Trouble with difficulty of books

[IKonquer]

I am very confused as to what type of books are appropriate for my level of mathematics. I am trying to learn Abstract Algebra myself so I am reading from Artin's Algebra. Unfortunately I am having a lot of difficulty understand the proofs he presents in the book. So am I right to say this book is way above my head? I've had linear algebra already, but there was no significant proof content. Should I just try an easier book and try to read Artin later? Or am I not spending enough time learning the material?

Also how should books like Artin's Algebra be read?

Thanks in advance.

 

[Sankaku]

If you are not familiar with Proofs, try something a little easier than Artin:

Pinter is a great start for Algebra (and cheap):
https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
or
http://www.bookdepository.com/-Abstract-Algebra-Charles-Pinter/9780486474175

After that, have another try at Artin.

You might want to get a basic book on proofs first:
http://www.bookdepository.com/How-Prove-it-Daniel-Velleman/9780521675994
or
https://www.amazon.com/dp/0521675995/?tag=pfamazon01-20

 

[Goldbeetle]

I second Pinter as first book on Abstract Algebra. I also second the suggestion of a book on how to do proofs.

 

[Sankaku]

Also how should books like Artin's Algebra be read?

Thinking more about your general question...

Textbooks in mathematics can be very misleading. The introduction usually says something like: "This book should be accessible to an undergraduate with only a course in X and Y." This is almost always completely false.

The fundamental material in something like Artin is not that hard if you have actually covered all the (real) background material and have some of that nebulous quality of "mathematical maturity." This is a good general rule: Math is easy if you have seen some of it before, it is hard if you haven't. More effort at a book beyond your level is usually not the solution. Go back a step and try to fill in the holes, then try again.

People on this forum have good recommendations for many different topics. However, it can be very difficult to know what level they are aimed at and the recommender may not remember the stage they were at when they read it. Some of the best books out there are almost impossible if you are unprepared, but almost divine if you are ready.

This goes for courses as well. Many people take the wrong course at the wrong time and get convinced that they are bad at mathematics. A good university will design the course progression to get you from A to B with all the right tools. However, you may have to do some of it yourself.

If there is one secret to doing well in math, it is to make sure you have the background sorted out for the next step you are attempting.

 

[rezeew]

I understand the challenges of learning complex topics and the importance of finding the right resources to support your learning. In this situation, it seems that the book you are currently using may be too advanced for your current level of understanding. It is important to start with foundational knowledge and build upon it, rather than jumping into advanced concepts before having a solid understanding of the basics.

I would recommend seeking out a more introductory book on Abstract Algebra that includes more practice problems and explanations of the proofs. This will help you build a stronger foundation and prepare you for more advanced books like Artin's Algebra in the future. Additionally, you may benefit from seeking out supplemental resources such as online lectures or study groups to help you better understand the material.

In terms of how to approach books like Artin's Algebra, it is important to take your time and not rush through the content. Make sure you fully understand each concept before moving on to the next. It may also be helpful to break down the proofs and try to understand each step individually before putting them all together. And don't be afraid to ask for help or clarification when needed.

Overall, it is important to find the right balance between challenging yourself and building a strong foundation in your learning journey. I wish you the best of luck in your studies.