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Math_QED

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## Main Question or Discussion Point

Hello all. I'm a mathematics undergrad student who finished his first university year succesfully. I got courses of calculus, but these weren't very rigorous. I did learn about stuff like epsilon and delta proofs but we never made exercises on those things. The theory I saw contained proofs but the main goal of the course was to succesfully learn to solve integrals (line integrals, surface integrals, double integrals, volume integrals, ...), solve differential equations, etc.

I already took proof based courses like linear algebra and group theory, so I think I am ready to start to learn rigorous real analysis, so I'm looking for a book that suits me.

I want the book to contain the following topics:

The usual analysis stuff:

- a construction of ##\mathbb{R}## or a system that takes ##\mathbb{R}## axiomatically for granted

- rigorous treatment of limits, sequences, derivatives, series, integrals

- the book can be about single variable analysis, but this is no requirement

- exercises to practice (I want certainly be able to prove things using epsilon and delta definitions after reading and working through the book)

Other requirements:

- The book must be suited for self study (I have 3 months until the next school year starts, and I want to be able to prepare for the analysis courses).

I have heard about the books 'Real numbers and real analysis' by Ethan D. Block and 'Principles of mathematical analysis' by Walter Rudin, and those seem to be good books. I have also heard these books are very hard to start with, so maybe I need something easier to start with.

Can someone hint me towards a good book? If you want me to add information, feel free to leave a comment.

I already took proof based courses like linear algebra and group theory, so I think I am ready to start to learn rigorous real analysis, so I'm looking for a book that suits me.

I want the book to contain the following topics:

The usual analysis stuff:

- a construction of ##\mathbb{R}## or a system that takes ##\mathbb{R}## axiomatically for granted

- rigorous treatment of limits, sequences, derivatives, series, integrals

- the book can be about single variable analysis, but this is no requirement

- exercises to practice (I want certainly be able to prove things using epsilon and delta definitions after reading and working through the book)

Other requirements:

- The book must be suited for self study (I have 3 months until the next school year starts, and I want to be able to prepare for the analysis courses).

I have heard about the books 'Real numbers and real analysis' by Ethan D. Block and 'Principles of mathematical analysis' by Walter Rudin, and those seem to be good books. I have also heard these books are very hard to start with, so maybe I need something easier to start with.

Can someone hint me towards a good book? If you want me to add information, feel free to leave a comment.