Exercises in Analysis: Part 1 - Problem Book in Mathematics | Advanced Calculus Practice for University Students & Self-Study

Mathematicians, Physicists, STEM teachers and students, as well as older Engineers like me, who grew up with the 1,000 page plus REA Problem Solvers series (eg: Finite and Discrete Math Problem Solver (Problem Solvers Solution Guides)), will be overjoyed at this new series.There are two senses in which it is a wonderful new approach-- first, it is one of a kind in topic (analysis, as you know touches thousands of subjects in and out of math), and second, it is completely focused on problem solving, as in advanced exam prep. I'm a quantitative/ math volunteer at preptorial dot org and our lives there are about the best test prep tools available. Today, this is a tough job because many text authors (or more specifically their publishers) love "splitting" their work into a series of expensive instructor and student student manuals, to make even more money after gouging students with the primary text.Not so this text! All questions and answers are given in the text, and the focus is on problem solving-- giving exercises relevant to the material, then giving problems marked by difficulty level with fully explained solutions. Note that this material is clearly graduate level, or very bright ready for grad undergrad math majors. Even the "easier" problems are professional exam level.The text is the most up to date analysis text out, regardless of format. I review hundreds of these for preptorial and none comes even close if your objective is problem solving or exam prep. In fact, going back even 10 years, the only series that even comes close is the outstanding MIT/China PhD series of test prep, and they are not nearly as comprehensive or up to date at this volume (example: Problems and Solutions on Thermodynamics and Statistical Mechanics (Major American Universities Ph.D. Qualifying Questions and Solutions) published by World Scientific Pub Co Inc (1990)).In today's desktop supercomputing, Matlab, Mathcad, GNU Octave, NumPy worlds, "analysis" can be limited to formula application in some narrow definitions. That runs counter to the real world problems today that involve all four tools-- analysis, qualitative, numeric and stochastic. Amazingly, even with the analysis title, the problem set up and definition techniques are just like the exams-- and I see the real ones every day-- and DO NOT shy away from all three other techniques.The price at $70 US from Springer is a shocker-- 1,000 page technical books from this publisher, especially with good journal references, are normally $300 plus and often don't even have websites or solution manuals, let alone complete solutions IN the text.Given the formula formats, with thick graduate level notation on every page, I'd be extremely suspicious of a Kindle version if we get one, and also, there is an e-book version on Springer dot com but it costs $70 US anyway!Although there is no "look inside" (Springer: please?), the Springer site has a brief shot of metric spaces that isn't helpful as it doesn't let you know that the "easy" problems are still grad level! Here is the missing table of contents:1. Metric Spaces.- 2. Topological Spaces.- 3. Measure, Integral, and Martingales.- 4. Measures and Topology.- 5. Functional Analysis.- Other Problem Books.- List of Symbols.- IndexHighly recommended for all fields involving analysis, especially functional analysis, but also the numerous applications of stochastic techniques like Martingales, as long as you bear in mind the quick/graduate level of the material. Even the hints, explanations and "easy" problems assume you've completed grad level analysis courses and are ready to "learn by doing" problems and solutions you'll encounter in interviews, real life applications, and advanced professional and academic exams.Every time I make that comment in a review, a smart undergrad emails to say they even find the hard problems easy, but I'd rather take that risk than have you pay this much only to find you're lost even in the "easy" problems. You have to learn this by doing, and the undergrads I teach, even in the advanced MIT and Coursera online courses FOR grads in topics like advanced quantum computing, are sometimes lost with real number/set mapping notation without review. And with today's numeric techniques and algorithms lurking beneath every function, even in analysis, you HAVE to know your matrix manipulations. That's not to take away at all from the execution of this volume, bravo Dr. Gasinski and Springer for contributing to the problem/solution field in so fine a fashion.Emailer answer: Self teaching? Yes and no. Due to the fine explanations, this would be great for test prep without an instructor, BUT you might also have a lot of questions that you'd have to look up as you go along in other analysis texts or online. The bibs are excellent, and sites like preptorial dot org and textextras dot com are preparing adjuncts and online ponies for these volumes right now.