Comparing Book A & B: Which to Read First?

[bigmike94]

Summary: Would somebody be kind enough to explain the difference between these books and what order would be most natural to read them in. Thank you

 

[berkeman]

Have you used an Amazon Books search to "Look Inside" at the Table of Contents of each of those books? Not all books have the Look Inside feature at Amazon, but quite a few do. I use that feature often.

 

[bigmike94]

Have you used an Amazon Books search to "Look Inside" at the Table of Contents of each of those books? Not all books have the Look Inside feature at Amazon, but quite a few do. I use that feature often.

Ive got both samples on kindle and can see the contents. But I am still not sure about which one should be read first or if they’re the same thing but different names.

I had a similar issue before I did multivariable calculus, I was searching for the difference between calculus 3, multivariable calculus, multivariate calculus, vector calculus etc etc. at the time I didn’t really know they was more or less the same thing or at least all contained within one group namely calculus 3

 

[robphy]

It might be helpful to the readers of this thread if you typed out the title and author and or the ISBNs,
or provided links (from Amazon or Google books).

From the titles alone, "surfaces in Euclidean space" is a special case of "manifolds".

 

[malawi_glenn]

The one the right is more "classical" differential geometry not using differntial forms and such and restricted to Euclidean space.

The one to the left is a more modern take on differential geometry and is more "general" (studies manifolds)

It is more natural to study the one to the right first, or "Differential Geometry of Curves and Surfaces" by Tapp.

"Visual Differential Geometry and Forms" by Needham, is more in between those two you listed I'd say.

 

[malawi_glenn]

If you want a really good book, get Hubbard "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach"

Expensive as gold, but you should be able to find a used copy of an earlier edition for a cheap penny.
Or, check your library!

All that said, have you done formal real analysis and Topology yet?

 

[MidgetDwarf]

If you want a really good book, get Hubbard "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach"

Expensive as gold, but you should be able to find a used copy of an earlier edition for a cheap penny.
Or, check your library!

All that said, have you done formal real analysis and Topology yet?

To second the suggestion above, Hubbard's book is really great. There is a more basic book titled Vector Analysis by Snider, although it does not go into all the topics Hubbard does.

A book at a similar level to Hubbard is, the book by Shifrin. I prefer Shifrin, since it gets to the point, but Hubbard may be better for beginners.

the price for a hardcover of Shifrin's book is extremely high. stick to Hubbard.

 

[bigmike94]

Just to notify the moderator that edited the post title, “muestra” isn’t the names of the authors, it’s Spanish for “sample”, they was both samples downloaded on my kindle

 

[bigmike94]

If you want a really good book, get Hubbard "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach"

Expensive as gold, but you should be able to find a used copy of an earlier edition for a cheap penny.
Or, check your library!

All that said, have you done formal real analysis and Topology yet?

I start topology in October, I originally thought real analysis was needed for topology but apparently for this textbook it’s not a prerequisite. I have linked the textbook below.

Topology for Beginners: A Rigorous Introduction to Set Theory, Topological Spaces, Continuity, Separation, Countability, Metrizability, Compactness, ... Function Spaces, and Algebraic Topology https://amzn.eu/d/8OcmwMl

I am not ready for differential geometry yet and won’t be for awhile I was just trying to create an ordered timeline of what to study and what order etc. sometimes it can be a little confusing

 

[MidgetDwarf]

I start topology in October, I originally thought real analysis was needed for topology but apparently for this textbook it’s not a prerequisite. I have linked the textbook below.

Topology for Beginners: A Rigorous Introduction to Set Theory, Topological Spaces, Continuity, Separation, Countability, Metrizability, Compactness, ... Function Spaces, and Algebraic Topology https://amzn.eu/d/8OcmwMl

I am not ready for differential geometry yet and won’t be for awhile I was just trying to create an ordered timeline of what to study and what order etc. sometimes it can be a little confusing

Formally, Topology is its own field. What is required is mathematical maturity, ie., the ability to read and write proofs. Topological concepts are found in Analysis, ie., open/closed/compact, metric spaces, continuity to name just a few. Having Analysis under your belt helps, since you will study some of the ideas from Analysis in a more general setting in Topology. Analysis also familiarizes one with examples/counterexamples. This is the reason why most schools have at least the first part of single variable analysis as a prerequisite for an introductory topology class.

 

[berkeman]

Just to notify the moderator that edited the post title, “muestra” isn’t the names of the authors, it’s Spanish for “sample”, they was both samples downloaded on my kindle

Lo siento!

It was I who tried to add more detail to your thread title -- we try to make thread titles very descriptive at PF, and without the author names the title was too generic. What are the two author names so I can update the title please?

 

[bigmike94]

Lo siento!

It was I who tried to add more detail to your thread title -- we try to make thread titles very descriptive at PF, and without the author names the title was too generic. What are the two author names so I can update the title please?

No worries. One is by L.M woodward & J. Bolton and the other is by Jon Pierre Fortney

 

[bigmike94]

Formally, Topology is its own field. What is required is mathematical maturity, ie., the ability to read and write proofs. Topological concepts are found in Analysis, ie., open/closed/compact, metric spaces, continuity to name just a few. Having Analysis under your belt helps, since you will study some of the ideas from Analysis in a more general setting in Topology. Analysis also familiarizes one with examples/counterexamples. This is the reason why most schools have at least the first part of single variable analysis as a prerequisite for an introductory topology class.

Ah thank you, the authors above also have real analysis for beginners so maybe them two should be on my reading list to get my feet wet. The chapters are split into lessons and are apparently very readable. We’ll see about that aha

 

[MidgetDwarf]

Ah thank you, the authors above also have real analysis for beginners so maybe them two should be on my reading list to get my feet wet. The chapters are split into lessons and are apparently very readable. We’ll see about that aha

I read that you mentioned starting topology in October. Are you taking a formal course? Or is it for self-study? If you have not done proof based mathematics, then you should self-study or enroll in a proof methods course. Taking the Topology class, without having taken a proof based math course, is guaranteed failure. After the proof methods course, study real analysis (single variable is fine), then proceed to Topology.

But I recall you are majoring in physics, not mathematics, so maybe a math methods book for physicist would suit your analysis/topology needs. But it never hurts to study math for its own sake.
I majored in mathematics (pure), and was a few units short for a BS in physics, so I am not sure how the typical Physics students learns Topology.

Moreover, you have more important things to learn first. Such as PDE, Vector Calculus at the level of Hubbard or similar book, Complex/Fourier Analysis, before trying to learn Topology, or even Differential Geometry.

 

[malawi_glenn]

the authors above also have real analysis for beginners

You should check out that book and the "pure mathematics" first yes, perhaps also the "set theory" and "abstract algebra" but some of those topics are included in "pure mathematics" (which is more of a compilation of sevaral topics)

 

[vanhees71]

I start topology in October, I originally thought real analysis was needed for topology but apparently for this textbook it’s not a prerequisite. I have linked the textbook below.

I'd say it's the other way around: If you want to do analysis, you need topology! In "real analysis" you use the "standard topology" for sets of real numbers (or tupels of real numbers) induced by a metric, but this is already a quite special case of a topology defined on these sets.

 

[malawi_glenn]

I'd say it's the other way around: If you want to do analysis, you need topology! In "real analysis" you use the "standard topology" for sets of real numbers (or tupels of real numbers) induced by a metric, but this is already a quite special case of a topology defined on these sets.

Usually, intro to real analysis books do cover some topology, so its all good :)