Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
Product ID: 149823354
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This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com. This is the 2 + epsilon edition of this book. The second edition was published in July 2019. In January 2024, an epsilon of changes were made and the manuscript was updated, without officially creating a new edition. Review: Fantastic treatise of proof-extensive Real Analysis - 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. Review: A superb tour de force of Real Analysis with excellent proofs - 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.
| Best Sellers Rank | 46,252 in Books ( See Top 100 in Books ) 653 in Mathematics Teaching Aids 2,229 in Scientific, Technical & Medical |
| Customer Reviews | 4.8 out of 5 stars 826 Reviews |
K**L
Fantastic treatise of proof-extensive Real Analysis
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.
J**S
A superb tour de force of Real Analysis with excellent proofs
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.
D**.
Title your review
Very well-written book and I enjoy the constant humour littered in.
K**X
As advertised
All OK
T**R
A perfect introduction
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.
S**Z
101 real analysis in a sympathetic style
Start with this one
M**M
A great effort
Nicely written account and very affordable
A**R
No enough examples.
The book lacks examples; it's just a collection of theorems and proofs. I don't recommend starting real analysis with this book.
R**.
Teaches easily, most effectively.
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.
R**S
Great Book
Very well written.
V**O
Testo eccezionale
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.
N**I
One of the best real analysis books I have read so far
The chapters are very simple and have a lot of examples that is probably contributed to it be written with the students, which is why I am very pleased with it so far. It gives good explanations has good proofs and the best thing it also gives you open questions which is very nice considering that this is not given during standard uni-classes or at least not the ones I went to and the most other books that I have looked at did not give me any. Or not as many as this book does. I really am presently surprised with this book it is such a good read.
S**.
Es de lo mejor en su género para aprender.
Profundo, pero agradable de leer. Está en mis top. Ojalá hubiera tenido un libro así cuando estudié la carrera. Muy recomendable.
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