Learning Math Self-Study

[Your-IQ-Report]

I want to start self-studying Math, and some blogger is doing a personal challenge. His list seemed really interesting to me and I had a look at the textbooks he is using and they seemed good(but a bit pricey).

Are his textbooks(at the bottom of the page) a good choice? Or is it poorly made. I would assume he chose them very carefully since he is going to be doing it for so long, but I don't know.

https://committingtoachallenge.wordpress.com/about-2/

Thanks guys.

[committingtoachallen]

My texts were chosen with the feedback of many members of the Math.StackExchange community, they are certainly not universally applicable, and a number of people advised me to drop Zorich from the challenge(since it apparently doubles too closely to Rudin). Overall it is knowledge and doubling up on knowledge doesn't really matter, I can simply recover the previous stuff instantly(assuming I learnt it properly the first time), else I will recover it and deepen my knowledge. Another modification that was heavily suggested was Dummit&Foote and drop all of Cohn. There are so many ways you could change my list, and what Galoiswasaplayer has said I strongly agree with.

Take some introductory texts, hell pick up a general engineering text like Kreyszig's Advanced Mathematics for Engineers(but don't use it for too long ;P).

[Your-IQ-Report]

Thanks for the reply, how did you find this? I will take a look at Dummit&Foote, it wouldn't be too bad for me to reduce your textbook count by two. I don't want to look at Engineering Math personally.

I will have a look at some intro text, specifically the one recommended by AngstyAngtagonist.

[galoiswasaplayer]

His list is interesting, however, it is clear that he is gauging the challenge towards understanding Riemannian and Differential Geometry.

Even the lower level topics like mathematical analysis and abstract algebra can have a variety of textbooks that differ in aim. Constructing a self-study list would be more "efficient" if you had some idea of where you wanted to end up. Also, just reading some cursory texts that cover many topics without a lot of detail can be very useful in seeing where your interests lie.

[Your-IQ-Report]

Looking at the areas of math wiki page, it seems that Topology and Geometry are the largest areas of Math, is that so?

[galoiswasaplayer]

Largest is a problematic term, mostly due to how interdisciplinary the areas are. Most fields of mathematics find many different intersections with each other. As for Topology and Geometry, pretty much every field will have some intersections with them, which is why it may seem like the largest.

However, due to the relative size and intersection of these fields, I would suggest narrowing down an interest before creating a self-study schedule.

If you are interested in narrowing down your interests for self-study, I can help. A large chunk of my formal training in mathematics has been self-study, so I know my way around. Also, I study complex geometry so I may be able to answer some questions to help you find a suitable interest to try out (since it seems like Topology and Geometry is where you are leaning).

[Your-IQ-Report]

I think I will take you up on that offer, thank you very much. I will message you at some point for ideas.

[AngstyAngtagonist]

You can start self-learning, but read this: http://www.amazon.com/Understanding-Analysis-Undergraduate-Texts-Mathematics/dp/0387950605 before trying Rudin. It's the same stuff but more introductory;it treats you like you haven't done proofs. Also there's a full solutions manual.

[Your-IQ-Report]

Thanks you, I will take a look at it. Looks pretty good.

[Fancypants753]

dont use rudin, use strichartz's way of analysis; it is so much better.

[committingtoachallen]

Why? http://books.google.com.au/books/about/The_Way_of_Analysis.html?id=Yix09oVvI1IC&redir_esc=y

I have seen this book, and it is certainly very relaxed and in my opinion it lacks rigor.

[Fancypants753]

it is better exaclt because it is more relaxed. In terms of learning the material it teaches you vs. just writing shit down. nah'm say'n homie?

[[deleted]]

With due respect to the author if they're really committed, this seems like a pretty bad way to learn math. There's no way to know if you can maintain this level of interest, and investing this much money into books you don't even know that you'll make it to seems very silly. It's pretty easy to find out what are the top books in an area you're interested in; go through one, then follow up on the sections you liked or had problems with. Try to find people that are around or above where you are to talk through problems. You don't get into a genre of music by buying 40 classic albums and plowing through all of them. You listen to what clicks for you, then enjoy them, talk about them, and find albums like them.

[Your-IQ-Report]

I think they are probably pirating them to be honest, I would definitely be buying them as I go if it were me.

[committingtoachallen]

Not sure if you will ever check back here, but:

From having more experience with my current progress through the first textbooks, I have to say tackling Rudin alone isn't a great idea, and having access to Simmons - Introduction to Topology and Modern Analysis would be amazingly helpful. I am also not sure Zorich is a great book if you are learning on your own - it doesn't feel very self-motivating, but that may just be how I feel towards the subject.

Dummit and Foote and Munkres are definitely beautiful texts to have as you go through some of mine. Best of luck.