Should I Become a Mathematician?

[jammidactyl]

I always get hung up on logical dependencies when I'm studying... takes me so much longer! I blame this on my reading Suppes' "Axiomatic Set Theory" last year. Tonight while reviewing analysis I'm getting wrapped around the axle with ordered rings and the Cauchy-Schwarz Inequality.

Does this happen to anybody else?

 

[mathwonk]

as my prof told one very bright student who was complaining: "well, mathematics IS difficult"

 

[Umer_Latif]

Hmmm, well yeah - I do have intentions to do masters and even PhD. in Mathematics. Thanks for your suggestion.

I've been reading the book "Trigonometry" - by Michael Sullivan these days, is that a good book?

 

[Umer_Latif]

Should a person whose very good in Mathematics do masters degree in Maths?

 

[Umer_Latif]

BTW, right now - I'm student of Engineering, Telecommunication engineering.

 

[mathwonk]

if you are just now learning trigonometry, it will be awhile before you decide whether phd is your cup of tea.

i was just trying to think of a math activity that was less committed than phd and would both give you an idea and some background of what math is like.

 

[Umer_Latif]

Well actually I've been studying Trigonometry for almost 4 years and Calculas for about 3 years (Differentiation and Integration etc.), but as I said previously, I didn't had any interest in Mathematics then so my concepts weren't really good. I have some knowledge about these things - it's just that I'm trying to be VERY GOOD in it, especially Trigonometry is really interesting and easy as compared to other things.

I'm usging the textbook of "Thomas' Calculas" for Integration/Differentiation etc. is that good?

 

[symbolipoint]

Well actually I've been studying Trigonometry for almost 4 years and Calculas for about 3 years (Differentiation and Integration etc.), but as I said previously, I didn't had any interest in Mathematics then so my concepts weren't really good. I have some knowledge about these things - it's just that I'm trying to be VERY GOOD in it, especially Trigonometry is really interesting and easy as compared to other things.

I'm usging the textbook of "Thomas' Calculas" for Integration/Differentiation etc. is that good?

You could at least apply Trigonometry and Calculus to the study of physics and engineering until you decide what you want regarding Mathematics. Realize that studying mathematics is not exactly the same as using it as a tool in other subjects; but you can hopefully enjoy the power mathematics provides as a tool for those other subjects.

 

[Umer_Latif]

Thanks a lot for the suggestion, symbolpoint.

Yeah, I've been studying applied Mathematics in Engineering - doing world problems in Differentiation, Integration, Applications of Integration and Differentian, problems regarding Polar coordinates etc.etc.

Also been using softwares like Mathematica in Calculas and for Electric Circuit graphing etc. I'm yet in my 3rd semester, I hope I'd study more applications in coming semesters.

BTW, they teach you pure Maths in Masters and PhD. right? But, I never clearly understood the difference between Pure and Applied Maths! ;(

 

[J77]

BTW, they teach you pure Maths in Masters and PhD. right? But, I never clearly understood the difference between Pure and Applied Maths! ;(

The teaching of pure maths would begin as a core 1st year subject in uni. Here I take pure maths to mean proofs.

These sills will be assumed if you require them at a masters level and beyond; and, here in Europe, they don't "teach" you anything at PhD level -- it's up to you to teach yourself necessary skills/techniques.

 

[Umer_Latif]

So, what do you think is more useful - Pure or Applied Maths? As an Engineer, I think it would be more important for me to stress on Applied Maths, right?

Is there any relation between Pure and Applied Maths?

 

[Umer_Latif]

And BTW, thanks for your reply!

 

[Darkiekurdo]

I would like to become a mathematician. Though I am just fourteen I already study the concept of the derivative and other parts of mathematics. Some people may find it weird, but it is so much fun.

I don't know how it is in the United States, but in here there isn't a lot of help for someone like me. The mathematics that I get now is too easy. So my question is; is there someone who would like to answer some questions and give some lessons about mathematics? I would really appreciate it.

But beware of some stupid questions I might ask. ;)

Thank you.

Greetings,
Darkiekurdo.

 

[quasar987]

I would like to become a mathematician. = So my question is; is there someone who would like to answer some questions and give some lessons about mathematics? I would really appreciate it.

This is a forum just for that. If it's a homework-type question, you should post in the appropriate forum from this list: https://www.physicsforums.com/forumdisplay.php?f=152

If it's a more conceptual or general question, there is the mathematics section of PF: https://www.physicsforums.com/forumdisplay.php?f=4

Welcome to PF!

 

[Darkiekurdo]

This is a forum just for that. If it's a homework-type question, you should post in the appropriate forum from this list: https://www.physicsforums.com/forumdisplay.php?f=152

If it's a more conceptual or general question, there is the mathematics section of PF: https://www.physicsforums.com/forumdisplay.php?f=4

Welcome to PF!

Aha, thank you.

 

[mathwonk]

there is a great conference in algebraic geometry coming in june, with registration closing now, april 30, check it out. if you want to see what is the current state of the field, come on down.

this is most practial for europeans, since travel costs are the main expense.

http://www.science.unitn.it/~occhetta/aghd/

 

[quasar987]

MW, do you know the textbook "Elementary Classical Analysis" by Mardsen & Hoffman?

I don't think I've ever seen it discussed or recommended on this forum, but I think it is absolutely fantastic.

What do you think about it and what does it have to envy to the books considered the "bests", i.e. Spivak, Apostol, Rudin?

 

[mathwonk]

well jerrold marsden is one of my favorite speakers and authors, and i especially liked marsden and tromba on several variables, and taught out of it at advanced high school level. so probably i would like this book.

as i get older i have become less familiar with new texts on subjects i do not teach often anymore. but if i run acorss a copy in the libs i will comment further.

 

[J77]

well jerrold marsden is one of my favorite speakers and authors, and i especially liked marsden and tromba on several variables, and taught out of it at advanced high school level. so probably i would like this book.

An engineer ?

Aside from the , it's a good example of how you don't have to be categorised as a "pure mathematician", in order to do nice maths -- maybe something for the younger guys on this thread who keep asking the differences between pure and applied to take heed of.

 

[hrc969]

An engineer ?

Who said he's an engineer?
He's written many mathematics textbooks:https://www.amazon.com/s?ie=UTF8&se...=Jerrold E. Marsden&page=1"&tag=pfamazon01-20
He's a math PHD and has advised many mathematics students:http://genealogy.math.ndsu.nodak.edu/html/id.phtml?id=28380"

Here's something from Caltech:

Expertise:

Mechanics, dynamics and control systems. Mechanical systems with symmetry analyzed using geometric, analytical, and computational techniques as well as dynamical systems, control theory, and bifurcation theory. Applications are made to a variety of engineering and spacecraft systems.

Research Areas:

Jerrold Marsden is a professor of Control and Dynamical Systems at Caltech. He has done extensive research in the area of geometric mechanics, with applications to rigid body systems, fluid mechanics, elasticity theory, plasma physics, as well as to general field theory. His work in dynamical systems and control theory emphasizes how it relates to mechanical systems and systems with symmetry. He is one of the original founders in the early 1970's of reduction theory for mechanical systems with symmetry, which remains an active and much studied area of research today.

Notice that the work he does is primarily mathematics.

So I would say he is a mathematician doing a lot of APPLIED work in engineering. I have a (mathematics) professor who started out in the engineering department (even though he is a mathematics PHD), he said he had gotten bored of pure math, that he thought it was too cooked up... whatever now he's in the math department but occasionally teaches in the engineering department. He teaches things like applied functional analysis.
So I don't think its that uncommon to find a mathematician doing engineering.

Aside from the , it's a good example of how you don't have to be categorized as a "pure mathematician", in order to do nice maths -- maybe something for the younger guys on this thread who keep asking the differences between pure and applied to take heed of.

I'm really curious to read where you saw him categorized as an engineer.

 

[mathwonk]

I may be confusing him with jerry Kazdan whom I have heard speak, but i did teach out of his (pure math) book with tromba.

 

[J77]

Who said he's an engineer?

So I would say he is a mathematician doing a lot of APPLIED work in engineering. I have a (mathematics) professor who started out in the engineering department (even though he is a mathematics PHD), he said he had gotten bored of pure math, that he thought it was too cooked up... whatever now he's in the math department but occasionally teaches in the engineering department. He teaches things like applied functional analysis.
So I don't think its that uncommon to find a mathematician doing engineering.

I'm really curious to read where you saw him categorized as an engineer.

Arggghhhh... my attention was the complete opposite of wanting to categorise. The intention was for those who seek to categorise between applied and pure, and even engineering to have a person who bridges the divides.

Here's Jerry's website: http://www.cds.caltech.edu/~marsden/

"Carl F Braun Professor of Engineering and Control & Dynamical Systems"

(mathwonk: yes, he has written books with Tromba on mv calc.)

 

[hrc969]

Arggghhhh... my attention was the complete opposite of wanting to categorise. The intention was for those who seek to categorise between applied and pure, and even engineering to have a person who bridges the divides.

Here's Jerry's website: http://www.cds.caltech.edu/~marsden/

"Carl F Braun Professor of Engineering and Control & Dynamical Systems"

(mathwonk: yes, he has written books with Tromba on mv calc.)

Well like I said there are some mathematicians that work in engineering for whatever reason. I looked at the Caltech site. I even posted the excerpt from the site which described his work. Its mathematics work with applications to engineering.

If you did not want to categorize the why did you say "an engineer?" That's categorizing him as an engineer.

Maybe if you had said "a guy who does work related to engineering?". Or maybe not have even said that.

You could just have used that to make your point. But yes I agree if someone is interested in engineering and math then there are things they could do where they could work in both.

There is very little divide between dynamical systems and some engineering. That's why the professor I was talking about was able to go to the engineering department, because he does dynamical systems and that kind of math is directly applicable in engineering. If someone really wanted to study category theory then maybe trying to do engineering as well would not be the best idea.

It all depends on what mathematics subject one is interested in. I was trying to decide between mathematics and physics and decided to do math. But am still interested in physics. It seems that I might be able to study theoretical physics after all (if I wanted to) since I am focusing in (complex) geometry. But if I was focusing in number theory then I doubt I could go to physics as easily.

 

[mathwonk]

In fact it was Jerry Marsden who gave the 1996-97 Cantrell lectures, so I have also heard him and greatly enjoyed his lectures, as well as taught from his book.

http://www.math.uga.edu/seminars_conferences/marsden-lectures.htm

In fact I taught someone who is currently a Professor at Brown, from that book.

 

[J77]

If you did not want to categorize the why did you say "an engineer?" That's categorizing him as an engineer.

The point of the " " and the " " is for people who take things too literally

I'll leave it at Jerry Marsden is a good example as to the topics to which mathematics can be applied.

 

[hrc969]

The point of the " " and the " " is for people who take things too literally

I guess that would be me.

I'll leave it at Jerry Marsden is a good example as to the topics to which mathematics can be applied.

I agree.

 

[mathwonk]

Well i have opted out of the conference in Italy, but am going to the one in Paris, June 11-15, on the ocasion of the 60th birthday of my good friend Arnaud Beauville,

http://www.math.polytechnique.fr/confga/

. Indeed much of my research activity over the years have been guided by work of his. This is my first international conference in some time, and although i am not a speaker, I am very excited about hearing from the outstanding people who will be there. If you will be in providence, R.I. on June 1,2, you should go to the 70th bday conference of David Mumford, the Fields medalist in algebraic gometry who went over into artificial intelligence for maybe the past 20 years now. Valery Alexeev from UGA is a principal speaker.

 

[mathwonk]

Right now I am struggling to choose a book for a course in geometry for high school teachers. The usual problem exists, the good books assume the students already know high school geometry and go deeper and beyond that material. The reality is that many college students do not know high school geometry at all. So the course should ideally review the content of high school geometry, then make some effort to expand the understanding beyond what is taught in high school. There are essentially no books written in this way. Hartshorne's nice looking book for instance begins by asserting that it will be assumed the reader is familiar with all of high school geometry. people like that, teaching at Berkeley, seem unaware that high schools often teach little or no geometry nowadays, and what is taught is not even taken by all students. Of course he says also he is writing for math majors, but who is writing for future high school teachers?

I tried to use an actual high school book, the great classic by harold jacobs, only to find that in the current edition it is has been extensively dumbed down, so as to be inappropriate even for a good high school course.

So I am looking for the non existent book, one by an author who realizes the students know essentially nothing prerequiste going in, and yet who still tries to present a high level of material by the end of the course.

[edit: It turned out the best book is Euclid!]

 

[NeoDevin]

Sounds like a good book for you to write.

 

[Cincinnatus]

This book looks like it might be appropriate:
http://uk.arxiv.org/abs/math/0702029v1"

 

[symbolipoint]

Mathwonk,
The answer to your post #589 is the book titled,Geometry, published by Prentiss-Hall; ISBN 0130625604, written by Bass, et. al.

 

[mathwonk]

Thank you for the suggestions. I have already ruled out Hartshorne, Euclid and Beyond; Millman and Parker; Moise, Elementary Geometry from an Advanced standpoint; Modern Geometries by James Smart;... all as excellent but too difficult.

 

[mathwonk]

ok, all sharipovs books are excellent, but the approach here assumes a good bit of mathematical maturity, not really written for students many of whom actually struggled with high school geometry, so it looks too abstract and too hard for my purposes.

 

[mathwonk]

bass et al, has no reviews on amazon, not even by the publisher, and it is unsearchable, hence impossible to get any idea of the content or intended audience or the coverage. What can you tell me? did you use it in a course? what level? it looks like a high school book, is it?

does it use protractor and ruler axioms? or hilbert's synthetic axioms? does it cover only euclidean geometry? hyperbolic geometry? are subtle axioms not in euclid like the Pasch plane separation postulate introduced?

Is SAS congruence, an axiom or a theorem? (Euclid's proof of this theorem is apparently flawed, since he apparently assumes there exist transformations that preserve angles and lengths, but does not hypothesize this.)

does he treat hyperbolic geometry at all? does he discuss the use of models to prove consistency?

I understand if you don't care to answer such picky questions, and thank you for the reference. I always hyperventilate when choosing a book.

 

[mathwonk]

sharipov's book does look nice, and maybe i should try to teach a course like that, but it seems reminiscent of books like millman and parker that I have tried with small success.

i.e. these books, like the description of my course, assume people already understand elementary high school geometry, which seems to need review in practice.