Recommendation on good Analysis textbook to supplement class

[M1STERMARBLES]

Just a quick question for those who have had plenty of exposure to Analysis.

Currently, I'm in an Analysis class. We are using Arthur Mattuck's "Introduction to Analysis" textbook. While I think it's a good book and I enjoy the class, I can't help to think that the teacher is watering down our class, especially when I looked at other Analysis textbooks. This semester, we covered Chp 1-15 (Pretty much everything but integration), as well as some topology, but I feel as if though this class is moving a bit slow.

Question is, does anyone have a recommendation for a good book which I can supplement my class? I heard Rudin's was good. I'm looking for something rigorous but readable.

Any help?

 

[SiddharthM]

if you are almost done with the class, rudin cannot hurt. The problems will help the most. Theres a lot of interesting stuff too - a nowhere differentiable continuous function and the reimann series theorem for example.

for a supplement this late in the semester it probably makes the most sense just to find good problems and to use wikipedia as a reference for definitions you are not aquainted with. this is easy to do, look at analysis exams (prelim grad exams as well). berkeley has a exam archive, 104 is their first analysis course. there's good stuff there.

 

[tacman]

Based on your description, it sounds like you are looking for a more challenging and rigorous textbook to supplement your Analysis class. In that case, I would recommend "Principles of Mathematical Analysis" by Walter Rudin. This textbook is often considered the gold standard for introductory Analysis courses and is known for its clear and concise writing style, as well as its rigorous approach to the subject. It covers all the topics you mentioned, including integration, and goes into more depth than Mattuck's textbook.

Another option could be "Real Analysis" by Royden and Fitzpatrick. This textbook is also highly regarded and offers a good balance between rigor and readability. It covers all the topics you mentioned and also includes some additional topics, such as measure theory.

Ultimately, the best textbook for you will depend on your personal preferences and learning style. I would recommend taking a look at both Rudin's and Royden and Fitzpatrick's textbooks and seeing which one resonates more with you. You can also ask your instructor or classmates for their recommendations and see if you can borrow their copies to get a feel for the content before making a purchase. Good luck with your studies!