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#math #books

Очередная подборка книг по математике

https://www.reddit.com/r/maths/comments/14budyz/comment/jykhuyv/

Копирую сюда на всякий случай. Также рекомендую почитать другие коменты этого человека https://www.reddit.com/user/srsNDavis/



We can answer better if you specify individual topics, but without an explicit topic, my general recommendations would be:

Best Beginner's Book: 'Advanced Problems in Mathematics'. This is a great (and free) text on the art of problem-solving. This is really a book on 'how to think like a mathematician', which is why it's often recommended as prep for those who want to take up maths in university.

Best Prep for Maths at University: 'Proofs' (Cummings) outlines the art of writing proofs and how to make sound inferences in mathematics (here's a free alternative). 'Proofs and Fundamentals' (Bloch) may be used for a university course. Another great text is 'Mistakes in Geometric Proofs' (Dubnov). This is narrower, but highly recommended nonetheless, because learning to spot misleading proofs or unreasonable inferences is at least as critical a skill as drawing the right inferences and writing correct and concise proofs.

Best Prep for Graduate Mathematics: 'All the Mathematics You Missed' (Garrity). This is a crash course of the big ideas in virtually everything you'd study if you go for a bachelor's in mathematics. I like how the author breaks down each topics into big ideas (e.g. fundamental objects of study, fundamental theorems, etc.), though for topics you have never seen before, you should probably supplement this book with other resources (from this answer or any other great answers you get).

Best Higher Maths: Controversially, I recommend 'A Course in Higher Mathematics' (Smirnov). Covers calculus, modern algebra (linear algebra and abstract algebra), complex variables and special functions, integral and partial differential equations, functional analysis. Mostly stuff you learn in your typical BSc, but with occasional advanced topics thrown into the mix. Smirnov might be a terse read (like most other Soviet-era books), but it's highly recommended for its rigour and content coverage.

Best in Discrete Maths: As someone with a mathematics and CS background, it has to be 'Concrete Mathematics' (Graham, Knuth, Patashnik). I'm biased towards this book because it's quite an entertaining read - something you can't really say about all the recommendations here (at least not unless the beauty of pure mathematics has dawned on you). 'Discrete Mathematics' (Biggs) is another common resource used at university. The latter text can bridge nicely into modern algebra.

Best in Number Theory: The classic text is 'An Introduction to the Theory of Numbers' (Hardy & Wright). This is a great introduction and also includes lists for further reading about particular topics, should you get interested along the way. 'A Friendly Introduction to Number Theory' (Silverman) may be more readable when starting out. 'Elements of Number Theory' (Vinogradov) is another good text that starts off with what should be familiar terrain - divisibility - to ease you into number theory.

Best in Algebra: 'Algebra' (Lang) should be titled 'The Algebra Bible'. It has enough to put you in a position to produce research at the PhD level. Lots of advanced stuff here (I don't claim to understand all of it... Yet), but like Smirnov, could be a slightly terse read. (This is a great point to admit my bias towards advanced maths in this answer, mainly because I'm at a relatively advanced level in learning mathematics, but also because having good resources for higher maths can make or break folks' interest in the subject)

Best Intro to Modern Algebra: 'Galois Theory' (Edwards) is an unconventional introduction which focuses on introducing concepts without losing focus of the problem they were formulated to address. 'Contemporary Abstract Algebra' (Gallian) is a more traditional introductory text (groups --> rings --> fields --> special topics, as you would proceed in a standard one or two-semester course at university)

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167 viewsJan 6, 2024 at 07:31

#math #books

Очередная подборка книг по математике

https://www.reddit.com/r/maths/comments/14budyz/comment/jykhuyv/

Копирую сюда на всякий случай. Также рекомендую почитать другие коменты этого человека https://www.reddit.com/user/srsNDavis/



We can answer better if you specify individual topics, but without an explicit topic, my general recommendations would be:

Best Beginner's Book: 'Advanced Problems in Mathematics'. This is a great (and free) text on the art of problem-solving. This is really a book on 'how to think like a mathematician', which is why it's often recommended as prep for those who want to take up maths in university.

Best Prep for Maths at University: 'Proofs' (Cummings) outlines the art of writing proofs and how to make sound inferences in mathematics (here's a free alternative). 'Proofs and Fundamentals' (Bloch) may be used for a university course. Another great text is 'Mistakes in Geometric Proofs' (Dubnov). This is narrower, but highly recommended nonetheless, because learning to spot misleading proofs or unreasonable inferences is at least as critical a skill as drawing the right inferences and writing correct and concise proofs.

Best Prep for Graduate Mathematics: 'All the Mathematics You Missed' (Garrity). This is a crash course of the big ideas in virtually everything you'd study if you go for a bachelor's in mathematics. I like how the author breaks down each topics into big ideas (e.g. fundamental objects of study, fundamental theorems, etc.), though for topics you have never seen before, you should probably supplement this book with other resources (from this answer or any other great answers you get).

Best Higher Maths: Controversially, I recommend 'A Course in Higher Mathematics' (Smirnov). Covers calculus, modern algebra (linear algebra and abstract algebra), complex variables and special functions, integral and partial differential equations, functional analysis. Mostly stuff you learn in your typical BSc, but with occasional advanced topics thrown into the mix. Smirnov might be a terse read (like most other Soviet-era books), but it's highly recommended for its rigour and content coverage.

Best in Discrete Maths: As someone with a mathematics and CS background, it has to be 'Concrete Mathematics' (Graham, Knuth, Patashnik). I'm biased towards this book because it's quite an entertaining read - something you can't really say about all the recommendations here (at least not unless the beauty of pure mathematics has dawned on you). 'Discrete Mathematics' (Biggs) is another common resource used at university. The latter text can bridge nicely into modern algebra.

Best in Number Theory: The classic text is 'An Introduction to the Theory of Numbers' (Hardy & Wright). This is a great introduction and also includes lists for further reading about particular topics, should you get interested along the way. 'A Friendly Introduction to Number Theory' (Silverman) may be more readable when starting out. 'Elements of Number Theory' (Vinogradov) is another good text that starts off with what should be familiar terrain - divisibility - to ease you into number theory.

Best in Algebra: 'Algebra' (Lang) should be titled 'The Algebra Bible'. It has enough to put you in a position to produce research at the PhD level. Lots of advanced stuff here (I don't claim to understand all of it... Yet), but like Smirnov, could be a slightly terse read. (This is a great point to admit my bias towards advanced maths in this answer, mainly because I'm at a relatively advanced level in learning mathematics, but also because having good resources for higher maths can make or break folks' interest in the subject)

Best Intro to Modern Algebra: 'Galois Theory' (Edwards) is an unconventional introduction which focuses on introducing concepts without losing focus of the problem they were formulated to address. 'Contemporary Abstract Algebra' (Gallian) is a more traditional introductory text (groups --> rings --> fields --> special topics, as you would proceed in a standard one or two-semester course at university)

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