Other Should I Become a Mathematician?

[MathematicalPhysicist]

mathwonk, Do you know anyone who actually owns all of the five intro to Differntial Geometry of spivak besides spivak, it's quite pricey, from the retailer publish or perish it costs about 180 dollars all of the five, I wish I had the money for that, it's something of around 2000 pages, so I guess it's the best guide for this discpline (you can't publish 2000 pages of rubish can you?!).

 

[mathwonk]

well i do not, but they are worth it. a single copy of any cruddy first year calc book costs 140 dollars now.

one of my students once received a free set from spivak while teaching in africa in the peace corps.

i am confident my colleague ted shifrin owns them, and they are in libraries. actually you remind me i should buy them.

i have owned volumes 1 and 2 for decades.

so i guess also i should read them again and try to master the curvature tensor.

 

[quasar987]

Why not start with volume 1&2? This should keep you occupied long enough.

 

[mathwonk]

i guess i know most of volume 1, so i just need volume two.

 

[torquerotates]

Would being a part time student give me a disadvantage in terms of gradschool admissions ?

 

[mathwonk]

not as a part time under grad, only letters, grades, and scores matter, but part time grad students are very rare.

 

[tronter]

I am going to teach an "informal" course in Probability Models so that I can learn it myself (this gives me motivation to learn it). This is my first time teaching a course (its still an informal one). How do you prepare when you teach a course? How do you know what problems to assign? Should you be able to solve all the problems? What happens if you get stuck? Do you prepare for your lectures a lot?

Thanks

 

[quasar987]

I always wondered about this too.

How much do professors prepare for their lectures? It is obvious some prepare very little or not at all, but others seem to come to class knowing exactly where they're going.

So what about you mathwonk? How long do you prepare for your courses and what do you do to prepare?

 

[symbolipoint]

I am going to teach an "informal" course in Probability Models so that I can learn it myself (this gives me motivation to learn it). This is my first time teaching a course (its still an informal one). How do you prepare when you teach a course? How do you know what problems to assign? Should you be able to solve all the problems? What happens if you get stuck? Do you prepare for your lectures a lot?

Thanks

Find out what is the content of the course, either from your institution or from your state's content standards. Your institution must have a course outline and a list of textbooks chosen. You choose the textbook from the approved list that you believe is best. Select the topics and their sequence to teach based on the content standards or based on the school's course outline. From this selection of topics and their sequences, decide each day exactly what you want the students to understand and what skills you want them to know to do. From these things you want them to know and do, create your weekly or daily lesson plans, and YES ---- solve seveal example problems BEFORE each class meeting. You must avoid becoming lost during instructional classtime.

 

[mathwonk]

i prepare as much as possible. more important perhaps is regular preparation each night before the class. one does not have to know everything, how to solve every problem, etc..

one only needs to convey what one has to offer. sometimes that is a desire to learn the material, or the ability to appreciate the material, or to enjoy it.

as a beginning teacher in calculus, i worked out every problem at the end of every section of thomas before class. then i began to find out that i did not need to work every problem to understand how to do all of them.

the point is to be mentally ready to motivate the class to learn, and to share something you know that they can learn from.

just never go in there not caring, always prepare something for them every night. care about them and give them something.

 

[mathwonk]

as one friend put it to me when i was trying to prepare a course: " you cannot accomplish your goal unless you have a goal, (for the class)". that time i set a goal i did not accomplish, to reach the concept of canonical class by the end of the first course in algebraic geometry. but the goal guided the class anyway, and i achieved it in the next semester.

another fine teacher and colleague repeated a few days ago the importance of knowing what you want to accomplish. He mentioned the error of John Saxon's approach (whom he largely respected). As my friend put it, "you want to teach them to solve problems, not just to solve THESE problems."

in my current intro to abstract algebra syllabus, I say something like the following: "the goal of this course is to move beyond treating mathematics just as computation, and begin to view mathematics as reasoning."

each day in there i try to make a single point, such as the importance of the the root factor theorem, the theorem that says that if k is a subfield of E, and c is an element of E, the only polynomials over k which have c as a root, are those having the minimal polynomial of c over k as a factor.

the overall goal of this course technically is to teach the uses of the euclidean algorithm, which turns out to be one of the key ideas and methods in all of basic algebra, including linear algebra.

i.e. euclidean rings are principal ideal rings, and have unique factorization, this lest one use Gauss integers to solve fermat's problem on sums of two squares, all finitely generated modules over them decompose into sums of cyclic modules, hence they help understand the structure a single linear transformation imposes on a vector space via rational and jordan form, etc.. etc

 

[mathwonk]

this week I am presenting triple integrals in polar, cylindrical and spherical coordinates, and I have to prepare a lot for them.

one thing i do is try to make the picture clear in the students minds eye, of what is happening geometrically, i.e. a square or cube is being mapped by a non linear map, onto a circle, cylinder or sphere.

'i try to make the basic picture clear so they can recapture it even after forgetting the specific formulas for the transformation.

then i try to motivate them to learn this tedious stuff, by saying how it makes their work easier in certain problems. I always try to point out that a certain math tool is designed to make some job easier, so they begin to want to learn it.

i.e. integration is easier over squares than over circles, so polar coordinates unwind circular discs so they become squares.

i give a mental image of spherical coordinates using the image of a telescope in an observatory so they can remember the three coordinates. picture the slot in the roof of th observatory, and rotate it aroundn until it points toward the star you want to see. that's theta. then let the vertical telescope rotate down until it has the correct angle from the vertical, that's phi. then focus it out to the correct distance for the star, that's rho.

of course after many years i have a collection of these little insights. still young people often have better ideas than older people to make these concepts seem real.

one of my most cherished positive comments on a recent class evaluation was "math just seems more alive after dr smiths class."

still maybe a lot of people in that class did not appreciate it, and cared more about the grade they got, but i take solace in that comment.

but the last part anyone can prepare, which is to make the calculations in advance of the examples that illustrate the theory.

one thing somewhat frustrating is that it seems that just as one starts to get competent at this game, it is time to retire. if teaching well is your goal and main focus, you might want to avoid a big university and try to find a small high class college where that is valued more than striving for grant dollars, if such places exist.

this forum is such a place in some sense, in that many regular contributors are apparently amateurs who work in related fields, but are not all professional research scientists. (but you can't earn a living here.)

 

[mathwonk]

grading is another aspect of teaching that is very tiresome but useful.. i have spent over 9 hours today mostly at my desk, writing a test, taking it to be sure all questions are correct and doable, then grading another test given monday, finding out how terrible (almost) everyone did, rethinking how to represent this material, and how to try to give people a chance to pass the course.

it is not encouraging that some people who are failing never come for help, even sit reading a newspaper when I try to begin the lecture, not even realizing how rude this is, and that it is symptomatic of an uncommitted student, ... but this is the reality of teaching in an average state school. these are the students i have, and i need to do something if possible to motivate them, but it is challenging.

 

[yhp266]

Does anyone have advice on how to read textbooks. My university offers good courses, but not enough of them.

I seem to learn much better with a lecturer talking at me, rather than reading through text.

 

[yhp266]

it is not encouraging that some people who are failing never come for help, even sit reading a newspaper when I try to begin the lecture

There's always some annoying people especially in lectures with bigger groups >150. I think worse though, are the people who talk during lectures, and actually make it hard for others to learn. It seems to get better in 2nd year, where classes are smaller..

 

[DeadWolfe]

I read newspapers in lectures all the time, but I certainly don't fail those classes...

 

[torquerotates]

But if do that, why attend lecture?

 

[DeadWolfe]

It's fun.

 

[mathwonk]

actually my situation is likely just karma, as i myself was one of the worst possible student auditors, smoking cigars in the back of class under the "no smoking" sign, etc...

 

[rodigee]

Mathwonk, you appear to be algebraist so I pose you this question: How important is knowledge of probability theory (if at all) to the aspiring algebraist?

I'm an undergrad who hopes to study algebra in graduate school, and I ask this because my advisor is recommending I take a course next semester in probability theory. However, I'm not very interested in the subject, and it's offered at a terrible time so I'd rather pass on it in favor of something cooler such as more number theory. So what do you think? Is probability an important weapon in the algebraist arsenal?

Thanks for the thoughts.
-Rodigee

 

[symbolipoint]

Use an extension from Rodigee's question above: Notice that some college Mathematics programs do not list "Probability" or "Probability & Statistics" as part of their "common core" courses for Mathematics major-field students. Why do they not all do so?

 

[tgt]

I note that many keen maths students spend all weekend on their subjects as well as weekdays. However when they become paid academics, do they continue this hard labour? Or do they just fall back to rest of the work force which is work on weekdays only? What do you do?

I guess there is a difference between teaching and reasearch so maybe only teaching on weekdays but research on weekends if necessary (which offcourse it is if one wants to aim high)?

 

[mathwonk]

deadwolfe,
remember, it is your own time you are wasting. you could be learning something if you were paying attention.
i apologize for being so blunt.

probability has no value known to me in algebra, but is used in number theory.

 

[tgt]

Mathwwonk, surely you have an answer to my question in 1524? I just want to know what mathematicians get up to during the weekend.

 

[mathwonk]

to survive, i.e. get both my teaching and research done, I have had to work almost all waking hours for decades.

academics must work extremely hard for years and years. i realize now i have spent far too much time entering comments here on PF, since it has cost me time i should have spent doing research.

that is probably why matt grime is no longer here regularly.

mathematicians often begrudge any time at all they must spend away from their work. it is a struggle to have anything like a normal life with family or friends.

but we enjoy our work, many of us would be considered workaholics.

i am working now, but have gotten in the habit of looking on PF to get a brief respite, as the work i am doing at the moment is not fun research, but painful grading.

our days are completely filled with teaching preparing, grading, doing research, writing it up, applying for grants, giving and preparing talks, doing committee work, traveling,...

best wishes.

 

[mathwonk]

i think i told the story of the day when i arrived home from work about 4am, slept 45 minutes, then got up again and went back to the office.

 

[dsbyt]

I want to know more about getting a job outside of academia. My situation is I am working towards a (pure) math Phd. I love math and love doing research but I also could imagine myself not doing it. If I could get a 'normal' job with my Phd I would consider pursuing it. I did not think there were any real jobs for pure mathematicians though.

Do I need other qualifications? On typical job websites I don't see jobs for people with pure math Phds, and I imagine my BS in physics is even more limited. Where did those other people you talk about find those jobs? Did they find jobs coming straight out of grad school?

 

[mathwonk]

i recommend getting as much experience as possible in computers.

your pure math background gives you a big advantage at the reasoning and problem solving skill that helps you in this area and every area.

 

[tgt]

to survive, i.e. get both my teaching and research done, I have had to work almost all waking hours for decades.

I remember being so tired at the end of a day I could barely think straight, and still trying to force myself to stay up another hour to study.

I also recall thinking about my problems at night while supposedly asleep, to the point where if I felt energetic in the middle of the night i would wake up and get up and put my ideas down on paper.


academics must work extremely hard for years and years. i realize now i have spent far too much time entering comments here on PF, since it has cost me time i should have spent doing research.

that is probably why matt grime is no longer here regularly.

mathematicians often begrudge any time at all they must spend away from their work. it is a struggle to have anything like a normal life with family or friends.

but we enjoy our work, many of us would be considered workaholics.

i am working now, but have gotten in the habit of looking on PF to get a brief respite, as the work i am doing at the moment is not fun research, but painful grading.

our days are completely filled with teaching preparing, grading, doing research, writing it up, applying for grants, giving and preparing talks, doing committee work, traveling,...

i regret somewhat not being home a lot when my younger son was growing up, even to the point where he came home alone as a 9 year old to an empty house.

i think i have mentioned in the old days even working 20-30 hours in a row on weekends when a lot of work was pending.

Many many days I have left home at 8am and returned at 11pm.
best wishes.

Fascinating. Any normal job that recquires to work that much probably pays millions per year? That could be why they hate talking about pay so much as they know they are severely underpaid?

Do all professors work this hard? Does it apply to maths professors in every developed country?

You say academics work extremely hard for years and years. Does it mean the hard work will stop at some stage? If so when? Assuming you still cling to a full time position in academia. How come you can work less hard at that stage?

 

[mathwonk]

we only stopped working so hard after we became too old to do so in my case.

but some people are very successful who do not seem to work this hard, and perhaps instead work more consistently, steadily.

maybe its like the successful student who works a little every day instead of having to cram at the last minute.

i don't know. most math professors i know work very long hours and have done for years. it is sometimes hard for us to relate with students who think they will succeed by only studying a minimum amount.

 

[tgt]

we only stopped working so hard after we became too old to do so in my case.

So I guess your role and responsibilities (i.e number of publications) have decreased as you got older? But still keep the professor title? Is that kind of the university?

 

[dsbyt]

my elder son has a real job, but he is also expert in internet hardware and software. i recommend getting as much experience as possible in computers.

your pure math background gives you a big advantage at the reasoning and problem solving skill that helps you in this area and every area.

Did he have actual qualifications in internet hardware and software and what were they?

Before with the other people you talked about (one went into something with CAD) it sounded like they were making quite a bit with a math PhD and presumably some other qualification. Do you know what other qualifications they had which let them get those jobs?

 

[mathwonk]

my son was a math major, when he went to work at a computer oriented firm.
while there he observed what was going on and began to educate himself further by reading and experience.

He used to say what he learned there could not be learned in class, as it was so far advanced from what is learned in school.

so he knew something about computers, something about programming, and was smart and had a math major. i myself am too ignorant to assess well what he knew, but it seems he learned much of it on the job, and that his math training in logical problem solving was key.

 

[mathwonk]

a professor's role and responsibilities include three areas: research, teaching, and service. If the participation in one area diminishes, it is usual for it to increase in another. kindness is not a word that comes frequently to mind in a professional setting, but it would seem odd to me to remove the title of professor from someone who begins to work less than 30 hour days as he ages.

 

[uman]

Mathwonk,

My dream is to become a professor, but I don't know of what. Math interests me however I don't know if I want to be a professional mathematician. Specifically what you've said about math consuming your life and requiring insane amounts of work scares me. Do all professors work this hard, or only mathematicians?

 

[mathwonk]

it is not only mathematicians who work hard. Virtually everyone works very hard who becomes successful at what they do. I suppose you have heard of medical doctors working 100 hour weeks as medical students, and I can assure you this happens.

In fact medical doctors apparently work even harder than mathematicians.

people who open their own businesses, such as restaurants, work amazing hours. Just talk to any successful person in business about how much time it takes to succeed.

The secret is to find a job you enjoy working at.

 

[tgt]

Do you think it's better to work consitently everyday, all year round or work in extreme amounts then totally relax for a short period like a vacation. I prefer the former what do you think? People who choose the latter are more the people who don't really enjoy what they do and need to take big breaks like CEOs. The great mathematicians worked ocnsistently and constantly?

 

[tgt]

a professor's role and responsibilities include three areas: research, teaching, and service. If the participation in one area diminishes, it is usual for it to increase in another. kindness is not a word that comes frequently to mind in a professional setting, but it would seem odd to me to remove the title of professor from someone who begins to work less than 30 hour days as he ages.

When thing I realized is that when you're a professor at the top of a field in your university, not many people in your university are able to understand let alone access your work. So who is going to judge your performance for the year?

Maybe when you get older, you are more experienced and recquire less time to do the three areas so don't need to work as much as you use to? But still get similar results?

 

[mathwonk]

unfortunately, partly for the reasons you mention, some people at a US university tend to simplify the evaluation of your scientific work, and often reduce it simply to: "how much grant money did you bring in?", which should be almost irrelevant.

a number of years ago we had a famous mathematician interview with our administration, and he was asked if he had any current grants, since none were visible on his vita. He responded indignantly, "No self respecting mathematician would list his GRANT MONEY on his vita!"

I assure you those days are long gone.

 

[tgt]

unfortunately, partly for the reasons you mention, some people at a US university tend to simplify the evaluation of your scientific work, and often reduce it simply to: "how much grant money did you bring in?", which should be almost irrelevant.

a number of years ago we had a famous mathematician interview with our administration, and he was asked if he had any current grants, since none were visible on his vita. He responded indignantly, "No self respecting mathematician would list his GRANT MONEY on his vita!"

I assure you those days are long gone.

Quiet unfortunate but it's happening as you say. One thing I often ask myself is if you can't beat them, join them. In other words, why not use your brains to make the most amount of money possible like in financial services? Have you considered such an option? Having witnessed the current situation in academia, do you think it's a worthwhile pursuit for the younger generation? Or does academia still have a decent, uncorrupted, anti money grabbing future?

 

[mathwonk]

well money is very helpful, but not sufficient. there is a dilemma, as one cannot be happy without enough money to pay bills, have healthcare, etc,...

but one has to do what one enjoys, and what one feels good about doing. when i am discussing math, i am a happy man, at least temporarily.

so do what you love primarily, but save your money, or invest it wisely.

 

[mathwonk]

it is probably best to work consistently. i am trying now, even in the midst of my teaching, to set aside at least an hour a day for research thoughts. that's enough to seed them, and then my mind takes over and pursues the themes many more hours in the day and night.

 

[PhysicalAnomaly]

I was forced to take the maths unit that is below my level because it is a prerequisite for later classes even though I've already covered all the material because of a technicallity. I've gotten into the habit of getting my hands on final year maths assignments from my friends and doing them. I've been finding them quite easy so far (been helping my friends in fact) but am worried that by the time I do those units, I'll be caught in the same situation as I'm in now - with all the material covered years before. Should I desist? What will I do to keep me occupied when I reach the final year units?

 

[mathwonk]

i am puzzled that you find it difficult to be challenged by math when math is so hard. have you read my recommended books?

 

[Gib Z]

I was forced to take the maths unit that is below my level because it is a prerequisite for later classes even though I've already covered all the material because of a technicallity. I've gotten into the habit of getting my hands on final year maths assignments from my friends and doing them. I've been finding them quite easy so far (been helping my friends in fact) but am worried that by the time I do those units, I'll be caught in the same situation as I'm in now - with all the material covered years before. Should I desist? What will I do to keep me occupied when I reach the final year units?

Personally, and not trying to brag, I am quite a few years ahead of my class mates (who are reviewing the Sine rule at the moment) and yet, it has never bothered me once. It doesn't matter if you have covered that work before - continue ahead on your own, and only do the set homework from those classes for some good revision all year round to make sure you don't fail your test and don't forget your basics. Nothing wrong with already knowing the material, just go ahead.

PS. Sorry to hijack this a bit mathwonk :( Just a personal view

 

[mathwonk]

happy to have your input.

 

[bubbles]

My professor is teaching introduction to linear algebra by copying definitions from the book onto the board and does not explain them. I am trying to do independent study for that class since both the textbook and the professor are bad. The professor said to "unlearn" geometry since algebra is not about geometry and told us to think algebraically. He teaches linear algebra from a computational/applied perspective (since that is his specialty), but does nothing but copy proofs and definitions onto the board and told us to memorize them. Is that good? I have always seen math geometrically as well as algebraically when possible. I am having trouble with my linear algebra course right now. Can you give me some advice on how to really learn linear algebra?

Also, how strong of a background do I need in linear algebra to take more advanced math courses (Linear Algebra II, Abstract Algebra, ...etc.)? How should I prepare?

 

[PhysicalAnomaly]

First of all, I'd like to note that I'm not trying to brag or anything. I'm just quite desperate to not go over stuff that I've already learned a few times over. For example, my lecturer is teaching us the binomial distribution as if it were something new. I learned that 4 years ago and have learned it or used it every year since! I feel pretty guilty about not paying attention in the lectures but neither can I bring myself to listen...

I'm breezing through Spivak. A lot of the exercises are at the A levels further maths level. I am working on Munkres and that's fun to read. But I'm worried that if I finish that in my first semester of the first year and then tackle other books at that level like Rudin and Dummit, I'd be bored in my 3rd year classes. In australia, it all seems to be pretty laidback, unlike the uk system. If I'm able to do the 3rd year assignments now, how bored will I be in the 3rd year?

PS I've not been neglecting my unit's work or anything. Been doing all the exercises and assignments like a good boy...

PPS The cause of all this is probably switcing to the australian system after A levels further maths. Going from learning linear algebra and groups to stuff that was learned years ago isn't very enjoyable.

 

[Gib Z]

Did you just completely ignore my post? I do happen to be in a similar position to you.

You have two choices:

Don't go learn ahead. That way you won't go over things you've learned before, maybe pay a bit more attention in class. Not further yourself, not actually achieve anything. Just slow yourself down for a stupid reason.

Or, Learn ahead. That way, you DO go over things you've learned before, which is a GOOD thing. When you learn ahead by yourself, you don't always pick every skill up at that one time. Many teachers have their own unique skills that they pass onto students, and going over the work again you'll always learn something new, even if its something small.

More concisely: Either learn ahead, and actually do something worth while, or just stay with your class and be an average student.

And yes, I know the Australian System is a bit slow compared to the UK, but that's still no excuse.

 

[mathwonk]

i guess after you solve the riemann hypothesis and the ABC conjecture, youll really be bored.

If you will go back and read a few of the recommended books in this thread, you'll find enough to interest anyone for life.

and i question whether you are really breezing through spivak unless you are not doing the problems. please try all the problems and then see how breezy it is.