Programs In need of advice: How do I become a mathematician?

[MidgetDwarf]

also, read and work through your textbooks.

 

[gleem]

I have no idea of what’s coming next and what should I be reading at all. I don’t know what particular area I will be interested in because I don’t have enough knowledge to even choose. Therefore, I was just wondering if any advices could be given on what should I start reading and what should I do next to learn more about mathematics and about being a mathematician.

You have probably taken more math courses than most entering math majors. Don't try to learn anything new. Review your previous course work with the intention of thinking that you will teach courses in those subjects. Many will tell you that you do not understand a subject until you teach it. Maybe you could try and tutor someone.

How did you do on the SAT math? Did your score indicate a good aptitude for math?

Every year there are about 30,000 math BS degrees are awarded and about 1200 Ph.D.s.

Are you familiar with the type of jobs available for a math major? see for example see https://www.geteducated.com/careers/jobs-for-math-majors/#/

When you say you are interested in math do you mean pure or applied? Pure math is a whole other ball game.

When you get to university you will be ahead and you will finally be able to talk to others who share your interest in math. Be warned that university may be more challenging than you expect. It is important to get off to a good start, starting by developing a sound foundation. Talk to the faculty about your background and any concerns you might have. Do not hesitate to retake any course you took in HS that you feel weak in. Remember your confidence is important especially when things become difficult.

As you firm up your goals develop a sensible plan. Keep in mind there are many who can help including faculty and PF. Good luck.

 

[Muu9]

There is a kind of anxiety that students have when learning new things. Often they convince themselves that they understand a concept only to get frustrated when using it to solve a problem.

The student will say: "I understand the concept, but I just can't apply it to the problem."

If so, you must change your thinking and not delude yourself. As you read passages in your book, ask yourself what they mean; write FAQ-like notes of your questions and what you've discovered.

"The first principle is that you must not fool yourself—and you are the easiest person to fool. So you have to be very careful about that. After you’ve not fooled yourself, it’s easy not to fool other scientists. You just have to be honest in a conventional way after that." - Richard Feyneman

 

[bhobba]

You have probably taken more math courses than most entering math majors.

You certainly do. If it's not on your list I always suggest Virginia Tech - great school - easily in the 99 percentile for math, but for some reason is easy to get into - from Big Future 'Virginia Polytechnic Institute and State University is less selective with an acceptance rate of 70%. Students that get into Virginia Polytechnic Institute and State University have an SAT score between 1180–1390 or an ACT score of 26–32'When I read that my eyes bulge - that is far too easy for a school of that quality - maybe there is some self-selection going on - don't really know. Anyway since it is basically a waiting game here are two books I suggest:

Boaz: https://www.amazon.com/dp/0471198269/?tag=pfamazon01-20
Hubbard: https://matrixeditions.com/5thUnifiedApproach.html

Taken together will give you a great foundation and an excellent head start in both pure and applied math.

Thanks
Bill

 

[WWGD]

You can do it. Just remember that it's a long way to the top if you want to Mathematics. ;) (AC/DC)

 

[gleem]

I have always been told that mathematicians are for pure genius and the more I learn the more I start to be scared. What if I am not suitable for learning math? This is my biggest fear.

@Eveeeeeelynzzz Please read this article. https://talentdevelop.com/articles/HTBAG.html

 

[omega]

Rigor and intuition are both important in math. Try the books How to Prove It and How to Solve It

 

[jedishrfu]

Curiously I found this book on Amazon with good reviews while looking fr the How to Prove It book:

https://www.amazon.com/dp/052171978X/?tag=pfamazon01-20

How to Prove It
https://www.amazon.com/dp/1108439535/?tag=pfamazon01-20

and How to Solve It

https://www.amazon.com/dp/069116407X/?tag=pfamazon01-20

 

[jedishrfu]

My favorites are:

Mathematics: From the Birth of Numbers by Gulberg with great asides on math history:

https://www.amazon.com/dp/039304002X/?tag=pfamazon01-20

and Mathematics 1001 by Elwes which has nice summaries of many math topics so you can search on them if interested:

https://www.amazon.com/dp/B0791M9X4P/?tag=pfamazon01-20

 

[Muu9]

Read books by Lara Alcock, specifically "How to study as a mathematics major" and "How to study for a mathematics degree". If you want to get a taste of proofs, check out Book of Proof by Hammack (free)

Just wanted to mention that the first is for US student while the second is for UK students

 

[mathwonk]

here is a famous mathematician weighing in on the question:
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

 

[bhobba]

here is a famous mathematician weighing in on the question:
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

I want to mention you may think that's OK for a genius like Terry to say. A little-known fact about Terry is he took QM undergrad at Flinders University, where they designed a special program for him, so he graduated with a Master's at 16. Of course, he breezed through all his math subjects but came a cropper with QM. It was not because he didn't know QM or anything like that. The problem was an assignment where he had to research the history of QM. His normal practice was to cram the night before an exam. Well, it turned out that a large number of marks on the final was to write up the history of QM. He flunked - yes, the great Terry Tao flunked QM. Evidently, he was inconsolable - but learned a valuable lesson. It doesn't matter who you are; you must do the work.

As an aside, Terry was concerned a few years ago with the quality of math education in Australia:
https://terrytao.wordpress.com/2008...ics-at-the-university-of-southern-queensland/

I am happy to report since then, things have changed significantly. When I did my math degree, they changed from a BSc with a major in Math to a rather unique degree, an actual Bachelor of Mathematics. That has now taken off like wildfire - nearly all institutions offer a Bachelor of Mathematics, including Flinders, where Terry went. They also offer a unique degree you take while doing any other degree:
https://handbook.flinders.edu.au/courses/2023/BLITTMT

The government has also come to the table, and now math degrees are the lowest cost of all degrees. About $4k py. For comparison, a Bachelor of Political Science costs about $16k py.

Thanks
Bill

 

[symbolipoint]

they changed from a BSc with a major in Math to a rather unique degree, an actual Bachelor of Mathematics.

Probably not on the point, but the statement quoted seems a little strange. Distinction between "BSc with major in Math" and "actual Bachelor of Mathematics"? (I did not read the linked article).

 

[bhobba]

Probably not on the point, but the statement quoted seems a little strange. Distinction between "BSc with major in Math" and "actual Bachelor of Mathematics"? (I did not read the linked article).

My old alma mater was the first in Aus to do it. In most universities in Australia and the US, you get a Bachelor of Arts in Math or a Bachelor of Science in Math. It didn't change the subjects you take, but to give it a higher profile, they created a degree called a Bachelor of Mathematics rather than a Bachelor of Arts or Bachelor of Science. It's simply a marketing thing to raise the profile of a math degree. I thought I piped the change when I got my degree and told people I had a Bachelor of Mathematics - but technically, when I got my academic transcripts, it just missed the change, and I got a BSc majoring in Math and Computer Science.

My old alma mater has replaced the double major in Math and Computing with a Bachelor of Mathematics, including a major in Data Science or Computational Science:

https://www.qut.edu.au/courses/bach...E09Z1bqUVqkUCBJnHJKPFY_Sm3ilST2RoC39EQAvD_BwE

But you can double major in tons of stuff like Math- Physics, Math-Finance, etc.

Since then, many universities have followed suit.

Thanks
Bill