Does my Bachelor's have enough mathematics?

[Qui-Gon]

Other than Garling's three volumes, there's also the thre volumes by Amman and Escher, which can again be unequivocally recommended. And also the books by David Bressoud. Zorich is fine as well. I just don't see the rationale in using a book which came out when Elvis Pressley was singing "You ain't nothin' but a hound dog."

Postscript: And the three or four volumes by Stein and Shakarchi are also fine.

I personally don’t see the rationale in critiquing introductory analysis texts which were written 50+ years ago. After all, most—if not all—of the material was developed pre 1900s. What is the problem, aside from typesetting?

 

[Daniel Duffy]

Real analysis is not entirely non-constructive… better? Double/triple negatives are not uncommon in proof writing…

Yes. Measure theory in particular is by and large very non-constructive. You in fact were who made an even broader claim: “Most real analysis is non-constructive...”

Fair enough. I'll post soon a nice example of an ordinary differential equation (ODE) from Rudin (1964) himself;

page 102, exercis 17
page 156, exercise 22.

The exercises are incomplete as he is essentially trying to jam ODE into 2 exercises, something 1st/2nd year undergrad will not grasp. In my ODE/PDE course for US students (e.g. UCB), we devote a full module (module A) to ODE, taken from multiple perspectives.

https://www.datasim.nl/application/files/9015/4809/1157/DL_Ordinary_and_Partial_Differential_Equations.pdf

You in fact were who made an even broader claim: “Most real analysis is non-constructive...”
Generallly, most pure maths is concerned with existence and uniqueness proofs. In contrast, see Bishop.

Foundations of Constructive Analysis: Bishop, Errett, Beeson, Michael: 9784871877145: Amazon.com: Books

Buy Foundations of Constructive Analysis on Amazon.com ✓ FREE SHIPPING on qualified orders

www.amazon.com

Many of the pure mathematicians I knew were focused on one approach to solving problems. I like Polya's approach

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//
“It is better to solve one problem five different ways, than to solve five problems one way.”
― George Pólya

e.g. for ODE we have

analytical solution (most students seem to learn ODE in this way only, grosso modo??)
Picard iteration
Finite difference
Transformation (variables separable)

 

[Daniel Duffy]

I personally don’t see the rationale in critiquing introductory analysis texts which were written 50+ years ago. After all, most—if not all—of the material was developed pre 1900s. What is the problem, aside from typesetting?

I agree.
But that is not the point. The style of the book is outdated and does not have decent examples/applications.