Other Should I Become a Mathematician?

[dkotschessaa]

The size of this thread would only be a problem for me if there were too many daily posts to keep up on it. Currently that's not happening. It's less busier than the "Random Thoughts" thread, which is 1197 pages long and gets several posts a day, and even that one is not hard to navigate.

Thanks to all contributors to this thread.

-Dave K

 

[mathwonk]

I'm sorry to seem to jump on you Sankaku. I thought it was plausible that the smart alecky remarks were my own!

"absolutely! hear hear! what else could possibly be learned here? popularity is its own curse. If we let this thread go to a million views it may never die!"

 

[dkotschessaa]

What grave misunderstandings abound!

Does studying math make you more smart alecky? I think my wife thinks so...

 

[shezi1995]

Are the proofs we do in the olympiads(like IMO) upto the level required for maths study at university level? I have been studying stuff, in the training camps for the olympiad, that goes way beyond my school curriculum like classical inequalities(cauchy shwartz, chebychev), functional equations, number theory, proof based euclidian geometry and combinatorics. So how beneficial is this study with regards to a preparation for a career in mathematics? The level of problems in this olympiad math is quite high compared to the normal school curriculum.
Secondly, does undergraduate education play a big role in your future math education leading to research? Does one need to study in really good universities to get good undergrad education?

 

[DeeAytch]

Are the proofs we do in the olympiads(like IMO) upto the level required for maths study at university level? I have been studying stuff, in the training camps for the olympiad, that goes way beyond my school curriculum like classical inequalities(cauchy shwartz, chebychev), functional equations, number theory, proof based euclidian geometry and combinatorics. So how beneficial is this study with regards to a preparation for a career in mathematics? The level of problems in this olympiad math is quite high compared to the normal school curriculum.
Secondly, does undergraduate education play a big role in your future math education leading to research? Does one need to study in really good universities to get good undergrad education?

These will all act as either tools in your proverbial toolbelt, examples to consider in further analysis, or a foundation for future insights.

Learning math is independent from where you go to school. Some schools will be more useful, but you can always learn on your own. As far as research goes, getting into research programs at more competitive schools is harder, and so in this case going to a less prestigious university may play into your favor.

 

[Ryen T.]

Is it possible to get into a good (top 20-30) PhD program in mathematics with a B.A. in math? I know a BS is usually the norm--however, if I have already done some research, expanded on my interests, etc. do you think it is possible to get into one of these programs?

 

[mathwonk]

its all about how good people think you are. presumably some of your teachers have an opinion about this. letters on your degree are less important except to admissions committees who know no math.

 

[Ryen T.]

its all about how good people think you are. presumably some of your teachers have an opinion about this. letters on your degree are less important except to admissions committees who know no math.

Thank you. As a result, my courseload will be quite heavy. I will be taking Abstract Algebra, Real Analysis II, Complex Analysis, PDEs, and possibly an independent study in Riemann geometry next semester. Is that a doable courseload considering I go to a top 10ish school already?

 

[mathwonk]

that's more than i could handle, but so what?

 

[nitro_gif]

Currently relearning H.S. Math from near scratch.

Current books:
- Serge Lang - Basic Mathematics (Certainly challenging but in a good way.)
- Algebra - Gelfand
- No B.S. Guide to Math and Physics - Ivan Savov (Enjoying this as it covers a lot of math and physics)
- Reading and thoroughly enjoying Ian Stewart's "Letter's to a young mathematician."

I am near clueless when it comes to geometry, I can't remember ever touching it initially in H.S. and haven't really encountered it in remedial courses nor in self study.

Does Serge Lang's Basic mathematics cover enough geometry to be successful in math intensive programs in University?

Debating whether I need a dedicated geometry book as well.

 

[Coolguy100]

I think you should follow your dreams, because if I didn't I would still be a McDonalds cook and not the C# engineer that I am today. Hope I helped

 

[mathwonk]

I don't much like serge lang's basic math book. It seems like one of those books he dashed off on a weekend. i recommend a great book like euclid, with a guide such as my free epsilon camp notes our hartshorne's great companion book geometry: euclid and beyond.

 

[Eango]

Hey guys, I'm a 10th grader in High school right now. I am "ahead" in math right now, meaning I'll being finishing the BS high school calculus classes next year. Yet I'm still with other "gifted" kids who know jack all about maths :P

My Senior year I plan on taking HL Math and tbh, I don't know much about it. I mean:
What do I learn? Is it harder calculus or a mix of a lot of stuff?
Is it even worth doing? I don't think colleges don't really look at it much despite it supposedly being hard.

It seems like i minus well take because, its math... As long as I'm learning. just wondering if there are better options, preferably that would also "impress" colleges.
Thanks for your time.

 

[Eango]

Oh, and this is the IB program... Kind of regret doing it but we have no good ap classes where i live :(

 

[hsetennis]

Oh, and this is the IB program... Kind of regret doing it but we have no good ap classes where i live :(

I don't know if I'm supposed to give input on this sticky because I'm no expert of math, just a student of math.

I enjoyed IB HL Math. It's good because it's less rote than AP BC Calculus, having topics like inductive proofs and options like group theory. Interesting and challenging. If you do a bit of self-study, IB Math HL will be good preparation for the AP Stats and AP BC exams.

 

[IGU]

Hey guys, I'm a 10th grader in High school right now... As long as I'm learning. just wondering if there are better options, preferably that would also "impress" colleges.

So it sounds like you're in a school with no math geeks? A shame, but not a big problem as there is so much on line nowadays. The middle school and high school math geeks I know are enjoying math by:

• doing math contests: lots of good choices (start with USAMTS if you're on your own)
• doing classes using Art of Problem Solving (start with Intro to Number Theory or Intro to Counting and Probability). Play with Alcumus. Check out their forums to find like-minded students. Use their books (which are great) to teach yourself.
• learning calculus for real (use Apostol or Spivak and do all the problems)
• taking a MOOC in math in related topics (there's a Coursera/Stanford Cryptography class taught by Dan Boneh that's not bad). There are tons of these (e.g. search here).
• going to a good class at a nearby college and sitting in on it (ask the prof)
• going to math circles: find one near you by searching online (although this is more useful for younger kids)
• going to math summer camps (Mathcamp is one of the best for your age, but you're too late for this summer -- check out their qualifying quiz for fun)

I coach math contest teams for middle school and high school kids whose schools don't serve them sufficiently, so I have quite a bit of experience with frustrated math geeks here in Silicon Valley. My 16yo (home schooled since 8th grade) is one of them. He doesn't like contests much, but it's just one thing among many.

Don't worry about doing things to impress colleges. The thing is, they're not very impressed by people who are doing things specifically to impress them. Going above and beyond to do stuff you love does impress them.

-IGU-

 

[mathwonk]

I think I just gave advice for you one post above yours. i.e. read euclid. and euler. and my notes. good luck, but keep your eyes open.

 

[Eango]

Thanks guys!
I'm glad to hear IB HL math is better than ap calculus from someone in it. Thanks for your perspective. I now don't feel to bad being enrolled in it. I just hope my math teacher makes smart cuts (only 3 kids should be in it at my school).

I have been looking into competition math a lot lately too! I didn't do the math counts in middle school do not sure how it works :) (i was good at math at the time, but not near as smart and passionate). Thanks for the links there. I'm guessing it would be a team thing? If so, that would be awesome communicating with others who may be smarter than me :) art of problem solving looks like a great community! I will definitely check out their classes and soam their forums this summer and hopefully get a book asap. I've heard spivaks book starts out extremely hard whereas others will get progressively harder from the Internet. I guess I could handle it senior year if I do that art of problem solving exercises right?

Mathwonk, I'm definitely not ignoring you, I've read many of your helpful posts. This summer and doing next school year I'm going to really focus my efforts on Euclidean geometry since geometry is my weakest area.

Do my plan next year (junior) is ap calculus bc, competition math, and some self studying in Euclidean geometry and maybe some algebra if I find the time (which I will). Hopefully senior year I will be in good shape to start spivaks book during HL math (which will be a breeze then). I know jack about probability too so I guess HL math will teach me enough of the basics...

Also I'm not sure whether I want to become a mathematician or computer engineer/computer scientist. I've always wanted to be a computer guys but lately I'm starting to realize my talents and my likes are more in math :)

 

[mathwonk]

sorry for any testy post. sometimes l unwisely post when I'm tired.

 

[mathwonk]

there is a search function here. there is also a separate thread for sharing feelings of depression,

https://www.physicsforums.com/showthread.php?t=530550&highlight=depressed

In general it is poor form to begin by saying you are unwilling to search for existing answers to your own question.

 

[jimmyly]

Hello all, I will be starting university in September in physics(mathematical physics honours, its just a double major) but I have started to realize that I spend a lot more time on math then I do on physics. I have finished a few basic calculus books; Quick Calculus - Kleppner/ramsey, Calculus made easy - Thompson, and a first course in calculus - lang. I also have apostol coming in the mail and have a copy of courant's book. also have a copy of pinter's abstract algebra book as well as lang's intro to linear algebra.

I feel a strong passion for mathematics building up each day. But i also feel my passion for physics slowly diminishing. i still enjoy reading physics textbooks and doing problems, but i would much rather be doing mathematics. The thing is, i know very little about the branch of mathematics and all its sub-fields. So just a few questions i have are:

1)What is mathematics research? (i.e. how do you conduct an "experiment", what do you do etc.) I realize this question is very broad and there are many different fields of mathematics but i am very curious to know.

2)What separates a good mathematician from a good physicist? this is more a question so i can find out more about myself and my interests. I want to know why i am getting more passionate about mathematics rather than physics. at the moment I find doing physics problems to be more of a drag whereas studying math i feel more excited and engaged.

3)since it's the title of the thread, Should i become a mathematician?(this ones just for fun, not serious)I do realize that I am just beginning university and don't need to pick a major yet, but I'm trying to do some self exploration and find out whether I really have a passion for math, or if it's just a summer fling :P

Thanks in advance!

 

[Dens]

Random question here.

When applying for grad school, in your personal statement, is it silly to include your math background? Should I assume the reader already knows my background (the transcripts)? I've TAed before, but I am not sure how to throw that into my PS.

Also I recently did some work for my prof. Basically he gave me a paper (I think he wrote it by hand) about an algorithm. He wrote some predictions and what not and asked me to write out the algorithm and comment on some runs. He later asked me to give him all the code, including the latex file. I am somewhat shy to ask him what he did with it.

In particular I feel like asking for authorship if he is going to include it in a paper, but I am embarrassed to ask since I didn't write anything, rather I just did some runs for him. The LaTeX file took a long time to prepare as well as the code.

 

[mathwonk]

never be shy about asking for credit for your own work. no matter how little it is, the credit should be there.

 

[Luxflux]

I've found this thread, and forum, most interesting.

I'm going to try not to write a wall of text, but I've had a lot of thoughts and ideas with no outlet for the last few months and it seems I've just found one. So apologies if it's long-winded. I'm probably going to ask about 3 semi-related questions so I'll try to section this thing off so it can be read...

1. My background in school/academia is as follows: Dropped out of high school in 9th grade, so middle school education. Found my way into university (don't ask how XD) and have junior status currently. I grew tired of the simplicity of my major (psychology) which is...a joke in difficulty, so I took calc 1 on a whim. I realized quickly that it was "plug and chug" I think they call it...but at least it was harder than social sciences. I am accustomed to solving most things faster/easier than most of my peers, as meaningless as SAT may be, I got a 1450 with 8th grade education, maybe that will give some indicator of natural ability for what it's worth. I give this as some kind of context to measure my first question.

I recently bought spivak's book on calculus since I actually want to learn it, not just do glorified algebra masquerading as calculus. It's certainly rigorous. However, as I'm accustomed to learning things much faster than most (academic things anyway...life is another matter), I'm a little curious about why...the proofs...make my head hurt XD. Should I expect to be able to do these? I'm talking chapter 1 mind you. I looked at a few of the problems...I've solved 3 after an embarassing interval it seems...maybe 4 hours of looking at them. Is this a sign I'm not suited for "real" math? It's not the difficulty, I enjoy that for a change, I know everything isn't easy. But I just kind of sit there and look at it...I try different avenues that don't really help. And some of them, I just can't see a way to even simplify at all. Should I just keep at it or what? Is it normal to struggle like this when it's your first time seeing it? What kind of strategy should I take? I'm confused b/c just sitting looking at these problems when I have no insight doesn't seem to be the best way to learn. I'll do it if that's what you have to do though, I really want to be able to understand this stuff.

Do bear in mind that my uni calc was a joke and really just consisted of plug n chug, we didn't learn *any* proofs or theory whatsoever. Felt easier than algebra really.

2. I'm trying to find tools and a vocabulary for the kind of research I'll eventually want to do. It's nebulous to say the least but...I'm looking at mathematics as a possible way to give me those tools. I want to be able to design simulations of populations of human beings exhibiting behaviors, maybe using computer models, to see what comes out. This would most certainly require designing models of some kind which involves math at least more complex than what I currently am able to do/grasp. I already think about things in this way, but I don't know *what* it is I'm wanting to do. I'm certain it has been thought of/tried before. I don't know what it's called. Game theory? Decision Theory? Nonlinear Dynamics? A branch/area of statistics? At this point in my understanding of maths I'm not really qualified to understand what I could do with those, let alone if I can find some novel applications in social sciences for them. Or if I can apply them in the way I'd like, or if it is even wise/logical to do so. Anyone have any insight into this?

3. Also, what would you suggest for someone with a spotty education to "shore up" their gaps in maths? I tried to go back and review high school curricula, but it's hard to see exactly what I'm missing. I couldn't tell from my calc and stat courses at my uni since they were a joke(we used set notations and whatnot in stat which were never explained...that my reason for taking calc, I wanted to see the nuts and bolts under the math which I knew they glossed over). I don't know if I can understand/complete spivak with my present knowledge base.

 

[mathwonk]

doing spivak takes a lot of time. if you can do them at all, even in several hours, it is a good sign of your ability to me. it also teaches you a lesson in how hard math really should be if you are challenging yourself.

 

[Dens]

Hey mathwonk, would a grad admission officer laugh at me if I write I want to study differential geometry because of Spivak in my personal statement? And possibly mentioning going through his first year calculus book? Or would it be better to not write the latter at all? Depending on the pace, I am thinking about writing that I independently studied Spivak's Manifold book in my personal statement.

Thanks.

 

[mathwonk]

that should be fine. just tell the truth. it helps you find your right place. good luck.

 

[gunslinger]

I'll be studying computer science and engineering in three months time so I thought I'd use these three months for some preparation. I have calculus and discreet math in the first two semesters so I got Calculus Vol 1 by Apostol but it's proof heavy, do I need that much for college or should I get another book?

 

[IGU]

I'll be studying computer science and engineering in three months time so I thought I'd use these three months for some preparation. I have calculus and discreet math in the first two semesters so I got Calculus Vol 1 by Apostol but it's proof heavy, do I need that much for college or should I get another book?

Not to put too fine a point on it, but Apostol is for those who want to understand calculus. For computer science and engineering there's no need to do that. For engineering calculus is a tool, so you have to know how it works, but not really why it works. For CS, calculus is hardly needed at all -- CS is mostly discrete math.

But if you want to learn calculus like a mathematician, then go for it. There's no way you'll get very far in Apostol in three months, but trying will certainly be good for you. You will likely find it quite difficult.

-IGU-

 

[mathwonk]

i think it is beneficial to everyone to actually understand the tools they intend to use.

 

[gunslinger]

I started the Coursera course "Introduction to Mathematical Thinking" which is a course that helps students shift from high school level mathematical thinking to university level mathematical thinking. I couldn't continue with Apostol I was way too slow. I might continue tho, after I get a solid background on logic and proofs.

 

[IGU]

I started the Coursera course "Introduction to Mathematical Thinking" ...

This panel discussion includes Keith Devlin, and he has some comments on the MOOC you are taking. I like what he says about using peer grading as a pedagogical device.

I'd suggest you get a bit more serious than just that class, perhaps Courant's What is Mathematics? would suit you well.

-IGU-

 

[gunslinger]

ok then, the MOOC + the book it is. thanks for the advice.
https://fbcdn-sphotos-a-a.akamaihd.net/hphotos-ak-ash3/575518_3878275874048_1306831904_n.jpg

 

[Dens]

that should be fine. just tell the truth. it helps you find your right place. good luck.

Wouldn't they find it stupid that you are listing a first year calculus book in a graduate personal statement?

 

[dkotschessaa]

never be shy about asking for credit for your own work. no matter how little it is, the credit should be there.

This is timely advice for me. I'm working on a paper with another student who is way ahead of me mathwise, but has very poor english. By our collaboration I'll essentially be writing the paper though she will have done most of the mathematical work (the proposed topic is also based on something suggested by me.) I feel a bit redundant to the process right now, but I think it will still be a good experience.

 

[mathwonk]

@dens: au contraire. going successfully through Spivak is exactly what many grad math programs would like to know about you. It's not going to impress Harvard, but at the University of Georgia (my university), it should count for something.

We recently began a remedial program for grad students because today many come to us not knowing advanced calculus, or even how to really make proofs. Spivak is one variable calculus sure, but it is that topic done well, and thoroughly, and deeply. It is the sort of thing many programs hope their seniors can master, not their freshmen. Calling it a first year calc book, is not descriptive. This is only a first year calc book at places like the University of Chicago, and even there it is only for their best students.

But again the point of describing yourself includes telling the truth so you can find the right place for you. Sure a lot of things i say might sound stupid, but as one of my friends said about me, I became a mathematician when others around me did not, because I was not afraid to ask stupid questions, even at Harvard.

 

[deluks917]

I actually mentioned Spivak's Calculus prominently in my personal statement. Since reading it the summer after my freshmen year was what showed me math was interesting and beautiful (the difference between Spivak and the math I had in HS should be apparent to readers of ths thread). I got in a decent grad school (despite only taking math serious after my freshmen year).

 

[Alpharup]

I have taken electrical engineering in a top notch college in India...I wanted to be mathematician in 10th grade but my family background, lack of awareness, the social pressure all prevented me. Neverthless, I liked physics and mathematics and so I took engineering...Here engineers are respected more than physics and math students...This is because, they see that engineers can earn more than physicists and mathematicians...There is a general lack of awareness in the society...Many students don't know what is engineering but want to take it in college!(some want to get placed in top companies)...

Now, I will come to the discussion... It is a well known fact than engineering mathematics is less rigorous than actual mathematics...But I want to learn almost all the concepts of mathematics atleast to the point of understanding general relativity in physics... I know that it is a painstaking job and I should spend a lot of time on it...Here there is a general saying "Dont learn what is outside the syllabus as you will waste 'time'...Do what you can to get good marks or grades"...This is the attitude of general population.If I fail in my college due to reading mathematics, they would blame me for wasting time...So, Iam in a position to learn what is only needed...I have decided that I would learn mathematics after I finish engineering...Would learning mathematics in depth and rigour make me a successful engineer(which the society expects)? Would it help me applying engineering concepts to real life problems? Will I have edge over other engineers of my time?

 

[IGU]

I have decided that I would learn mathematics after I finish engineering...Would learning mathematics in depth and rigour make me a successful engineer(which the society expects)? Would it help me applying engineering concepts to real life problems? Will I have edge over other engineers of my time?

It is a good thing to understand the tools you use, especially their limitations. It will make you a better engineer and certainly help to distinguish you from the common herd. You are, I think, showing maturity in your decision to put it off. There are several reasons this is wise:

• for an engineer, theoretical understanding is secondary to being able to use the tools proficiently
• rigorous understanding will come more quickly and efficiently after you are proficient at techniques
• you will understand how proofs are truly important better later on (you'll quickly see how the assumptions limit where the results can be used)
• you'll be in a better position to know what subset of pure math is important to you

All that said, it wouldn't hurt to take one class meant for pure mathematicians now, so you can see whether you like it. Maybe a semester of group theory if you want it to be hard, or number theory if you want it to be totally irrelevant to engineering, or an introduction to analysis if you want it to be somewhat useful. Easy to drop the class if you find it not worth the effort.

Be aware that your tastes will change as you learn more, and you might get much more busy as opportunities come along, so if you put off learning any pure math you may never find the time. C'est la vie. It's one of the down sides of being mature rather than impulsive.

Also there are many things you can learn to help you become a better engineer: philosophy, writing, drawing, architecture, astronomy, biology (especially bio-electricity). Pure math may not be the best use of your time, even if it is a good idea.

-IGU-

 

[mathwonk]

These little pieces of wisdom seem highly culturally motivated. there is a famous western quote: "A man should read exactly as his interests lead him, for what he reads as a task will do him little good." attributed to Samuel Johnson.

Also in India, the greatest gurus and scholars despise learning primarily for gain, according to my limited understanding. I myself admire Ramana Maharshi and Sri Ramakrishna. These saddhus teach that the primary obstacle to realization is "woman and gold", and that "desirelessness is wisdom".

there is little room in these philosophies for grade grubbing and money seeking. But I must add that life is difficult without prudent concern for ones well being in some form. Thus the hard task is to survive, to pursue ones true and pure passion, without becoming tainted by shallowness and greed. One must also learn to preserve respect for our forebears, even as they urge us to abandon our intellectual dreams for material stability.

 

[Alpharup]

@ mathwonk..Yes many Indian philosophers dislike the work being done to get material benefits...They feel that such materialism brings bondage and results in "Fittest will survive" nature...I personally appreciate you for seeing the good in other traditions(that too being in USA)...Afterall, truth is truth...Indian philosophers have developed a method for doing work only for attaining god and not for the fruits which the work gives...This method is called "Karma yoga"...In this method, you should do the work which you are interested in( which may depend upon the inbuilt traits) and chanting the holy name of any god...You should not think about success or failure...

But whatever I mentioned here is not properly followed by Indians themselves...Almost all the people in different strata and culture of country respect only certain kinds of people..These include politicians, engineers and people who have some technical knowledge and some power...Some occupations are seen as superior and others as inferior like that of mechanic, etc..This attitude is highly prevalent among the middle class.. Here many people work day and night for just a few rupees...They lose their sleep in these processes...Almost every person has social insecurities.. India is in a transition state and this has affected education a lot...

Education is in the same way as it was in Europe in early 1900's..Rote learning is prevalent here...In my mathematics board exam, they never ask questions which is outside the textbook..If you show some creativity in answering some math questions, you have to leave the fate to the teacher who corrects it!Financial insecurity is also a problem..Unlike USA where bright students take teaching jobs, here only the students who got low grades take them...So, professors and teachers are looked down upon...
The basic principle is; memorise->marks->good course->good job...Thus almost all the activities pertaining to education is against this Karma Yoga...Private schools are run mostly for money...Creativity which is a part of Karma Yoga is lost in this process...But USA has a very different culture than that of India...Students atleast have the freedom to raise questions in class,I suppose...But here it is not the case...If you ask, you are a blasphemer...

All these factors are present in India...I may take mathematics(or physics) and I may like to do it..But I don't know whether I will be able to get material success which I don't prefer much...I may not enjoy what engineers enjoy in society..Leave all these..Inspite of all these,Even if I take pure mathematics(or physics) and I don't succeed, my parents will be disappointed..Atleast for their sake, I took engineering(Engineering syllabus is dependent on mathematics and physics)...

 

[mathwonk]

It is perhaps only when one finds disappointment in pursuing material goals that one begins to turn to philosophical ones instead, in search of peace, or understanding. Paradoxically, at this time one may find that practical success is also more within reach.

Those with understanding of themselves and others, may find it easier to obtain jobs, grants, promotions, and to manage others, than those who are consumed with self interest. Even if we lack recognition for our work, or material success, it matters less if the fruits of that work are "dedicated to God". Indeed that is one coping mechanism, in a situation where one is unappreciated by superiors or peers. One cannot control the response to ones efforts, but one can try to control the spirit in which those efforts are given.

There is a beautiful line in Nan Yar?, something like: "when one enters the train, one does not any longer carry ones little bag on ones head, but puts it down, for the train carries all loads. In the same way the great God supports us by His grace."

With some little understanding, and the peace it brings, one may find more time to study. At least the scriptures seem to tell us this. Of course sometimes divine wisdom speaks to us also through our parents.

 

[Alpharup]

It is perhaps only when one finds disappointment in pursuing material goals that one begins to turn to philosophical ones instead, in search of peace, or understanding. Paradoxically, at this time one may find that practical success is also more within reach.

Those with understanding of themselves and others, may find it easier to obtain jobs, grants, promotions, and to manage others, than those who are consumed with self interest. Even if we lack recognition for our work, or material success, it matters less if the fruits of that work are dedicated to God. Indeed that is one coping mechanism, in a situation where one is unappreciated by superiors or peers. One cannot control the response to ones efforts, but one can try to control the spirit in which those efforts are given.

.

These are all advantages of Karma Yoga..When we attain materialistic success through Karma Yoga, we don't rejoice instead we take it as a blessing of god...This reduces our ego..When we realize that success or failure is due to god, we can never have ,"I'am the greatest. I can do whatever I want with hardwork(without god).I'am an expert. Iam a success. Everyone is below me".This attitude will surely bring depression..There are many self help books which stress the importance of success...One book says "Why do you need success? Without success, there will be few friends and there will be less enjoyment in life" This is what it gives on why we need success! In fact we are born to die but people are mad for success by compromising their health and family...Iam sorry to say but these books and motivational speakers are breeding a whole class of egotistic people who recognise themselves as successes.

Many successful people lack humility and are indulgent in pleasure giving work without heeding to moral values. Almost all the so called successful people(including people in academia, business, sports, politicians, serviceperson and so on) have atleast a little attitude like these. They officially or unofficialy become atheistic(I too became one)...When we believe that fruits, intelligence, well-abled body, strength are given by god, we will have a peaceful life(our mind is happy in the presence of god) without endangering other species in nature...

 

[mathwonk]

I confess that I struggled hard for years to make my way in my career, and was helped greatly by a study of various yogic disciplines, karma, swar, and others (yantra, tantra, mantra,...). I have great respect for the wise seers and gurus who made their teachings available to us. But there is not only one path to enlightenment. One should think hard about his definition of success before pursuing it with all his self. A man who knows who he is does not need to tremble when his boss or professor calls him. If he does so, it may be a sign he should reconsider his priorities and recapture his self.

 

[Tim92G]

I have a question for the professionals in mathematics here: Do you think competing in the IMO in high school is necessary in order to become a successful mathematician? Currently I am an undergraduate in math, and have considered taking the Putnam exam to help build my resume for grad school, but I am ashamed to say I have never participated in a formal mathematics competition before. Growing up I had always done GOOD in maths, but it was not until later (around 16) that I found an interest in advanced maths. I chose not to go to a STEM high school ( a decision I bitterly regret), therefore I never went to any summer camps like some of my friends did, or ever had any formal competition training. Many of my friends in my undergrad program even qualified on their AIME tests. I feel as if there is an exclusive industry of training students with an interest in mathematics early on to do well on competitions such as the IMO, and later the Putnam (in college), grooming them to become the mathematical prestige, and that I have missed out on this. Although my creative thinking abilities (high understanding of proof writing, and developing my own intuition behind theorems) make me believe I have what it takes to become a mathematician, I fear my lack of competition experience will limit me. Lately, this has discouraged me to the point that I have considered abandoning the field of math entirely, and changing my major to engineering or economics. What are your opinions?

 

[mathwonk]

No your situation is not hopeless, even without the advantages you lack. The strengths you mention are more than enough to succeed. But you are advised to proceed based on how much satisfaction and pleasure you gain from doing your subject. The rewards for a mathematician are not great monetarily, so one needs to enjoy the work. My friends with degrees in economics earn far more.

 

[IGU]

I have a question for the professionals in mathematics here: Do you think competing in the IMO in high school is necessary in order to become a successful mathematician?

I'm not a professional mathematician, but I am involved with math kids and competitions. From talking to many professional mathematicians, it's pretty clear that they are divided on the value of competitions. Certainly nobody thinks that competitions are a prerequisite for becoming a real mathematician. Many think they are a bad idea, pushing promising kids into wasting their time on irrelevant nonsense. I haven't found anybody who thinks that ignoring competitions entirely is a problem for kids who love math. So I'd say your worries come from paying attention to the wrong people.

What I see as the main good thing about competitions is the social side -- they are a framework for like-minded kids to meet each other, work together, and play together. But doing well at competitions takes time and energy, so if you spent your time and energy on other things you didn't miss out on anything important. Here's something on the pros and cons of competitions by Richard Rusczyk, who's always worth reading.

From what you describe of your situation, I see no value in taking the Putnam. You might find going to the club or class or training sessions interesting -- you might meet people worth meeting and learn some things worth learning and have some fun. But you are unlikely to do well on the test; almost nobody does. So don't sweat it.

I'll tell you what I tell the kids who do competitions with me: if you're not having fun then you're doing the wrong thing. Do something else that is fun. Here's an idea. Start a study group to work through some interesting math book or paper or MOOC or whatever. Finding like-minded people who want to grapple with some difficult math during their recreational time is more likely to be fun than trying to compete on somebody else's agenda. Most important is that if you don't find math fun then you ought to be pursuing something else. But competitions are not math, and aren't even a little like what real mathematicians do.

-IGU-

 

[mathwonk]

I agree with most of what the previous poster said except the somewhat cynical tone. Also i would suggest trying the Putnam just for fun and education. And I am a professional mathematician.

 

[Alpharup]

I recently bought Apostle calculus for self study...It is much cheaper than Spivak in India...I love Apostle's calculus and it is very thought provoking...I have read a few pages and the way the subject is presented is great...The use of inequalities and method of contradiction, induction for proofs is much logical...I have never known how simple axioms can be used to prove many results...But it is a little bit time consuming...For undertstanding a single result, it takes many strategies like linking many axioms, using comparisons, etc...All these are little difficult for beginner like me...So please suggest some simple strategies for undertstanding the mathematics of Apostol in a much easier way by and in much lesser time...
(Note; Iam in vacation and after my college is opened, I won't have time...So, I want to cover as much material as possible within short duration)

 

[IGU]

So please suggest some simple strategies for undertstanding the mathematics of Apostol in a much easier way by and in much lesser time...

This stuff is hard. What you're doing is learning a new way of thinking. Apostol will give you the best kind of start, but I don't think you'll find a way to make it easy and quick. Even just doing a couple of chapters, working the hard problems (not just the ones that are for practice), will give you a big advantage going into an engineering calculus class. You'll notice when they're not being rigorous (this proof is beyond the scope of this book, or we'll assume this lemma), and you'll feel more in control.

It's somewhat of a cliche, but the more you put into it (the harder you work), the more you'll get out of it. And once you work through some Apostol, the class you take will probably seem easy in comparison.

-IGU-