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I'm studying Mathematics in the UK. Back in Italy, where I am from worked-out problems books are very popular in mathematics and they are always recommended or compulsory at university. Going through some of them I found them extremely helpful and interesting.

Hence, I wanted to know if you can give me some lists of great (and possibly modern!) books were the main focus (if not the only, that'd be better!) is to solve problems.

I am not looking for books such as "problem solving in mathematics" or "how to think like a mathematician". I mean books like "Worked Examples in Applied Mathematics" by HART.

I would like to know if you know any in the following areas:

  1. Applied Mathematics (Kinematics, Particle Motion, Fluid Dynamics, etc, even more advanced)
  2. Probability (Distributions problems, Bernoulli, Poisson, Normal, Gamma, Beta, Erlang, etc)
  3. Statistics (Confidence Intervals, Hypothesis Testing, Clinical Trials, etc)
  4. Core Mathematics (Analysis, ODEs, PDEs, etc)
  5. Vector Calculus/Complex Variable (Stokes, Greens, Divergence, Cauchy, etc..)
  6. OR

I know this is probably the best place for this. However I know the community of StackExchange is very active and prolific, so I am sure anyone will have some recommendations. I will mark as a final answer just the most useful and comprehensive list, which actually will suggest problem-based books.

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    $\begingroup$ I think the Schaum's Outline series may have (some of) what you are looking for. $\endgroup$ – Michael Joyce Dec 1 '16 at 14:17
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I can give you some: Collection of Problems in probability theory - Leo F. Boron One Thousand Exercises in Probability - Grimmett Theory and Problems of theoretical mechanics - Spiegel

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There aren't many, however Introduction to Applied Mathematics by Strang is good,McGraw-Hill Introduction to the theory of probability and statistics is great too, and Complex Variables and Applications by McGraw-Hill again.

Hope this helps

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