriculum and tutoring, which she's happy with, but I think she wishes she'd known more of what to look for going in ask that she had found a better fit. I hope you are able to help your child get a few mental pictures of what it could be like so that he can search out the one he really wants.

[8filltheheart]

7 hours ago, xahm said:

I don't know if this is any help, but my cousin dropped out of a math PhD program. She liked the classes and loved the undergrad teaching she did, but as she advanced in the program, her advisor wanted her to do less teaching and more research. She hated the research end of things, or at least she hated her advisor's project that she was required to work on. She now works developing curriculum and tutoring, which she's happy with, but I think she wishes she'd known more of what to look for going in ask that she had found a better fit. I hope you are able to help your child get a few mental pictures of what it could be like so that he can search out the one he really wants.

Choosing your grad program around your research objectives and possible future mentor should be a student's goal. Spending their UG yrs doing research is vital for more than just grad admissions.  It is vital for the student to narrow down such broad fields into the focus they want to pursue long term.  For example, our ds started off doing graphene research in high school.  His first UG project  was radon research.  Then he moved onto neutrino and muon research.  (He did that on campus until he graduated.) But during the summers he pursued different fields.  I'm trying to remember what his REUs were.  I think one had something to do with nuclear physics.  I can't remember the other one.  But, the point being that between his courses and his various research projects as an UG, he was able to decide what fields he liked and what he didn't.  He decided early on that he did not want to do anything with material physics (which is a huge field in physics careers in industry.)  His interest always stayed with theory and cosmology.

I can't fathom pursuing grad school without an interest in research.  Ds spent about 18 hrs per week on research starting his freshman yr.  Considering how many yrs he says it is going to take to complete his grad and post-doc degrees, I am glad he knows he loves it. 

[Gil]

@regentrude Lol, I know right. He does have a pretty decent idea about undergraduate and that's pretty much the first thing I told him and it's about all that I could tell him, but that's not at all satisfying to him. *shrug*. 

@4KookieKids Definitely. If he's going to meet someone, the point is for it to be a person who thinks and speaks of doctoral level work, and the grad-culture and experiences positively.

@quark Thanks for the book and double thanks for the essays! We printed the article for him and it's already highlighted and getting dogeared. 🙂 And he's switched his memorizing assignment to Sir Michael Atiyahs essay.

@xahm Thank you because that does help. It's something to keep in mind. 

@8FillTheHeart Thanks chiming in. What are REUS? Given that research is such an important part of a doctoral degree, then what happens if you gain a new interest, or lose your interest in your original focus and want to change your area?

I've never been to grad school and only considered going for practical/job-related reasons. The program that I'm looking at is 100% online so will not provide any of the insightful experiences that a traditional on-campus program would. I'm considering a MS for economic/career reasons only. Frankly, I would never pursue a degree for "love of" a field, but I don't want them restrained by my limitations. 

I want him (and his brother) to be informed enough and confident and capable enough to build their own dreams and form their own decisions and make their own choices, even if it means taking actions that no one else has and doing stuff that people mock or discourage them from. They'll get a different result, by doing different things, living out different life choices than those who came before them and who are around them.

[8filltheheart]

REUs are Research Experiences for Undergraduates.  https://www.maa.org/programs-and-communities/member-communities/students/undergraduate-research/research-experiences-for-undergraduates

[4KookieKids]

34 minutes ago, 8FillTheHeart said:

REUs are Research Experiences for Undergraduates.  https://www.maa.org/programs-and-communities/member-communities/students/undergraduate-research/research-experiences-for-undergraduates

 

Yes and REU's are really great for figuring out what field you actually find interesting in terms of research. For example, my favorite classes were modern algebra classes in undergrad and grad school. Hands down, they were my favorite classes! But it turns out that I didn't really like the research in that field because it was so far removed from what I actually learned about in my classes. The nice thing about an REU is that they don't expect much specialized knowledge coming in; they teach you everything they want you to know at the beginning, and then they teach you *how* to learn the other stuff that crops up that you also need to learn. So it's really self-contained, in a sense. You can often get one or more publishable papers out of it, as well, which grad schools absolutely *love.* 

[Frances]

On 2/3/2019 at 10:30 AM, Gil said:

@regentrude Lol, I know right. He does have a pretty decent idea about undergraduate and that's pretty much the first thing I told him and it's about all that I could tell him, but that's not at all satisfying to him. *shrug*. 

@4KookieKids Definitely. If he's going to meet someone, the point is for it to be a person who thinks and speaks of doctoral level work, and the grad-culture and experiences positively.

@quark Thanks for the book and double thanks for the essays! We printed the article for him and it's already highlighted and getting dogeared. 🙂 And he's switched his memorizing assignment to Sir Michael Atiyahs essay.

@xahm Thank you because that does help. It's something to keep in mind. 

@8FillTheHeart Thanks chiming in. What are REUS? Given that research is such an important part of a doctoral degree, then what happens if you gain a new interest, or lose your interest in your original focus and want to change your area?

I've never been to grad school and only considered going for practical/job-related reasons. The program that I'm looking at is 100% online so will not provide any of the insightful experiences that a traditional on-campus program would. I'm considering a MS for economic/career reasons only. Frankly, I would never pursue a degree for "love of" a field, but I don't want them restrained by my limitations. 

I want him (and his brother) to be informed enough and confident and capable enough to build their own dreams and form their own decisions and make their own choices, even if it means taking actions that no one else has and doing stuff that people mock or discourage them from. They'll get a different result, by doing different things, living out different life choices than those who came before them and who are around them.

My husband and I both did grad work and have many friends and colleagues who also did. In my experience, those that enjoyed it the most were doing it for love of the field and not for specific career goals. Most people I know did not really enjoy their doctoral programs, but at least they were free and they got paid and gained some useful skills, knowledge, and experiences.

[Bristayl]

You know what I love about this board? Not once has anyone said, "Oh, he's too young to be thinking about a PhD."

[daijobu]

On 1/29/2019 at 9:19 PM, Gil said:

A lot of the commentary online about grad school and especially a phD can be self-depreciating or negative. There are tons of blogs, forums, instances of people stating how miserable life is for grad students or how unending graduate studies are. Or how it's so difficult to be married/a parent and a grad school student. Or how it ruins you financially, etc. Since he's curious about graduate school, that's not the sort of stuff that I what I want him reading/hearing while he's exploring it out of genuine personal interest. If he decides against graduate school, I want it to be based on what he thinks he wants or doesn't want.

 

 

Wow, that hasn't been our experience at all.  My DH got his PhD in CS, in machine learning specifically, back before ML was cool, in the 90s.  For awhile his thesis was the most cited paper in machine learning because the field was so young.  Because it was CS, he could do a lot of his work from our apartment, and it was fun for him.  He got to travel to conferences, and met many, many people who went on to become very rich and famous.  Like top executives at companies you've heard of.  I'll read about someone in his field in the WSJ, and guaranteed he will know him/her personally.  He made a fair amount of money from teaching classes and working at companies in the summer.  Back before the internet was widespread he was paid a premium for classes that were broadcast via closed circuit TV to nearby companies.  

So not miserable (if you enjoy the work), not financially ruinous (remember: you get paid to go to grad school, plus you make valuable contacts at conferences), not unending (only 4 years for dh), but actually really quite awesome career trajectory for him.  Tell your students to go for it.  

[kiana]

Personally, if I were aiming for a PhD in pure mathematics (which is what I ended up doing) from early on, I would go to a good undergrad school for math (it doesn't have to be top-line, but not some random state college, which is where I went -- it should probably have a graduate program) where I could take all kinds of upper-division electives and enroll early in graduate courses, and instead of applying for credit and accelerating graduation, get them to let me skip classes I'd learned through self-study and substitute graduate classes or advanced electives in the same area. For example, if I had already learned undergraduate abstract algebra, it would be perfectly reasonable for a college to let me skip it and take the graduate sequence instead. This would show up on a transcript just fine, and even if another graduate school did not transfer it in as equal to theirs, it would DEFINITELY satisfy requirements for admission. 

That being said, research was very different from the parts of math that I really loved. I loved solving problems that could be done in a day or two, but not working on the same problem for months. I think it might have been different if I had had my ADHD treated much younger, but I just got bored working on the same thing. However, I'm just getting back into a bit of research now (after starting treatment), and well, we'll see. 

Does he know what being a math professor is like? He should really look into seeing if he can job shadow a few. 

[Lawyer&Mom]

I did my undergrad at Berkeley, and one of the (few) perks of being taught mainly by graduate student instructors is you get to see/know *a lot* of graduate students, and observe them in the wild as it were.  (They are everywhere at a big research institution!)  Do you have any opportunities to interact with current graduate students?  It might inspire him.  I regret that even though I ended up doing lots of grad school, I didn’t have grad school on the horizon when I was in undergrad. (I didn’t know it would be an option for me academically/financially). I think it’s great he is thinking about it already, and you are so supportive. (Already going to PhD presentations!?!  Excellent.)

[Bristayl]

I haven't read this myself but it was recommended on another forum: 

Road Map for Graduate Study: A Guide for Prospective Graduate Students 2nd Edition

by Don Martin 

[daijobu]

I was thinking of this thread the other day when DH was showing me the Facebook feed of a friend who earned his PhD in CS along with DH.  It was unintentionally hilarious.  

After earning his PhD, he went on to found 2 companies.  His third company creates synthetic diamonds.  And apparently, when you are CEO of a synthetic diamond company, you spend a lot of time with supermodels and rappers.  (Presumably because you hand carry your wares when you are loaning them to a Kardashian or similar.)  

So I suppose you can tell your student if he or she wants to hang with supermodels, rappers or Kardashians, then getting a PhD in CS is the way to do it.