Ask HN: How to learn advanced maths
I studied physics as my undergraduate degree and, as such, only really studied up to differential equations in a pure maths context. However, since graduating, I've been working mostly as a maths teacher, and it's made me much more interested in learning more about advanced math, outside the basic geometry, algebra and calculus we teach. It's also made me much more interested in learning about rigorous mathematical proofs, especially in a research framework. Does anyone have any good textbooks or resources to help self-educate myself on more advanced maths? I still have my linear algebra and diff. eqs books that I'll go through again, but I'd love other recommendations. I've found the post series on Quantstart [1], which looks like it was never completed, and I know HN has discussed them some before ([2] being one example) but was wondering about anything else you all might know about besides going back to school (which I seriously might do, to be honest; teaching it has made me really fall in love with maths again, and made me regret studying physics as opposed to maths!). I do know this is vague, and mathematics is a huge field with lots of subbranches, so just any resource you'd like to recommend to any of those subbranches, or, perhaps, something of how an undergraduate curriculum would work leaning up to graduate level work? Thanks in advance! [1]https://ift.tt/1MbWk46 [2]https://ift.tt/1LgPGig ETA: I would much prefer materials that have solutions readily available. Since I am self-teaching, I want to be able to confirm my answers to problems without resorting to MathOverflow or other resources every time. Of course, I am not against materials without solutions, especially if they are the best materials available. 2 comments on Hacker News.
I studied physics as my undergraduate degree and, as such, only really studied up to differential equations in a pure maths context. However, since graduating, I've been working mostly as a maths teacher, and it's made me much more interested in learning more about advanced math, outside the basic geometry, algebra and calculus we teach. It's also made me much more interested in learning about rigorous mathematical proofs, especially in a research framework. Does anyone have any good textbooks or resources to help self-educate myself on more advanced maths? I still have my linear algebra and diff. eqs books that I'll go through again, but I'd love other recommendations. I've found the post series on Quantstart [1], which looks like it was never completed, and I know HN has discussed them some before ([2] being one example) but was wondering about anything else you all might know about besides going back to school (which I seriously might do, to be honest; teaching it has made me really fall in love with maths again, and made me regret studying physics as opposed to maths!). I do know this is vague, and mathematics is a huge field with lots of subbranches, so just any resource you'd like to recommend to any of those subbranches, or, perhaps, something of how an undergraduate curriculum would work leaning up to graduate level work? Thanks in advance! [1]https://ift.tt/1MbWk46 [2]https://ift.tt/1LgPGig ETA: I would much prefer materials that have solutions readily available. Since I am self-teaching, I want to be able to confirm my answers to problems without resorting to MathOverflow or other resources every time. Of course, I am not against materials without solutions, especially if they are the best materials available.
I studied physics as my undergraduate degree and, as such, only really studied up to differential equations in a pure maths context. However, since graduating, I've been working mostly as a maths teacher, and it's made me much more interested in learning more about advanced math, outside the basic geometry, algebra and calculus we teach. It's also made me much more interested in learning about rigorous mathematical proofs, especially in a research framework. Does anyone have any good textbooks or resources to help self-educate myself on more advanced maths? I still have my linear algebra and diff. eqs books that I'll go through again, but I'd love other recommendations. I've found the post series on Quantstart [1], which looks like it was never completed, and I know HN has discussed them some before ([2] being one example) but was wondering about anything else you all might know about besides going back to school (which I seriously might do, to be honest; teaching it has made me really fall in love with maths again, and made me regret studying physics as opposed to maths!). I do know this is vague, and mathematics is a huge field with lots of subbranches, so just any resource you'd like to recommend to any of those subbranches, or, perhaps, something of how an undergraduate curriculum would work leaning up to graduate level work? Thanks in advance! [1]https://ift.tt/1MbWk46 [2]https://ift.tt/1LgPGig ETA: I would much prefer materials that have solutions readily available. Since I am self-teaching, I want to be able to confirm my answers to problems without resorting to MathOverflow or other resources every time. Of course, I am not against materials without solutions, especially if they are the best materials available. 2 comments on Hacker News.
I studied physics as my undergraduate degree and, as such, only really studied up to differential equations in a pure maths context. However, since graduating, I've been working mostly as a maths teacher, and it's made me much more interested in learning more about advanced math, outside the basic geometry, algebra and calculus we teach. It's also made me much more interested in learning about rigorous mathematical proofs, especially in a research framework. Does anyone have any good textbooks or resources to help self-educate myself on more advanced maths? I still have my linear algebra and diff. eqs books that I'll go through again, but I'd love other recommendations. I've found the post series on Quantstart [1], which looks like it was never completed, and I know HN has discussed them some before ([2] being one example) but was wondering about anything else you all might know about besides going back to school (which I seriously might do, to be honest; teaching it has made me really fall in love with maths again, and made me regret studying physics as opposed to maths!). I do know this is vague, and mathematics is a huge field with lots of subbranches, so just any resource you'd like to recommend to any of those subbranches, or, perhaps, something of how an undergraduate curriculum would work leaning up to graduate level work? Thanks in advance! [1]https://ift.tt/1MbWk46 [2]https://ift.tt/1LgPGig ETA: I would much prefer materials that have solutions readily available. Since I am self-teaching, I want to be able to confirm my answers to problems without resorting to MathOverflow or other resources every time. Of course, I am not against materials without solutions, especially if they are the best materials available.
Hacker News story: Ask HN: How to learn advanced maths
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October 27, 2018
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