Should I Become a Mathematician?

[mathwonk]

what are you trying to tell me? I am working on a macbook and cannot rightclick.

i have copied exactly what I read in the guide here to setting tex commands. but it does not work.

what am i missing? a PC? a standalone copy of a tex program?

 

[GregJ]

Tapping with two fingers at the same time on the touch pad (on the macbook) should act as a right click if you have it enabled.

If it is not enabled and you want to enable it, go System Preferences->Trackpad
Under the "Two Fingers" section check "Secondary Tap".

 

[Number Nine]

[tex]x^2\sqrt{x}[\tex]well? why doesn't it work?

The slash on your closing tag is backward; it should be "/tex" not "\tex". Also, when raising something to a power, you should enclose the power in curly brackets (x^{2}).
$$x^{2} / \sqrt{x}$$

 

[mathwonk]

$$(x^{2})\sqrt{x}$$

thank you.

sorry to be so clueless but what now?

what the he**? this wasn't working 2 minutes ago and now it is.

ha ha and now it isn't again!

geez cappeez...

 

[Nano-Passion]

what are you trying to tell me? I am working on a macbook and cannot rightclick.

i have copied exactly what I read in the guide here to setting tex commands. but it does not work.

what am i missing? a PC? a standalone copy of a tex program?

I'm sorry I wasn't aware of that. Your mistake was that you forgot to put a division side in between x^2 and \sqrt(2).This is the exact code:

x^2 / \sqrt{2}

or \frac{x^2}{\sqrt{2}} to display it in fraction form

To add to what number nine said, if you want to put it in the proper fraction form, put \frac and then the two items in circle bracket. So \frac{x}{y} would be

$$\frac{x}{y}$$

 

[mathwonk]

thank you thank you thank you! i have been trying for 69 years to type in tex and this is my first successful output!

to paraphrase harry and sally: yes, yes, yes!

 

[Nano-Passion]

thank you thank you thank you! i have been trying for 69 years to type in tex and this is my first successful output!

to paraphrase harry and sally: yes, yes, yes!

Haha, very glad to help. Its quite simple once you get the hang of it. Feel free to ask me if you have any more questions of it.

 

[symbolipoint]

thank you thank you thank you! i have been trying for 69 years to type in tex and this is my first successful output!

to paraphrase harry and sally: yes, yes, yes!

Haha, very glad to help. Its quite simple once you get the hang of it. Feel free to ask me if you have any more questions of it.

Mathwonk's difficulties with LaTeX for so many years is encouraging, that maybe a person does not need to have such typesetting skills to become good at Mathematics. The pen-or-pencil on paper is always more natural for Mathematics and for Art.

 

[mathwonk]

Type setting has nothing to do with doing mathematics, but in todays world it has a lot to do with publishing it, and with convincing people to read it. A few years ago the best books, such as Fields medalist David Mumford's own algebraic geometry book, were typed in crude fonts and corrected in ink by hand.

Today some people (including some students I have taught) decline to read notes unless they are set in Tex. I found this almost unbelievable. Mumford's own "red book" for example has been reissued in beautiful type fonts. Although many mathematical errors are introduced in the new version that were not there in the old "ugly" version, presumably today's typical students prefer the error prone but pretty text.

I find it almost antagonistic to my way of thinking about geometry in big bold strokes, to worry about the difference between / and \, but in Tex this is a total game changer. Indeed in preparing manuscripts for my secretary in the old days I learned that it was unwise to concentrate too much meaning in a tiny symbol, since that almost guarantees errors in transcribing or in understanding it. The more important something is, the more difficult it should be to misread it. But even my brilliant colleague who has largely mastered Tex, seems to have trouble thinking about the mathematics he is typing while attempting to set it correctly in Tex.

This strange situation puzzles me but is a fact of life. Many mathematical journals now expect the author to submit articles in LaTex, and book publishers expect "manuscripts" [after all the word literally means handwritten] to be in the same ready to publish form. This is a huge inconvenience to those of us oldsters who always focused more on the content than the format, but it cannot be changed. Hence young persons are advised to learn the new techniques of communication.

 

[mathwonk]

those of you who wish to know more about the kind of person to whom they are entrusting their most sacred hopes and dreams via his advice may research my background further here:http://en.wikipedia.org/wiki/Roy_Campbell_Smithhttp://online.wsj.com/article/SB123396915233059229.html

 

[qspeechc]

those of you who wish to know more about the kind of person to whom they are entrusting their most sacred hopes and dreams via his advice may research my background further here:


http://en.wikipedia.org/wiki/Roy_Campbell_Smith


http://online.wsj.com/article/SB123396915233059229.html

Relatives of yours mathwonk?

 

[Number Nine]

Relatives of yours mathwonk?

Are you suggesting that Mathwonk isn't the governor of Guam?

 

[Nano-Passion]

Relatives of yours mathwonk?

I was rather confused here too. He said "can research my background further" and linked to someone that has already died. So I'm assuming he meant his history background?

 

[mathwonk]

sorry for the confusion. these posts get made late at night sometimes, when they strike me as funnier than they do to intelligent people in the daylight. But people often confuse me with wall street greed merchants and deceased 19th century imperialists, for some reason. maybe its the dumb things i say. apologies for going so far off topic. there are no mathematicians in my background, just one country school teacher, a country doctor, and some farmers and store keepers.

 

[Mépris]

sorry for the confusion. these posts get made late at night sometimes, when they strike me as funnier than they do to intelligent people in the daylight. But people often confuse me with wall street greed merchants and deceased 19th century imperialists, for some reason. maybe its the dumb things i say.

Oh, don't worry about it. I enjoy your particular brand of humour. Really nice change - I just got out of a dinner during which I thought of some interesting ways of killing myself, mostly because of the company.

As a follow up to what somebody else asked in the first pages of this thread:

Is doing a pure mathematics undergraduate degree a better idea (assuming one is interested in both pure and applied aspects), then doing either an MS or PhD in applied math, than doing a straight-up applied one? My understanding is that, in general, pure math is conceptually harder than applied and knowing that mean that picking up the applied parts needed easier. And what's considered pure math today, could at some point, be some kind of applied, is that right?

Also: I've PM'd you something.

 

[mathwonk]

I only studied pure topics because for me they were easier, but later in life wishes i knew more applied stuff. not only are more job opportunities out there for applied, but many of the pure topics came from applied questions so yes they illuminate each other. one reason for not understanding pure math may be not knowing the physical concepts that gave rise to it.

when i started out i was rather lazy had a good memory and did a lot of memorizing as opposed to understanding. i was also a good short term problem solver so did well on tests even of topics i had not learned well.

I did not realize that it takes effort to understand, and just looked for the easiest courses which for me were pure courses with a lot of memorizing. For me applied and physics based courses required understanding intuitively ideas that were not clearly formulated and I did not want to spend that much time.

So yes, pure and applied courses should go hand in hand for maximum understanding of both. People who specialize exclusively in one without the other are handicapping themselves.

I have written several times here and elsewhere how i came recently to realize that archimedes' analysis of work leads to an understanding of volume and even of 4 diml volume.

 

[Sina]

I did B.S in genetics, M.S in physics now doing Ph.D in mathematics. During all the years of my B.S and M.S I realized that mathematics is fundamental to everything and for instance as physics major let's say, the math in your standart cirruculum is usually not enough. Either start taking extra courses like real analysis (aside standart calculus), smooth manifolds or do a math double major if you want to become a natural sciencetist (any from biology chemistry to physics) or an engineer.

 

[Mépris]

when i started out i was rather lazy had a good memory and did a lot of memorizing as opposed to understanding. i was also a good short term problem solver so did well on tests even of topics i had not learned well.

I did not realize that it takes effort to understand, and just looked for the easiest courses which for me were pure courses with a lot of memorizing. For me applied and physics based courses required understanding intuitively ideas that were not clearly formulated and I did not want to spend that much time.

How/why did things change when you went back to school? What you described above sounds scarily like me.

I have written several times here and elsewhere how i came rcently to realize that archimedes' analysis of work leads to an understanding of volume and even of 4 diml volume.

Will look into it tomorrow morning.

I did B.S in genetics, M.S in physics now doing Ph.D in mathematics. During all the years of my B.S and M.S I realized that mathematics is fundamental to everything and for instance as physics major let's say, the math in your standart cirruculum is usually not enough. Either start taking extra courses like real analysis (aside standart calculus), smooth manifolds or do a math double major if you want to become a natural sciencetist (any from biology chemistry to physics) or an engineer.

That is, ahem, quite the route you took to get to mathematics! I'm not certain about a double major. I'm just going to go for math and pick any courses I like and go from there.

Thanks guys.

 

[Sina]

Well if you are theoretically minded that is the only way I suppose (reductionist way). In my major as a geneticists I was quite interested in protein folding and that carved the way. Theoretical questions in biology reduce to those of physics (or directly to mathematics) which reduce to those of mathematics :)

So biology is like the top of the funnel, physics the middle part and mathematics is the tip of the funnel. My initial condition was the top of the funnel :)

 

[mathwonk]

i managed to graduate harvard and get into brandeis on talent. 5 years later after a checkered career, i went to a small college as instructor where i fell in love and began a family. about this point i also met and learned from a spiritual teacher and started the long process of hard work raising a family and caring for it. i became a professor at a state college and took a stint as postdoc at an ivy league school. the harder i worked the luckier i got, as they say. my family supported me and as i rose in career i supported them. it has worked out well.

 

[simplicity123]

I need some help on noncommmutative algebra. It is too hard. Going to fail it. Anyone know any decent books?

It's all the linear algebra that is screwing me up.

 

[mathwonk]

give us a little more detail. what level are you, and what course or book are you struggling with? there are lots of good linear algebra books, some free.

 

[qspeechc]

Mathwonk, may I make a request?
If you don't mind and you have the time, please would you type up a document listing under the various fields of mathematics, books you recommend for study, accompanied by short notes, and saying what level the book is at, etc. You could then put it on your website or upload it here.

I'm sorry for being so forward, but your recommendations are scattered over thousands of posts, and it's difficult even just to search through this thread for them.

Also, it will save you a lot of time instead of having to repeat yourself millions of times, every time some one asks you about books you recommend.

I looked on your webpage and I didn't see any document like that.

 

[mathwonk]

what do you think of the book suggestions in the first 5 pages of this thread?

here are some remarks i wrote to guide pre phd quals students in algebra:

http://www.math.uga.edu/graduate/AlgebraPhDqualremarks.html

in general, the best books are by the most famous mathematicians, gauss, euclid, archimedes, courant, hartshorne, cartan, artin, jacobson, van der waerden, hilbert, milnor, thurston, riemann.

 

[sandy.bridge]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

 

[Number Nine]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

Linear algebra is a very nice bridge towards more theoretically oriented mathematics; you'll find it very different than any math you've done so far. The material will be considerably more conceptual than your calculus course (i.e. it becomes very important to understand the "big picture", and you'll spend a bit less time dealing with equations), and this might end up being your first exposure to proofs. That said, if you managed to get through vector calculus (a nightmare for many people), you should have no trouble with linear algebra if you put in the time.

If you want a taste of what you're in for, watch a few of the prophet Gilbert Strang's lectures on the subject...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

 

[Dembadon]

@ Mathwonk

I'll be taking my first Linear Algebra course next term. Is there any way for you to relate the difficulty of such a course, relative to Calc I, II, III, IV (differentiation, integrals, vector calculus, PDE, etc)? I'm merely taking the course for because it interests me, however, this will be my 7th course for that term.

Here's the outline of the material covered: Vector spaces, matrices and determinants, linear transformations, sets of linear equations, convex sets and n-dimensional geometry, characteristic value problems and quadratic forms.

The following link contains one of the best free books I've come across for linear algebra:

http://joshua.smcvt.edu/linearalgebra/

Down towards the bottom of the page, you'll see a link for the pdf of the book and its solution manual. I highly recommend it for a first course.

 

[qspeechc]

what do you think of the book suggestions in the first 5 pages of this thread?

I know about the beginning of this thread, but you have made many other recommendations, I believe.

here re some remarks i wrote to guide pre phd quals students in algebra:

http://www.math.uga.edu/graduate/AlgebraPhDqualremarks.html

i general, the best books are by the most famous mathematicians, gauss, euclid, archimedes, courant, hartshorne, cartan, artin, jacobson, van der waerden, hilbert, milnor, thurston, riemann.

Thanks for the link, and the recommendations.

 

[sandy.bridge]

The following link contains one of the best free books I've come across for linear algebra:

http://joshua.smcvt.edu/linearalgebra/

Down towards the bottom of the page, you'll see a link for the pdf of the book and its solution manual. I highly recommend it for a first course.

Thanks for the link.

Linear algebra is a very nice bridge towards more theoretically oriented mathematics; you'll find it very different than any math you've done so far. The material will be considerably more conceptual than your calculus course (i.e. it becomes very important to understand the "big picture", and you'll spend a bit less time dealing with equations), and this might end up being your first exposure to proofs. That said, if you managed to get through vector calculus (a nightmare for many people), you should have no trouble with linear algebra if you put in the time.

If you want a taste of what you're in for, watch a few of the prophet Gilbert Strang's lectures on the subject...
http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/

Awesome. I prefer the more 'theoretical' classes anyways.

 

[mathwonk]

for some reason, linear algebra is considered more advanced than calculus when the opposite seems more correct to me. if you look over the book by jim hefferon linked above, you will see how elementary all the ideas are in it. just adding and multiplying by scalars, and occasionally taking a square root. there are no limits, no complicated definitions such as riemann sums, which occur in calculus. actually linear algebra is prerequisite to calculus. not the other way round. the only reason it is taught in the opposite order in some schools, most schools, is that science courses want students to see calculus early, so it is taught in a mindless computational way. that is very hard to understand, hard partly because the students do not yet have linear algebra.

so if you have survived several quarters of calculus, i assume you will have little trouble with linear algebra.

having said this, it is true that if you have only had very computational courses in calculus, with no proofs or reasoning, courses which were never even offered in the good old days, you may be shocked at the level of abstraction in a theoretical linear algebra class.

When i was in high school in the 1950's, we still learned euclidean geometry with proofs, so this abstraction was not so new to us. indeed my freshman college calculus course also had proofs, so to me linear algebra was relatively easy except when it hit jordan canonical form, which can be made to look hard. your course description however does not even mention covering jordan form, and i think hefferon's book does not either.

as mentioned often, there are at least 3 or 4 linear algebra course notes for free on my website you might look at.

 

[sandy.bridge]

Interesting. I hope a 7 course load isn't too overwhelming.

 

[Number Nine]

Interesting. I hope a 7 course load isn't too overwhelming.

Which courses?

 

[sandy.bridge]

EE 212 Passive AC circuits, EE 214 System Modeling and Network Analysis, EE 216 Probablitly Statistics and Numerical Methods, EE 232 Digital Electronics, EE 292 Electrical Engineering Laboratory I (an entire class dedicated to lab work), Math 224 Calculus IV for Engineers, Math 226 Linear Algebra...

Lol, looks fun. Furthermore, I had a meeting with my department head and got approval to execute a dual degree in EE and Physics. I'm so happy. I was worried that the Engineering department was going to be annoying regarding me lengthening the program. I'm wanting to take 3 courses from each department each term, until I am fully finished.

 

[Sankaku]

...does not even mention covering jordan form, and i think hefferon's book does not either.

Chapter 5, Section 4
Page 379

Just to make sure no-one misses it.

 

[mathwonk]

thank you for that correction. i wonder if i was familiar with an older shorter version of hefferon's book, but anyway jordan forms are certainly in this one. note it seems to be dated 2011.

to learn that topic however, it is necessary to read all of chapter 5, and the key section is the section on nilpotence. he puts it all together in the section titled jordan form, but the main work had been done earlier. see especially the concept of a string basis.

to see the difference in pace between hefferon's book and my little primer of linear algebra, note that I cover jordan form from scratch in the first 10 pages compared to his almost 400 pages. Then I go on to cover also rational canonical forms in the last 4 pages, which I do think he omits to mention.

the difference is that jordan form only works when the minimal polynomial has all its roots in the given field, while rational canonical form always works under any circumstances.