Advice for a Math Major that wants to teach

[EbolaPox]

I've recently graduated from my High School and will begin my Math and Physics double major in the fall. I came to thoroughly enjoy mathematics during my time in High School and quickly went to the top receiving perfect scores in my Calculus classes offered in my school (AP Calc BC was the highest we did in high school.) During my 11th grade year I self studied single variable differential and integral calculus and absolutely loved the subject. I began studying multivariable Calculus and Linear Algebra shortly after I felt I was well enough prepared in single variable calculus. I currently am enrolled in a Differential Equations class at a local community college (Want to make sure I do something mathematically productive over my summer).

However, I found that not only do I love learning math, I thoroughly enjoy teaching the subject. I became a tutor for anyone that wanted to learn mathematics of any form from algebra to calculus. I mainly tutored my classmates in AP Calculus and they claim that whatever I did made math seem logical and helped them out. I decided that I wanted to make mathematics a career and also teach math. I've considered becoming a high school teacher for mathematics (or physics, I do love physics), however, I really enjoy teaching Calculus or something more intellectually entertaining. Due to the fact that I loved math and also enjoyed teaching, I have thought that perhaps becoming a university professor would be a clever choice. I know I'll need to go to graduate school and get a Ph.D. (I was hoping to do so anyways).

However, I have a few questions:
1: What sort of mathematical studies would be beneficial to me over my summer? I've been reading Calculus Volume I by Apostol and doing the problem sets (far more interesting than my other Calculus textbooks.) I wanted to begin studying Analysis, but wasn't sure what sort of mathematical preparations were required before one could study.
2: In order to become a professor, what must I do? Must I first get a Ph.D., do some mathematical work and then in a few years get a job as a professor?
3: Any helpful advice would be appreciated and any ideas on what textbooks are good for studying Analysis, Linear Algebra (Currently using Friedberg) and any other mathematics courses.

Thank you

 

[J77]

Firstly, well done for showing such enthusiasm.

The thing to do is to go to uni and major in maths - you'll then see how different university maths is from high school maths - this may change your mind or, maybe, not...

You can always become a maths teacher staright out of uni - perhaps in the states you can even do a degree in it (?) - though the maths degree seems the best choice for you.

If you want to lecture, you have to do that PhD. You then have options, either stay on as a postdoc - doing research for as long as possible; become a postdoc with some teaching; get a tenure track position which will involve a lot of teaching (and possibly a job after the tenure); or look straight for a lecturing job.

Best not to plan these things too far in advance - just keep up with the maths and you'll be fine

 

[matt grime]

The rough outline for a standard maths research career is:

1. PhD,

2. 3-6 years of post-doc (this is just research, unless you get unlucky and have to teach. This is not because teaching is bad (it isn't and I enjoy teaching maths), but because it is a distraction from setting up a research career, and that is what counts most when you come to get a permanent position).

3. Start a 'tenure track' thing. Ie you now are looking to gain a permanent position, and to do this you go through a sort of probationary period, at the end of which you're put forward for tenure. This is when you start to lecture.

Things vary country to country, obviously. They can even vary within a country: perhaps you'll find a temporary lectureship after your phd because someone has gone on sabatical or gotten a grant that means they don't have to teach that year. Given you're learning Apostol of your own accord I doubt that in the long run you'll find a high school teaching job very satisfactory: very few students you'll have will share your interest in the subject.

NB: I have no idea about things like Community Colleges in the US beyond the fact that you can get to teach 'university level' (this is moot depedent on your country of origin: people in Germany or the Netherlands might think it high-school material) without obtaining a PhD, though there is no research. Such teaching positions (instructorships) exist in US universities too.

 

[EbolaPox]

Hello, and thanks for the replies : )

Yes, I believe I would like to lecture. I love mathematics, so the idea of getting a Ph.D. (although difficult, I'm sure) has been something I've been planning on. I was curious about what sort of undergraduate classes I should take. I'll be doing a Linear Algebra class when I enter as a freshman and a multivariable calculus class. After that, I was thinking of taking an Intro to Real Analysis class or trying for Abstract Algebra. What year does a studnet (in U.S. universities) normally take these classes? I'll already have Calculus I and II and Differential Equations done by the time I enter.

Also, I love Apostol's Calculus so far, and due to the interest that it has piqued in me, I was thinking about doing some self-study on Analysis. I found this book https://www.amazon.com/gp/product/0486689220/?tag=pfamazon01-20
. Does anyone have any experience with this book, or is it far too high of a level for me? If so, what math should I be focusing on right now?

Thanks for any suggestions : )

 

[math-chick_41]

Hi there, that book seems fine to me if you want to self study basic analysis, but you should also pick up Principles of Mathematical Analysis by Rudin and get familar with that material as well. It covers most of the same stuff that the other book does, but Rudin is the standard for analysis. If you can grasp Rudin you will be leaps ahead of your classmates (sounds like you already are though:) When learning analysis it helps to have as many books as you can because each one is a little different and you pick up little tricks from each book. Some books that I found helpful were; Elementary Analysis by Ross, Foundations of Mathematical Analysis by Johnsonbaugh & Pfaffenberger, Introductory Analysis by Rosenlicht, and of course Rudin.

 

[mathwonk]

The fact that you are reading and enjoying apostol is sufficient evidence to me that you can do a phd and become a mathematician. I myself dislike rudin as a textbook, but if you like it you are also well on your way.

with your advanced level of precollege preparation you need to choose a school for college that will accommodate you with advanced work in the early years, such as an ivy league school, or chicago, or a high level teaching college like swarthmore, or even some state schools like georgia where we take an interest in bright and gifted young people.

The problem in america is that while we need people like you in high school teaching, there are not so many places that are suitable for you to do that at a high level.

you might like teaching at a super high level prep school like andover or exeter.

the situation is that unless you teach at a top university, you will be living a schizophrenic life in university, doing your resaearch on a high level, but often teaching on a low level.

the schools like swarthmore, have (perhaps?) a lower expectation of research from theior faculty, but offer a higher level of teaching opportunity to them, with brighter students.

state schools expect high level research but ioffer only moderate teaching opportunities.

the advice given above is good, not to plan too far ahead, but to adjust your goals, as your career develops.

I am a university professor with a PhD in math, and 29 years teaching and research experience.

you have a lot of options. just keep working and more will open up. go to the best school you can get into, and learna s much as you can from teachers and fellow students. if you find yoursef over your head, try not to be discouraged. you are very talented.

good luck,

and if you apply to georgia, let me know and i will give you any help i can. but i suggest you apply to harvard or yale or swarthmore, or some where with really strong students.

a superb analysis book for very high level work, after apostol, and amybe afgter basic several variable calc, is perhaps foundations of modern analysis by jean dieudonne.

good linear algebra books include adams and shifrin, and hoffman and kunze, or strang. see my webpage for a free 15 page introduction to linear algebra that covers a semester advanced long course. if you can do the exercises in there and read that you can do anything you wish.

my web address is on my profile.

i highly recommed anything by shilov, such as the book you linked above.

 

[EbolaPox]

Thank you for the encouraging words everyone :)

Unfortunately, due to the high cost of an Ivy League or school like MIT, I will be unable to attend a university of that nature. Therefore, I'm going to be going to a state school in Florida (Harriet L. Wilkes Honors College, which is a subdivision of Florida Atlantic University. They offered me a very nice scholarship and told me I'd be able to do plenty of mathematics and physics. ) However, I have been studying using MIT's fabulous Online OCW program which allows students to watch video lectures and practice with their old exams and also have 13 AP classes completed during my High School time.

I'm glad to know that the Shilov Analysis book is good, I plan on ordering it soon and begin studying. I have been watching Linear Algebra lectures by Dr. Strang on MIT's site, they are most interesting. I will check out your Linear Algebra notes, Mathwonk. Thank you very much for the encouraging words and recommendations for textbooks. If anyone knows of any good textbooks for Mathematics or Physics undergraduate classes, please recommend them.So, right now I should just focus on learning as much mathematics as possible and doing as well as possible. I'm rather unfamiliar with the curriculum an undergraduate mathematics student undertakes. My future professors at the univeristy I shall be attending have recommended that I enter into a Linear Algebra class in my first semester. I assume after that I will be able to take classes such as Analysis and Abstract Algebra. What comes after this? Topology?

 

[Brad Barker]

I assume after that I will be able to take classes such as Analysis and Abstract Algebra. What comes after this? Topology?

after that, it's whatever you want to do. you can do more abstract algebra, more analysis, or new stuff, like topology, more differential equations, combinatorics, etc. the world is your oyster!

(the recommendation by UF for serious math students is to take graduate level algebra and analysis.)

here are some math and physics books off the top of my head:

introductory physics with calculus: halliday, resnick, and krane
EM: griffiths
mathematical methods: boas
quantum mechanics: shankar
abstract algebra: gallian
complex variables: brown and churchill
mechanics: goldstein (we used thronton and marion at UF, and it sucks)