Other Should I Become a Mathematician?

[Zetetic]

sorry for the double post, I accidentally hit send before I finished.
Anyway, my question is: How much will my problems with details and my scatterbrained tendencies affect sucess in mathematics? Any advice on remedying my problem or assuaging my anxiety would be greatly appreciated.

 

[rudinreader]

... however, I put too much emphasis on really understanding the delta epsilon proofs for each rule of differentiation ect. and not enough directed towards the more topical approach and my knowledge of certain techniques (derivative of natural logs and inverse trig functions and population growth problems) was a bit deficient.

Did studying epsilon-delta make you forget how to add and subtract numbers? Drill problems alone will not get you to higher math. You probably just need to be patient, apostle is a good choice.

 

[adrian_durham]

No one seems to be interested in my post in the Calc/Anal forum...

I was wondering what would be the physics equivalent of the Courant Calculus text. Also, while we're at it, isn't Courant more rigorous than Apostol? I actually have the first volume of Apostol, and it's not bad at all. But, it still seems preoccupied with computational problems a lot of the time. I haven't really gone through it, myself, so maybe I am being too picky and not thorough enough. I took calculus out of a "normal" book and then only later on took real analysis, etc. out of more advanced books. At any rate, I have ordered some used Courant, wondering how different that may be. I am also interested in something along those lines for physics. You know -- like Halliday, Resnick and Walker is to Thomas and Finney as what is to Courant?

 

[mathwonk]

well there is a text by courant, (and hilbert) called methods of mathematical physics.

 

[adrian_durham]

well there is a text by courant, (and hilbert) called methods of mathematical physics.

Well, that probably isn't the equivalent, though, is it? It is more like a follow up to the Calculus book. And, does it really systematically hit classical mechanics, e&m, etc. like Halliday, Resnick and Walker -- perhaps the Thomas and Finney of physics -- would? I was also looking at the reviews in Amazon -- does it have exercises? (For some reason the "look inside" feature on Amazon stopped working for me.)

At any rate, I would expect that book to be the equivalent of books by similar names for like an upper level math sequences for scientists and engineers. I'm looking for the "calculus" of physics that all freshman take that hits all of the major areas of classical physics perhaps even with a little special relativity and quantum mechanics -- that kind of thing. Of course, most freshman would take Thomas and Finney and HRW. But, if you had a freshman taking Courant, then his physics text would be...? Suppose you did Courant in a 4 semester course sequence, what text would you use starting in the second semester, say, for a concurrent physics sequence like the way they do it with TF and HRW? (The real answer to that question might be that you just shouldn't do it that way -- you should do Courant and then skip up a level to better physics texts aimed at each specific area.)

 

[mathwonk]

well how about the berkeley physics course?

 

[adrian_durham]

well how about the berkeley physics course?

Alrighty I'll take a look at that, then. Thanks!

 

[rudinreader]

apostle is a good choice.

No one caught that? For the record my favorite fish is salmon..

well there is a text by courant, (and hilbert) called methods of mathematical physics.

Two book questions.

First, I have seen the book Differential Operators of Physics by Hellwig referenced a few places.. Is that good to plug?

Second (more important for me), The book (around 1972) Symmetry Groups and Their Applications by Miller (available online) comes across to me as very good for "serious reading", by looking at it's heavyweight bibliography. Yet, it's out of print and otherwise I never it mentioned on PF. The only critique I can give is not really criticism because I haven't read it - that he seems to write in a "low level language" (via use of the word "local") despite it seemingly being of "high level interest". This is not necessarily a drawback (but is it?). The other point is that finite representation theory, lie group theory, and mathematical physics don't seem to be presented in the same way as recent books. The only comment from a mathematician I have heard of the book is that it is "an invaluable reference for those interested in dynamics". So in conclusion, is this a fresh tomato that's been hiding, or otherwise is it not the best for the picking?

 

[KGZotU]

I just started reading into Apostol's Calculus and I have never seen a book quite like it. I have taken 3 semesters of calculus and after starting this book I realized I never had a deep knowledge of the subject at all. I wish I would have been exposed to this book years ago when I first started. I like it a lot.

I feel just the same way. The moment I knew what a great book it was was when he was giving the axioms for one of the number systems and he said something along the lines of:

Such and such, such that 1.
0 such and such.
..
Such and such, 0, such and such, 1, and this 0 and 1 are the same 0 and 1 referred to above

I got so excited that he would write that down, I ran downstairs and showed my wife.

I wanted to thank mathwonk for his inspiration. I realized that if I never spend any time at my desk over a book and a pad of paper that I'll die just as good at math as I am today. On that note, I wanted to ask a question of my peers. I use a stopwatch to time how long I'm at my desk, reading, working problems, or using LaTeX. I can get about 6 hours in a day before I stop picking stuff up. Am I wimping out? Can the brain do more? Can yours? I can add hours on by learning in other ways, like my course lectures, but that seems to be about it for learning at my desk.

Also as a note, I'm reading Ross's Elementary Analysis, and he is extremely easy to read. Great book for someone like me who is just getting into the underpinnings. Requires experience with proofs, though, which I'm taking this semester.

Thanks,
Joe

 

[rudinreader]

Also as a note, I'm reading Ross's Elementary Analysis, and he is extremely easy to read. Great book for someone like me who is just getting into the underpinnings. Requires experience with proofs, though, which I'm taking this semester.

Speak of the devil! I actually had a copy of that book and I mailed it to my brother who's serving in the army. To tell the truth, it was a difficult book to depart from - all of my good books are difficult to depart from. I'm not going to tell him that though! - better to give when you can!

 

[omgwtfbyobbq]

Does anyone have any recommendations for algebraic geometry texts? I've been bouncing back and forth between going back for a MS, and from there who knows, when I can (about three years from now) and since I liked algebra and algebraic geometry, I figure it's something to look into before I head back. I'm also planning on picking up baby Rudin, as well as his other real/functional/complex analysis, but aside from that I don't know what to look for. Any suggestion, thoughts, tomatoes? :)

 

[mathwonk]

for accessible introductions to algebraic geometry, there is miles reid's undergrad text, and william fulton's book on curves, and shafarevich's book basic alg geom, and phillip griffiths lectures on curves from china, and rick miranda's book on curves and riemann surfaces, and joe harris' book, ...just search on the topic on amazon... there are lots more.

the books by miles reid and shafarevich are algebro geometric, and the books of griffiths and miranda are more complex analytic.

it never hurts to just start with shafarevich, vol. 1, chapter 1. and work the exercises.

then there are more ambitious books by griffiths - harris, hartshorne, ueno, george kempf, mumford...

 

[qspeechc]

I am always amazed by how much maths you know mathwonk- it's quite incredile!

Apostol, Courant or Spivak? For Calc1 & 2? Or does it not matter (btw, we use Stewart, which I dislike for all its numerical stuff, and 'application to life sciences', and general lack of rigour, and so many just-so statements)

 

[symbolipoint]

I am always amazed by how much maths you know mathwonk- it's quite incredile!

Apostol, Courant or Spivak? For Calc1 & 2? Or does it not matter (btw, we use Stewart, which I dislike for all its numerical stuff, and 'application to life sciences', and general lack of rigour, and so many just-so statements)

Could anyone give their opinion of ranking of quality of these undergraduate Calculus books?

Thomas-single variable Calculus, Howard Anton Calculus-the thick old book with picture of some old man, published bout 20 years ago, Larson & Hostetler Calculus, Sallas & Hill Calculus...

Rank them any way you all think is best and give your feelings/reasonings. This may help some of us who may like to study on our own...

 

[torquerotates]

Salas and Hilles is pretty good. It fairly rigorous. And it also has numerous worked out examples. It has a wide range of problems. Ranging from easy to really hard. Its a book that's not a simple as Stewart but not as rigorous as Apostol.

 

[d_leet]

Salas and Hilles is pretty good. It fairly rigorous. And it also has numerous worked out examples. It has a wide range of problems. Ranging from easy to really hard. Its a book that's not a simple as Stewart but not as rigorous as Apostol.

I don't think I can possibly disagree more... My friends use this book for their calculus class, and it is without a doubt one of the worst math books I have ever seen, the organization of certain topics is very poor, in my opinion, and also some comments made at the start of chapters are completely worthless, stupid, and things no mathematician should ever say. Stewart's is not a great book, but it is pretty good for a first calculus course that does not intend to cover much theory.

 

[mathwonk]

for rigorous honors level books, spivak is the most fun, apostol may be the driest but very intellectually honest and excellent, courant has more physics and diff eq than spivak, but any of them is outstanding.

another superb honors level book on the same level is the one by joseph kitchen, but not easy to find.

I always heard salas - hille was a good honors level book, not on the level of the four just mentioned but better than average. most of the other books are all cookbooks, not theoretical. stewart is a well liked cookbook.

 

[torquerotates]

Well, according to amazon, stewart scored slightly lower

https://www.amazon.com/dp/0471316598/?tag=pfamazon01-20

https://www.amazon.com/dp/0534359493/?tag=pfamazon01-20

 

[torquerotates]

for rigorous honors level books, spivak is the most fun, apostol may be the driest but very intellectually honest and excellent, courant has more physics and diff eq than spivak, but any of them is outstanding.

@ mathwonk. I'm curious, is Apostol an analysis level book? I'm currently using it for self-study as a supplement to Rosse's elementary real analysis and it turns out that Apostol is on a whole different level! The problems in Rosses' book we're doable. With Apostol, I got stuck on the first problem.

Would you say that at most universities, Apostol is on the level of real analysis?

 

[d_leet]

@ mathwonk. I'm curious, is Apostol an analysis level book? I'm currently using it for self-study as a supplement to Rosse's elementary real analysis and it turns out that Apostol is on a whole different level! The problems in Rosses' book we're doable. With Apostol, I got stuck on the first problem.

Would you say that at most universities, Apostol is on the level of real analysis?

No, Apostol is about at the level of Spivak, which is quite a bit more advanced than most calculus books, but not quite a real analysis book.

 

[d_leet]

Well, according to amazon, stewart scored slightly lower

https://www.amazon.com/dp/0471316598/?tag=pfamazon01-20

https://www.amazon.com/dp/0534359493/?tag=pfamazon01-20

I could be thinking of a different book, but I'm pretty sure the Salas book is one I am referring to, but a different edition than the one at that link.

 

[JasonRox]

Hey everyone!

I'm off to graduate school in September. I was originally wasn't going to go and I didn't even apply.

The day I was going to starting applying in a coffee shop in town I saw my professor walk in. Of course, I greet him and start talking. Then it came on the topic on where I was going for graduate school because he was assuming I was going somewhere. I told him how I don't want to go and that jazz. He insisted that I go and offered me a spot with him with a good offer. I couldn't let the opportunity pass up, so now I'm going to graduate school!

Let me say that I'm really excited. I'm still waiting for my acceptance letter though to make it official. I'm in though!

Anyways, I'm excited!

 

[omgwtfbyobbq]

Thanks mathwonk!

 

[morphism]

Nice Jason! Funny how that turned out.

If I recall, you're in Canada, right? Which school? And what will you be doing?

 

[Helical]

Mathwonk, when you say a book is a cookbook do you mean it is bad for learning out of period or it is bad for learning out of as a math major who wants a good theoretical understanding. I ask because I'm planning on majoring in physics and I believe my Calculus class will use Stewart.

 

[qspeechc]

From my personal experience using Stewart, I think it will be pretty good for physics majors, as there is a bit dedicated to that, and physics comes up quite a bit in the challenge problems.

 

[torquerotates]

From my personal experience using Stewart, I think it will be pretty good for physics majors, as there is a bit dedicated to that, and physics comes up quite a bit in the challenge problems.

The thing is that the hard problems in most physics texts are much more harder then the hard problems in Stewart. And they include calculus too. Making it redundant for physics majors to use Stewart.

 

[qspeechc]

I suppose your correct- I really don't like Stewart (I'm a maths major though...)

 

[JasonRox]

Nice Jason! Funny how that turned out.

If I recall, you're in Canada, right? Which school? And what will you be doing?

Hey!

I'm going to Brock University (in Canada).

My focus will be in Number Theory with emphasis on Algebra. I'll get reading material as soon as the term is over. Plus, he's getting another student which I haven't met, but she (a girl) sounds top notch. I met some of the other graduate students too. Should be good times.

 

[Ephratah7]

^_^... I want to be a mathematician. I'm not that good in math but i can understand math easily...i think...XD.. ^^.. I am just a 15-year-old girl dreaming of becoming a mathematician. BUT! I'm very interested in Math. It's my favorite subject.