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.