Mathematics Books

[SamitC]

I am studying maths out of hobby. I feel sometimes that I can not move ahead because I get stuck with tough problems. Even after I move ahead, when i come back after quite some time, i get stuck with the same problems. Sometimes it is frustrating. And my interest and attention levels are going down.

Earlier, while learning calculus, i referred Paul Dawkin's online textbooks. There were no exercises but a good number (not too many) of solved examples selected in a very methodical manner for understanding. The flow was excellent. I could finish the courses and it helped me to understand each chapters and overall picture very well. It worked for me. And most importantly - it kept my interest and attention increasing. With that knowledge I successfully attempted solving many exercises from various sources.

I am looking for similar types of books in other areas like Discrete Maths, Linear Algebra, complex analysis, PDE etc.
Can you pls. help me with the name of those books (online or paper books) in case you are aware of?
Thanks

 

[MidgetDwarf]

I would actually work through a real Calculus textbook. I like Moise: Calculus. It is a between Spivak and Thomas textbook. Another book I like is Thomas: Calculus with Analytical Geometry 3rd ed.

For Linear Algebra: You can start reading Anton: Elementary Linear Algebra. I have the 10th ed (Very Cheap), and I like the layout of the book compared to older editions. It has a great balance of Theory/Application. My only problem with the book, is that Linear Transformations are mentioned really late.

After Anton's book, you can jump to Friedberg/Insel/Spence: Linear Algebra, or maybe even Shilov: Linear Algebra.

For Differential Equations: Ross: Differential Equations, not the Introduction to Differential Equations, is a very excellent book. One of my favorite math books.

I would learn from these books before attempting PDE, Discrete, etc. It should take you 1 to maybe 2 year to fully complete and understand these books.

 

[smodak]

I would actually work through a real Calculus textbook. I like Moise: Calculus. It is a between Spivak and Thomas textbook. Another book I like is Thomas: Calculus with Analytical Geometry 3rd ed.

For Linear Algebra: You can start reading Anton: Elementary Linear Algebra. I have the 10th ed (Very Cheap), and I like the layout of the book compared to older editions. It has a great balance of Theory/Application. My only problem with the book, is that Linear Transformations are mentioned really late.

After Anton's book, you can jump to Friedberg/Insel/Spence: Linear Algebra, or maybe even Shilov: Linear Algebra.

For Differential Equations: Ross: Differential Equations, not the Introduction to Differential Equations, is a very excellent book. One of my favorite math books.

I would learn from these books before attempting PDE, Discrete, etc. It should take you 1 to maybe 2 year to fully complete and understand these books.

I think what OP is looking for is books with many solved examples or one(s) with solution manuals. He also says he has done calculus and now looking for such books in Discrete Math, Linear Algebra, complex analysis, PDE etc.