[QUOTE="houlahound, post: 5470198, Member 551046”]dang it I’ve joined an analysis of my own. As luck would have it [USER=205308]@micromass[/USER] has an excellent guide for that: https://www.physicsforums.com/insights/self-study-algebra-part-ii-abstract-algebra. I got enticed slowly but surely , after going through the analysis and looking over the suggested documents.1

For anyone who is experiencing Bloch an extremely challenging to understand first book on analysis I’d recommend "Understanding Analysis" by Stephen Abbott to supplement. I’d like to learn more on the language and the use of sets. So far, I’m finding it to be more approachable, especially since I’m not able to dedicate time every day to work through it.https://www.amazon.com/Understanding-Analysis-Stephen-Abbott/dp/1493927116.1 There was a reason sets were a major subject in high school, however at the point I was into the first year of high school, they had been eliminated as a way to help students.

What got me interested in analysis started with the idea of "sigma algebras". Do you have any theories as to why educators believed sets were important?1 I think they were up until the 70’s and before they slipped off the radar of high school education until the 70’s/early 80’s. Once I grasped that concept the concept, I was on smooth sailing. and I’m not in the know about the language. as I scanned the understanding, the analysis is written in the set language? [/QUOTE] There was at the very least an additional or less well-known mathematician of the 20th century who self studiously studied mathematics at home at night and who did not go to in a I’m afraid that the concepts of set are crucial to everything mathematical.1 Thank you for taking the time to write your response I’m grateful! I was aware of Janich’s wonderful text, but I had not heard the book Gamelin or Greene’s novel.

I would recommend reading Velleman’s "how to demonstrate it" to become familiar with sets. I’ll make sure to look into this one as well.1 While any proof book should provide enough information about it. Another great book to learn basic topology would be Gamelin Greene and Gamelin’s Introduction to Topology 2e. It’s a shame, but I’ve taken up self-study on analysis. It offers excellent practice exercises, is compact, with only a handful of lost words as well as while doing so, it is not a slack in important explanations of the many nagging issues in learning about topology.1 I got sucked in slowly but steadily going through the analysis and looking over the recommended documents.

It’s a great supplement to Lee’s other books on manifolds.Also, The work by Klaus Janich on Topology is a fantastic addition to any learning path that involves topology. I’d like to learn more on the language and the use of sets.1 Janich isn’t equipped with a complete set of activities as well as doesn’t always provide the precise pedagogy that other books provide.

There was a reason, sets were an important subject in high school, however at the point I was into the first year of high school they were eliminated as a way to help students.1 However the book is filled with great, clear explanations and diagrams.Learning the fundamentals of topology can assist you in your future explorations into analysis, too. Do you have any theories as to why educators believed sets were important? I think they were up until the 70’s and before they slipped off the radar of high school education until the 70’s and early 80’s.1 The majority of proofs that are in analytical terms are much more beautiful and understandable when presented in topological terms instead of in epsilon-delta forms. and I’m not in the know about the language, and as I have read the insight, I can see that it is mostly written with the help of the sets language? ?1 Thanks for the help! I initially thought that Lee’s book already had point-set topology. [QUOTE="Saph (post number: 5411684, member number: 582117”] 1.) Are there any crucial theorems to learn and master in the field of analysis?

By that, I mean which theorems will be applied the most in subsequent courses such as differential geometry or functional analysis? [/QUOTE] However, it’s actually Introduction to Differentiable Manifolds .1 Everything. I’ll check out this book at the library at the university. Sorry however, that’s how it is. I’ll make sure to email you with any additional details. Calculus for single variables is crucial, and every theorem that you encounter should be something you comprehend and be aware of. Thank you!1

I cannot say that anything is more important than anything else, since that’s not true. In your instance it appears that Lee’s "Introduction to topological manifolds" is the ideal". The most important aspect is the method but. Here’s why.) The necessary prerequisites include a solid understanding of sets theory proofs as well as metrics spaces.1 In the process of constructing an epsilon-delta proof.

You appear to possess this, so you’re in good shape. A sequence is shown to exist and then converges. I suggest that you go through the annexes first.2) Even though it says "graduate math texts" it is one of the most simple and easy books in the field.1 Proving that a continuous operation with one positive number has an entire open range in positive value. I believe it’s the best for your first time encounter. Etc. You might want to go through another book later though, since it doesn’t cover everything you need to know.3) It is especially made for somebody interested in differential geometry and it focuses a lot on manifolds.https://www.amazon.com/Introduction-Topological-Manifolds-Graduate-Mathematics/dp/1441979395Feel free to PM me if you want more help.1

Things like that are things you’re required to do exceptionally efficiently. Micromass, welcome to the forum and thanks for the great insights! I’ve had some knowledge of Real Analysis from Abbott but the questions were difficult for me at that time. The fact that you didn’t remember a theorem doesn’t mean it’s terrible, as you could find it later.1 I’m currently reading Tao’s Analysis books along with a friend of mine and he’s providing me with additional assignments since he has already has a thorough understanding of the subject.My question is: Since I’m currently learning by myself Algebra (with Artin and Pinter) and Analysis do you think that I have the right prerequisites for studying General Topology?1

I’m able to use the entire summer to focus on math as I’m about to enter the university (as an undergraduate major in math in the fall) at the end of September. However, you must be able to deal with these methods cold. It’s not my first experience with topology, however I’ve never considered connectedness or compactness as an example. 2) My current focus is self studying analysis with two different books, Intro to Analysis from Bartle and Sherbert, 3rd edition.1 I’m familiar with metrics spaces.What books would you recommend given my interest in mathematical physics and differential geometry?

The majority of differential topology books that I’ve read suggest a program on point-set topology.Thanks for taking the time to assist me! And Understanding Analysis by Abbot, which do you think are the best books?1 And do you have any suggestions for me to overcome all the issues within these texts? If not, what issues will I solve ? [/QUOTE] [QUOTE="houlahound, post: 5470198, Member 551046”]dang it I’ve joined an analysis of my own. Yes, you must resolve all issues.

I got enticed slowly but surely , after going through the analysis and looking over the suggested documents.1 Analysis is so essential to your future studies that you should get all the training you can receive. I’d like to learn more on the language and the use of sets.

The techniques are crucial, and you can only master through doing them. There was a reason sets were a major subject in high school, however at the point I was into the first year of high school, they had been eliminated as a way to help students.1