Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

The author introduces all central proofs required for a one-semester long module on real analysis in an easily understandable and comprehensive approach. I will facilitate mastering the challenging, abstract syllabus of any undergraduate maths curriculum. However, every year-long modules will cover more topics and at greater depth, requiring an additional good textbook like Elementary Real Analysis by Bruckner, Thompson, Thompson. Nonetheless, the value of the book is at least 10 times as high as its very fair price, and it ought to be purchased as a treatise that covers the main proofs in all steps and details - way better than any video-course on YouTube.

I have a number of RA texts and I have to say this one really impressed. Obviously the thoroughness is there (it's a big book for such a low price) but what impressed most is the sketches of proofs before the proofs and the explanations within. The author really goes to great depths to fully explain everything which makes this an excellent text for self learners. Highly recommend, along with the author's other text on Proof. Hints to exercises are on his website, but I would have liked a more substantial bank of solutions.

Very well-written book and I enjoy the constant humour littered in.

All OK

If you are buying a first book in Real Analysis then this is the one, especially if you are quite new to proof in general. This book is much less terse than your typical Analysis book. You can use this book to build mathematical maturity and then move on to the more concise books. The author has done an amazing job here and deserves a lot of credit.

Start with this one

Nicely written account and very affordable

The book lacks examples; it's just a collection of theorems and proofs. I don't recommend starting real analysis with this book.

good way of presenting the matter

It costs a little higher vis a vis Indian market ,but it is worth every penny spent , because it teaches you , in a cheerful mood. Author not only presents the contents within a comprehensive single thread , he also breaks ur boredom , if any, with his witty remarks and humour ! Great book, strongly recommended. It is actually an introductory real analysis book, but deserves appreciation. Page and printing worth appreciation as well.

Very well written.

Questo testo è il link ideale fra i corsi di Calculus e Real Analysis così come vengono chiamati in UK/US. In Italia siamo meno abituati a questa distinzione, perchè almeno i nostri vecchi corsi di Analisi assumevano l'una e l'altra veste. In ogni caso, sia nello studio da autodidatta che di preparazione preliminare a corsi più avanzati, questo ottimo libro accompagna il lettore nel viaggio alla scoperta delle strategie di dimostrazione e del linguaggio tipico dell'Analisi Matematica. L'inglese utilizzato è davvero di facile comprensione e l'esposizione è informale quando opportuno, al tempo stesso è rigorosa nella presentazione delle definizioni, teoremi e dimostrazioni finali. Per alcune dimostrazioni si adotta una strategia graduale, prima una bozza informale e alla fine la "vera" dimostrazione, inutile dire come questo abbia un gran valore pedagogico, cosa di cui i testi più comuni devono fare necessariamente a meno. Il contenuto tocca gli argomenti tipici di un primo corso di Analisi: numeri reali, successioni e serie numeriche, limiti, continuità, differenziazione, integrazione, successioni e serie di funzioni. Consiglio di utilizzarlo come accompagnamento ai testi tradizionali sugli stessi argomenti.

Profundo, pero agradable de leer. Está en mis top. Ojalá hubiera tenido un libro así cuando estudié la carrera. Muy recomendable.