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TSAkatsuki0895
post May 12 2017, 06:43 AM, updated 7y ago

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Hello everyone,
I am trying to do some self learning on university level mathematics just for learning sake...
My math background is until A-levels pure math only..
Can anyone suggest where should i start with? Algebra, precalculus, calculus or others?

Critical_Fallacy
post May 12 2017, 10:00 AM

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QUOTE(Akatsuki0895 @ May 12 2017, 06:43 AM)
Hello everyone,
I am trying to do some self learning on university level mathematics just for learning sake...
My math background is until A-levels pure math only..
Can anyone suggest where should i start with? Algebra, precalculus, calculus or others?
If you are interested in physics-based courses, then consider teaching yourself the fundamentals of higher mathematics:

(1) Complex Analysis
(2) Linear Algebra (Determinants and Matrices)
(3) Vector Analysis (higher Calculus)
(4) Ordinary Differential Equations (including Laplace Transforms)
(5) Fourier Analysis

You should also take the opportunity to explore other mathematical interests:

(1) Elementary Number Theory
(2) Introduction to Metric and Topological Spaces
(3) Applied Statistics and Probability

This post has been edited by Critical_Fallacy: May 12 2017, 10:01 AM
mesothelium
post May 12 2017, 10:24 AM

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Nobel Prize winning physicist Gerard 't Hooft has a good set of links on how to become a GOOD theoretical physicist. If physics isn't your thing, note that he also has a section on "primary mathematics". This could be your first port of call.

Link below:
http://www.staff.science.uu.nl/~gadda001/g...athematics.html
maximR
post May 12 2017, 12:26 PM

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What are your aims? Do you want to use mathematics? Or are you interested in it for its own sake? I would recommend against going back to precalculus.
TSAkatsuki0895
post May 12 2017, 12:33 PM

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QUOTE(Critical_Fallacy @ May 12 2017, 10:00 AM)
If you are interested in physics-based courses, then consider teaching yourself the fundamentals of higher mathematics:

(1) Complex Analysis
(2) Linear Algebra (Determinants and Matrices)
(3) Vector Analysis (higher Calculus)
(4) Ordinary Differential Equations (including Laplace Transforms)
(5) Fourier Analysis

You should also take the opportunity to explore other mathematical interests:

(1) Elementary Number Theory
(2) Introduction to Metric and Topological Spaces
(3) Applied Statistics and Probability
*
Yes, I'm interested in​ physics... Aren't those maths too advance for me with only a-level pure maths background?
TSAkatsuki0895
post May 12 2017, 12:35 PM

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QUOTE(maximR @ May 12 2017, 12:26 PM)
What are your aims? Do you want to use mathematics? Or are you interested in it for its own sake? I would recommend against going back to precalculus.
*
I'm learning it so that i could understand physics better and interest... Should i start with algebra?
maximR
post May 12 2017, 12:45 PM

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QUOTE(Akatsuki0895 @ May 12 2017, 12:35 PM)
I'm learning it so that i could understand physics better and interest... Should i start with algebra?
*
I see. You mentioned university level mathematics. Bear in mind that university level mathematics for students interested in it for its own sake is a whole different story. For example, linear algebra for mathematicians cover abstract finite-dimensional vector spaces and linear maps between them, but physicists are largely uninterested in proofs and abstract properties and structures, so the course would focus more on doing computations with matrices.

Likewise, "algebra" in mathematics is about groups, rings, fields, and modules, which might not seem like algebra at all to those who are unfamiliar with modern mathematics.

Anyway, click here for very useful text on mathematical methods for physicists. The topics are pretty standard; undergraduates learn mostly the same topics all over the world.

This post has been edited by maximR: May 12 2017, 12:45 PM
maximR
post May 12 2017, 12:48 PM

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QUOTE(Akatsuki0895 @ May 12 2017, 12:33 PM)
Yes, I'm interested in​ physics... Aren't those maths too advance for me with only a-level pure maths background?
*
No. You could start with linear algebra, and then vector calculus, in that order. Don't worry too much about prerequisites; A-Level Mathematics doesn't cover too much important ground anyway. It's a waste of time, in my opinion.

This post has been edited by maximR: May 12 2017, 12:49 PM
maximR
post May 12 2017, 12:52 PM

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By the way, I think it's a good idea to study mathematical methods in tandem with the subject you're pursuing. That way, you don't constantly ask yourself "Why am I doing this?".

For example, you can pick up basic vector calculus from a good introductory book on electrodynamics. Search for Griffith's Electrodynamics and Purcell's Electricity & Magnetism in your library. Griffith's has an introductory chapter on vector calculus, and Purcell's includes one in its appendices. Similarly, you could always learn some linear algebra while reading a book on quantum mechanics. Shankar's book has a whole chapter devoted to vector spaces.

This post has been edited by maximR: May 12 2017, 12:53 PM
TSAkatsuki0895
post May 12 2017, 01:01 PM

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QUOTE(mesothelium @ May 12 2017, 10:24 AM)
Nobel Prize winning physicist Gerard 't Hooft has a good set of links on how to become a GOOD theoretical physicist. If physics isn't your thing, note that he also has a section on "primary mathematics". This could be your first port of call.

Link below:
http://www.staff.science.uu.nl/~gadda001/g...athematics.html
*
thanks for the link notworthy.gif
TSAkatsuki0895
post May 12 2017, 01:10 PM

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QUOTE(maximR @ May 12 2017, 12:48 PM)
No. You could start with linear algebra, and then vector calculus, in that order. Don't worry too much about prerequisites; A-Level Mathematics doesn't cover too much important ground anyway. It's a waste of time, in my opinion.
*
i feel so too... The thing is during, a-levels i am only doing exercise questions without exploring deeper into the subject... for example, what is Euler's number,why does dy/dx gives us the gradient at a particular point and how complex number is used in real life applications and etc.. I am finding to all those questions now. Even after googling , i cant seem to understand sweat.gif . Which is why i m trying to learn more about this subject.

maximR
post May 12 2017, 01:26 PM

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QUOTE(Akatsuki0895 @ May 12 2017, 01:10 PM)
i feel so too... The thing is during, a-levels i am only doing exercise questions without exploring deeper into the subject... for example, what is Euler's number,why does dy/dx gives us the gradient at a particular point and how complex number is used in real life applications and etc.. I am finding to all those questions now. Even after googling , i cant seem to understand  sweat.gif . Which is why i m trying to learn more about this subject.
*
Well, the rigorous definition of e, and the treatment of a derivative using limits are dealt with in sufficient detail in real analysis, a branch of mathematics. But you're right, these things require some background in mathematical proofs, which might be alien to most students who are only used to doing computations.

But if you want a gentle explanation of these matters without going into too much detail (presumably on the same plane as A-Level Mathematics), then there are plenty of resources. Are you familiar with the old red book by Bostock & Chandler, titled Mathematics: The Core Course for A-Level? It has a discussion on derivatives which might satisfy you. I think f(x) = e^{x} is defined in the book to be an exponential function which has a slope of 1 at x=0.

Of course, more advanced courses would give more rigorous definitions.
TSAkatsuki0895
post May 12 2017, 01:39 PM

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QUOTE(maximR @ May 12 2017, 01:26 PM)
Well, the rigorous definition of e, and the treatment of a derivative using limits are dealt with in sufficient detail in real analysis, a branch of mathematics. But you're right, these things require some background in mathematical proofs, which might be alien to most students who are only used to doing computations.

But if you want a gentle explanation of these matters without going into too much detail (presumably on the same plane as A-Level Mathematics), then there are plenty of resources. Are you familiar with the old red book by Bostock & Chandler, titled Mathematics: The Core Course for A-Level? It has a discussion on derivatives which might satisfy you. I think f(x) = e^{x} is defined in the book to be an exponential function which has a slope of 1 at x=0.

Of course, more advanced courses would give more rigorous definitions.
*
No, the only A-levels maths book that i m familiar with are the blue pure maths books XD .... but those books dont really go into details. I might be able to get that red book in my uni library tho..Anyway, thanks for the guide... I will start with linear algebra first since i m interested in quantum mechanics notworthy.gif ... icon_rolleyes.gif
maximR
post May 12 2017, 01:44 PM

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QUOTE(Akatsuki0895 @ May 12 2017, 01:39 PM)
No, the only A-levels maths book that i m familiar with are the blue pure maths books XD .... but those books dont really go into details. I might be able to get that red book in my uni library tho..Anyway, thanks for the guide... I will start with linear algebra first since i m interested in quantum mechanics  notworthy.gif ... icon_rolleyes.gif
*
My pleasure. I like helping out others who want to learn mathematics/physics (though I spend most of my time on maths now...). It's a shame that most people live their lives unaware of their beauty.

All right. My two cents: Don't be discouraged if you get stuck. Keep persevering, ask around, mull it over at night before you sleep, do calculations on paper, etc..

Have fun.
LightKeyDarkBlade
post May 13 2017, 01:46 AM

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For a start, you can look into A-Level Further Mathematics (which I assume you didn't take this subject?). It can be said to be equivalent to first year maths at university level.

You can also look into STPM Mathematics which I heard is more difficult than A-Level Mathematics (but I'm not sure about this).

Are you only interested in pure mathematics? From what I can infer from your posts (but I may be wrong), mechanics could be suitable for you too.

Many things that we've learned prior to and including A-Level, we didn't really explore the roots and the backgrounds. Once you've touched the mathematical proofs (which may not be easy), you'll have more proper understanding.

Have fun indulging in maths.
Kcdw96
post May 13 2017, 03:23 PM

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If I were you, I'd start on a course on discrete mathematics. It helps you to view maths from a different perspective, ie the logic and intuition behind relatively simple facts like why 1+1=2 or why is e irrational?

After that, I would follow up on a course on linear algebra and probability, things which for some reason, are not taught much in school. In my opinion, studying more calculus is not as useful as studying the above topics, as A level maths (if you get a good grade) already provides a good foundation for studying and understanding calculus concepts, should the need arise. Meaning, should you see a differential equation you don't understand, chances are that after googling for a while you should be able to understand it on your own.
TSAkatsuki0895
post May 13 2017, 07:26 PM

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QUOTE(LightKeyDarkBlade @ May 13 2017, 01:46 AM)
For a start, you can look into A-Level Further Mathematics (which I assume you didn't take this subject?). It can be said to be equivalent to first year maths at university level.

You can also look into STPM Mathematics which I heard is more difficult than A-Level Mathematics (but I'm not sure about this).

Are you only interested in pure mathematics? From what I can infer from your posts (but I may be wrong), mechanics could be suitable for you too.

Many things that we've learned prior to and including A-Level, we didn't really explore the roots and the backgrounds. Once you've touched the mathematical proofs (which may not be easy), you'll have more proper understanding.

Have fun indulging in maths.
*
u are right, i did not take further math during my a-levels. i might give it a go...
and yea , i can confirm that STPM math is more difficult because their syllabus is broader than a-levels normal math. I've never tried a-level further maths so i m not sure how is it compared to stpm maths.
i m interested in the roots and the background and how it is used in physics. i m not so into mechanics. however, i feel the need to master mechanics cause it seems like most of derivatives involves mechanics.
and thanks for ur suggestions thumbup.gif will definitely give it a go

This post has been edited by Akatsuki0895: May 13 2017, 09:03 PM
TSAkatsuki0895
post May 13 2017, 07:35 PM

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QUOTE(Kcdw96 @ May 13 2017, 03:23 PM)
If I were you, I'd start on a course on discrete mathematics. It helps you to view maths from a different perspective, ie the logic and intuition behind relatively simple facts like why 1+1=2 or why is e irrational?

After that, I would follow up on a course on linear algebra and probability, things which for some reason, are not taught much in school. In my opinion, studying more calculus is not as useful as studying the above topics, as A level maths (if you get a good grade) already provides a good foundation for studying and understanding calculus concepts, should the need arise. Meaning, should you see a differential equation you don't understand, chances are that after googling for a while you should be able to understand it on your own.
*
i will stick to linear algebra for now as i've already borrowed the book on linear algebra from my uni's library.
probably after linear algebra then i will try out discrete math. thanks for the suggestion biggrin.gif
maximR
post May 13 2017, 09:34 PM

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QUOTE(Kcdw96 @ May 13 2017, 03:23 PM)
If I were you, I'd start on a course on discrete mathematics. It helps you to view maths from a different perspective, ie the logic and intuition behind relatively simple facts like why 1+1=2 or why is e irrational?

After that, I would follow up on a course on linear algebra and probability, things which for some reason, are not taught much in school. In my opinion, studying more calculus is not as useful as studying the above topics, as A level maths (if you get a good grade) already provides a good foundation for studying and understanding calculus concepts, should the need arise. Meaning, should you see a differential equation you don't understand, chances are that after googling for a while you should be able to understand it on your own.
*
Firstly, TS is interested in physics. Discrete mathematics, while fun, has no immediate relevance. Calculus, however, is absolutely crucial. When I say calculus, I mean all the necessary methods a physicist needs: differential & integral calculus of one and several variables, complex methods, differential equations, fourier analysis, and so on, which are not covered in A-Level Mathematics.

I find your comment that A-Level Mathematics provides a good foundation for understanding calculus puzzling. I'd say A-Level Mathematics is close to useless when it comes to university level mathematics or mathematical methods for the sciences. It's just a hoop everyone is expected to jump over.
maximR
post May 13 2017, 09:37 PM

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What do you mean by "the logic and intuition behind 1+1 =2"? confused.gif

Also, how is the fact that "e is irrational" simple? laugh.gif

This post has been edited by maximR: May 13 2017, 09:37 PM

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