Name: Problems in Mathematical Analysis
ISBN: 9780846407614

What Hacker News says

JugurthaOct 2023

"A Course of Higher Mathematics" - Smirnov

"Differential and Integral Calculus" - Piskunov

"Problems in Mathematical Analysis" - Demidovich (exercises/problems)

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JugurthaAug 2023

- "Differential and Integral Calculus", Piskunov.

- "A Course of Higher Mathematics", Smirnov. This one could be a bit expensive, but if you find yourself in a country that has had good relations with the former Soviet Union, you might find it a a really affordable price because they had licenses to print these books, and generally speaking, the MIR Publishers, Moscow, books.

- "Problems in Mathematical Analysis", Demidovich.

- "Course of Theoretical Physics", Landau.

- "Problems in General Physics", Irodov.

You'll note that there are "course" books and "problem" books in there.

All the best,

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hintymadJan 2023

For what level and in which area? Books like _Methods of mathematical physics_ can be both too hard and irrelevant to your needs. For starters,

To become a better problem solver with high-school level maths:

  - Polya's How to Solve It.
  - Books of your choice about math contests.
  - Concrete Maths. I understand that this book is taught in college, but it requires very little advanced maths, and its techniques are hugely useful for high school students too.

To hone my intuitions. I learned it the hard way that college maths were different from high school math: in high school, my teachers painstakingly drilled intuitions into us with very targeted explanations and tons of well designed exercises. In college, we won't get such luxury. So, it's really up to us to understand mathematical concepts intuitively before diving into technical details. For that matter, the following books helped me a lot:

  - The visual series. Visual Complex Analysis and Visual Group Theory, for instance
  - Pinter's A book of Abstract Algebra
  - Strichartz's The Way of Analysis
  - Linear Algebra Through Geometry by Wermer. The book offers a comprehensive geometric interpretation to linear algebra concepts. It's especially helpful for me to understand quadratic forms.

To understand Analysis better. This area is vast, so I'll skip recommendations of excellent text books:

   - _Counterexamples in Analysis_. Those counterexamples in Analysis play a huge role in helping me truly appreciate the intricacies of Analysis. Similarly, books like _Counterexamples in Probability and Real Analysis_ are of great help too.
   - The Way of Analysis by Robert S. Strichartz. This books is AMAZING for laymen like me. You'd want someone to *explain* how concepts emerge, and how intuitions evolve.

To become good at maths by doing maths, so the following books used to help me a lot:

  - Problems and Proofs in Real Analysis
  - Putnam and Beyond. I still suck at maths, but those well designed problems in Putnam really taught me how to seek insights in higher maths.
  - Piotr's Problems in Mathematical Analysis. But really, any problem books that challenge you will do. I'd recommend you find problem sets from the website of university courses. They cover essential techniques, and will not be as overwhelming as the books.

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JugurthaMay 2022

- "A Course of Higher Mathematics", V. I. Smirnov.

- "Differential and Integral Calculus", N. Piskunov.

- "Problems in Mathematical Analysis", B. Demidovich.

These are great books. Demidovich's book is a collection of more than 3000 exercises. Smirnov's book is a course that takes you from what a value means, to advanced topics (5 volumes, in 7 books). Piskunov's book is in-between (course and exercises).

These are the books we've used and went to during the first two years of Engineering (all engineers civil/mechanical/electrical/etc. and phys/maths/chem students go through the maths/phys/chem heavy common core except CS/SE students).

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JugurthaOct 2021

- "A Course of Higher Mathematics", VI Smirnov.

- "Problems in Mathematical Analysis", Demidovich.

- "Differential and Integral Calculus", Piskunov.

That's what our courses in university followed (first and second year), but also high-school teachers were inspired by as they studied these in university themselves. Smirnov takes you from the "concept of number" into the deep. Piskunov is cool and full of examples, including operational calculus and probability theory. Demidovich is a problems book to exercise your hand.

They are concise and to the point. Smirnov's has five volumes across seven books, though, but they're concise (density of information is high).

These books have examples from physics as well. For instance, I didn't understand enthalpy from my physics course until I read about continuity in Smirnov's book as he masterfully gave an example of discontinuity using enthalpy (phases of water).

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vkazanovAug 2021

Not sure about these after-class schools, but I can compare my ex-ussr school and uni education with math or CS undergrad textbooks I read a lot in English these day. Not sure about early education though.

1. Russian math books are straight to the point, superconcrete. Hard to read in a linear fashion but very useful when student is serious about going through it ("Problems in mathematical analysis" by Demidovich is a perfect example, Mark Vygodskiy's "Elementary Mathematics Reference").

2. In most textbooks I remember nobody tries to build a dumbed down explanation of things. This might lead to the book being harder to understand without teacher's help. I remember how some American undergrad-level introductory math analysis books were trying to skip proofs, avoid certain details, giving too many intuitive explanations ().

3. Mid and late school math is pretty advanced, especially when compared to US typical level.

These days I live in UK. Kids go to school early here: 4-5 years. My daugther is 6 and is comfortable with trivial math. I've read a few secondary school textbooks and they feel quite ok.

So maybe this is a US problem.

EDIT: a few example books added

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