Foundations What are the best undergraduate math books?

[fxdung]

I intend to self-learn undergraduate math program.What are the books for undergraduate math?Please show me all some books that cover the whole program!

 

[sysprog]

There are some core courses, but there's not exactly a common complete program $-$ you can find out a lot by searching on 'college math major curriculum' $-$ e.g. this from Yale: https://math.yale.edu/undergraduate/mathematics-major

 

[fxdung]

Please show me some core books cover core program.
Is it correct books:
Mathematical Anlysis: Caculus by Apostle, Basic Analysis by Peterson.Algebra: by Dummit. Geometry: differential geometry by Spivak.And what are other subjects and other books?

 

[sysprog]

Those are all well-known as first-rate textbooks. I won't try to make such a list as you seem to be seeking. You appear to be doing fine at that yourself.

 

[MidgetDwarf]

Algebra: Artin

I did not like Dummit. It is devoid of character. Easer than Artin, but Artin offers far greater insights.

Analysis: Both volumes by Zorich ( if these are too difficult, then look at Abbot: Understanding Analysis, then read Zorich again)

Vector Calculus: Hubbard and Hubbard : Vector Calculus, Linear Algebra, and Differential Forms.

Linear Algebra: Axler: Linear Algebra Done Right

Topology: Munkres. I liked Simmons: Topology and Modern Analysis, but Munkres covers more.

The books by Hubbard can also be used as multivariable analysis book (intro). But a more advanced book is needed at some point. Hubbard and Axler complement each other well. So does Artin, since it introduces determinants in chapter 1 and Axler at the end of the book.

This covers the minimum topics a math major should know (or what I believe). Then read anything that you are interested in. Ie., graph theory, number theory, geometry, etc...

 

[Mondayman]

I found Serge Lang books to be okay for an introduction to "proper" mathematics. Specifically, his Basic Mathematics, calculus, and linear algebra texts. I had them, and could not find a buyer, and was forced to donate them to Value Village. I immediately regretted it and went to buy them back, but it was too late ☹

 

[MidgetDwarf]

I found Serge Lang books to be okay for an introduction to "proper" mathematics. Specifically, his Basic Mathematics, calculus, and linear algebra texts. I had them, and could not find a buyer, and was forced to donate them to Value Village. I immediately regretted it and went to buy them back, but it was too late ☹

I really like his books. My first intro linear algebra was proof based, and the textbook we used was Strang. I found it too verbose. So I ordered Serge Lang: Introduction to Linear Algebra, and finally understood what linear independence and span was. I read parts of his undergraduate analysis ( was recommended by a member here) to understand multivariable analysis. My course was based on Spivak Calculus Of Manifolds. After the implicit function theorem, I could no longer follow. But Lang made things click for me.

 

[fxdung]

I like to know what about Algebra by MacLane?Is it sutable for undergraduate?

 

[MidgetDwarf]

I like to know what about Algebra by MacLane?Is it sutable for undergraduate?

I have never looked at it. but I found Artin enjoyable.