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What is a math major really like? (1 Viewer)

yanujw

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I'm planning on doing a Bachelor of Economics at USYD beginning in 2023, and since I can pick two majors, I was considering mathematics to be one of them. I've always been very good at math, and learn independently and take a natural interest in the subject. My main concern is that uni math becomes 'dull' - rather than learning interesting concepts like binomial theorem and projectile motion, I feel like uni math tends to the less engaging topics of proof, math history and very technical concepts.
So I have to ask...

1) How much is uni math like high school math, in terms of learning and understanding a concept, practicing it and then gaining proficiency in doing hard questions? I've heard uni math is more proof based and focuses more on concepts rather than practice.
2) What careers/fields can uni math take you from just an undergrad level? Is it a good complement to an economics degree?
3) As a fallback option, if I study a math major in undergrad, is that sufficient enough to go into high school teaching if I choose to down the road?


@dan964 @Trebla @CM_Tutor @Paradoxica @quickoats tagging you guys in particular because I recall that you studied math/ know a bit about the field
But if anyone has any useful insight, please do let me know!
 

5uckerberg

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I'm planning on doing a Bachelor of Economics at USYD beginning in 2023, and since I can pick two majors, I was considering mathematics to be one of them. I've always been very good at math, and learn independently and take a natural interest in the subject. My main concern is that uni math becomes 'dull' - rather than learning interesting concepts like binomial theorem and projectile motion, I feel like uni math tends to the less engaging topics of proof, math history and very technical concepts.
So I have to ask...

1) How much is uni math like high school math, in terms of learning and understanding a concept, practicing it and then gaining proficiency in doing hard questions? I've heard uni math is more proof based and focuses more on concepts rather than practice.
2) What careers/fields can uni math take you from just an undergrad level? Is it a good complement to an economics degree?
3) As a fallback option, if I study a math major in undergrad, is that sufficient enough to go into high school teaching if I choose to down the road?


@dan964 @Trebla @CM_Tutor @Paradoxica @quickoats tagging you guys in particular because I recall that you studied math/ know a bit about the field
But if anyone has any useful insight, please do let me know!
The third question. Yep, you can in fact I consider it overkill because the amount of maths teachers is scarce, they are always looking for more. In fact, if you do so you are going down Jonathan Le's direction (aka @Carrotsticks who is an legend that left Bored of Studies to become a maths teacher after completing his Bachelors majoring in maths) which is pretty beautiful. For me, I say more math you know more you can share to your students if you know how to communicate it in a way they can understand.


First question, uni math is basically in my heart about exploring the aesthetic nature of mathematics so first year is still computational things but already even then you are going to be introduced to discrrete maths which is pretty interesting stuff out there. Uni math is proof based especially if you are going to be bringing about Linear Algebra, Complex Analysis. A lot of this is just understanding the proof and finding the steps involved.

A big difference is that in high school formulas constitute the whole course but in uni just knowing the formula is not enough to know what is happpening here. Nope you need to understand the generalised forms of the formula and they can get very interesting.
 

jazz519

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I have just completed a math minor recently so haven't done all the maths subjects a person undertaking a major would go through but it varies a lot in terms of how interesting it is. But in general sense yes it's same where you understand the concept, practice it and then apply it to harder questions. Some of the topics that I covered at uni in my subjects included vector calculus, complex analysis (if you liked complex numbers stuff in HSC then this will be interesting and the questions are challenging and different), partial differential equations, statistics. So it is quite varied. I did the minor in maths for other reasons since I just wanted to have a good maths knowledge being a scientist as it's needed to understand physical chemistry properly since things like complex numbers and partial differential equations show up in the Schrodinger equation which describes the electron properties of an atom, molecule etc, so for me it wasn't that much fun more something I did for a better knowledge but if you are interested in maths prior to uni then yeah I would say it would be pretty good. It's also a very flexible major because technically you don't really need to go to class which is another reason I chose it as a minor because you can watch the lecture recordings / live online lectures these days with covid stopping in-person lectures. You basically only need to attend an in-person tutorial (once classes go back to normal after covid) which is 1-2 hours and there are no extra classes like labs or workshops that other majors have, so if you live a decent distance from the uni then it has that benefit too. It also means if you are self motivated you can do as many practice questions as you want in your own time, which I enjoyed doing that part of it which felt similar to how studying for maths in high school can be enjoyable doing past papers.

Question 2 can't really answer as don't know enough

Question 3, it is not exactly enough to become a teacher straight away. You will need to do a master of teaching (1-2 year degree) most likely to become a teacher since being a teacher is not all about just your knowledge on the subject but you need to be able to manage classes and all those other skills.
 
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5uckerberg

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I have just completed a math minor recently so haven't done all the maths subjects a person undertaking a major would go through but it varies a lot in terms of how interesting it is. But in general sense yes it's same where you understand the concept, practice it and then apply it to harder questions. Some of the topics that I covered at uni in my subjects included vector calculus, complex analysis (if you liked complex numbers stuff in HSC then this will be interesting and the questions are challenging and different), partial differential equations, statistics. So it is quite varied. I did the minor in maths for other reasons since I just wanted to have a good maths knowledge being a scientist as it's needed to understand physical chemistry properly since things like complex numbers and partial differential equations show up in the Schrodinger equation which describes the electron properties of an atom, molecule etc, so for me it wasn't that much fun more something I did for a better knowledge but if you are interested in maths prior to uni then yeah I would say it would be pretty good. It's also a very flexible major because technically you don't really need to go to class which is another reason I chose it as a minor because you can watch the lecture recordings / live online lectures these days with covid stopping in-person lectures. You basically only need to attend an in-person tutorial (once classes go back to normal after covid) which is 1-2 hours and there are no extra classes like labs or workshops that other majors have, so if you live a decent distance from the uni then it has that benefit too. It also means if you are self motivated you can do as many practice questions as you want in your own time, which I enjoyed doing that part of it which felt similar to how studying for maths in high school can be enjoyable doing past papers.

Question 2 can't really answer as don't know enough

Question 3, it is not exactly enough to become a teacher straight away. You will need to do a master of teaching (1-2 year degree) most likely to become a teacher since being a teacher is not all about just your knowledge on the subject but you need to be able to manage classes and all those other skills.
Combining mine and @jazz519's response knowledge wise yes but the pedagogy side hmm need a lot of work. Masters of Education is compulsory, but hey you know the essentials to running a classroom and all the other things like students with disabilities, gifted students and classroom management.
 

Trebla

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I'm planning on doing a Bachelor of Economics at USYD beginning in 2023, and since I can pick two majors, I was considering mathematics to be one of them. I've always been very good at math, and learn independently and take a natural interest in the subject. My main concern is that uni math becomes 'dull' - rather than learning interesting concepts like binomial theorem and projectile motion, I feel like uni math tends to the less engaging topics of proof, math history and very technical concepts.
So I have to ask...

1) How much is uni math like high school math, in terms of learning and understanding a concept, practicing it and then gaining proficiency in doing hard questions? I've heard uni math is more proof based and focuses more on concepts rather than practice.
2) What careers/fields can uni math take you from just an undergrad level? Is it a good complement to an economics degree?
3) As a fallback option, if I study a math major in undergrad, is that sufficient enough to go into high school teaching if I choose to down the road?


@dan964 @Trebla @CM_Tutor @Paradoxica @quickoats tagging you guys in particular because I recall that you studied math/ know a bit about the field
But if anyone has any useful insight, please do let me know!
1) After first year (which is basically an extension of Maths Ext2), maths in uni is very different to maths at high school. In high school, there is a lot of rote learning and bypassing of proper rigour. In uni maths, there is a lot more rigour involved (e.g. the formal definition of limits in calculus) and introduction of abstract concepts (e.g. matrices and linear algebra). You cannot do well in uni maths without properly understanding the underlying concepts. It is indeed more proof based, but in later years there are choices to branch out into the pure, applied and statistics. Judging by the HSC topics which you appear to interested and not interested in, it seems like applied mathematics and statistics is more your thing (which most certainly will be part of your economics degree).

2) In economics you will most certainly encounter many math concepts which extend beyond what you have covered in the HSC - in particular, optimisation, inequalities and statistics (albeit taught in a more rote-learning way to cater for students with weaker abilities in maths). Having the maths major with proper foundations of these concepts certainly helps. In terms of career path, I take it that you're pretty set on economics so having a maths major could open you up for more advanced quantitative roles in economics/finance/commerce which typically entails developing models to estimate particular metrics (e.g. more sophisticated versions of the linear regression you learnt in the HSC). For example, if you ever wondered how economists come up with their forecasts, there is usually someone who helped do some mathematical/statistical modelling to inform that.

3) If you want to go into high school teaching then naturally you need an education degree as well to be a qualified teacher.
 

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