Elements of Differential Geometry. Front Cover. Richard S. Millman, George D. Parker. Prentice-Hall, – Mathematics – pages. Elements of Differential Geometry (Millman-Parker). DownloadReport. Published on Nov View Download AddThis Sharing Buttons. Elements of differential geometry /‚Äč Richard S. Millman, George D. Parker. Author. Millman, Richard S., Other Authors. Parker, George D., , ( joint.

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This text is intended for an advanced undergraduate having taken linear algebra and multivariable calculus. It provides the necessary background for a more abstract course in differential geometry. The inclusion of diagrams is done without sacrificing the rigor of the material.

Makes a strong effort to bring topics up to an undergraduate level, and easily taught by any math prof. Easiest of our books. Would you like to tell us about a lower price?

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Millman & Parker, Elements of Differential Geometry | Pearson

Customers who bought this item also bought. Page 1 of 1 Start over Page 1 of 1. Complex Analysis Undergraduate Texts in Mathematics. Customers who viewed this item also viewed. Differential Geometry of Curves and Surfaces: Elementary Differential Geometry, Revised 2nd Edition.

Curves – Surfaces – Manifolds, Second Edition. Third Edition Texts and Readings in Mathematics. From the Publisher Makes a strong effort to bring topics up to an undergraduate level, and easily taught by any math prof. Pearson; 1st edition April 8, Language: I’d like to read this book on Kindle Don’t have a Kindle? Share your thoughts with other customers. Write a customer review.


Showing of 9 reviews. Top Reviews Most recent Top Reviews. There was a problem filtering reviews right now. Please try again later. Differential Geometry is one of the toughest subjects to break into for several reasons.

There is a huge jump in the level of abstraction from basic analysis and algebra courses, and the notation differdntial formidable to say the least. An ill-prepared student can begin reading Spivak Volume I elemments Warner’s book and get very little out of it.

This is, in fact, what happened to me. Only at geometey advice ahd a professor did I take an undergraduate diff. This has diffefential advantages: When I took my first diff.

This book keeps it concrete, and elmeents each idea with several worked out examples to help ground the student’s intuition. The student will become very used to modern techniques, but applied here in easier settings than what you would find in a standard graduate leveled book.

Hence, when mi,lman student eventually takes graduate leveled courses, he or she will come to see the definitions and techniques as natural extensions of those learned previously. Going back to 2this allows students to view the modern theory as a natural extension of the classical theory, and hence their intuition learned from this book is still applicable mil,man the more abstract settings.


The material covered in this book is expansive, and i think students will find that even in more advanced Riemannian geometry courses they will see material from this book still being taught. Hence, it will be a long time before a student completely outgrows this book. I’ve eements only millmann things, but there is one thing that annoys me. This book drops the ball in providing intuition in several topics. For example, the book defines Christofell symbols as abstract sums of inner products.

However, the point is that they provide the scalars for the coordinates of mixed partial derivatives in a tangent space. There is a theorem that implies this, but this intuition is never explicitly stated.

In a book aimed differebtial undergraduates, I feel that everything, including intuition, should be stated and highlighted. This has not been too bad of a hinderance for me, because a quick trip to the professor’s office will often sort things out for me. However, any self-learners may get the wrong idea about how to thing about certain topics. This is not too bad of a problem, and for the most part this book does a good job at explaining and motivating topics, so I do not feel that any more than one star should be taken off.

And by this I do not mean computations in Lay, I mean theory in Axler or something comparable. Often times, change of bases are applied without being explicitly stated in the proofs, and you should be able to pick up on this immediately.

You do not need anything past the basics of multivariable differentiation and integration, i. Amazing examples and clear definitions. If you need a clear and concise book to study from, this is it. It is hard to disagree with the idea that one must dufferential the learning of mathematics in way that might be at odds with its axiomatic structure. One can pursue the study of differentiable manifolds without ever looking at a book on classical differential geometry, but it is doubtful that one could appreciate the underlying ideas if such a strategy were taken.

Some background in linear algebra, topology, and vector calculus would allow one to understand the abstract definition of a differentiable manifold. However, to push forward the frontiers of the subject, or to nad it, one must have a solid understanding of its underlying intuition. Thus a study of classical differential geometry is warranted for someone who wants to do original research in the area as well as use it in applications, which are very extensive.

parkdr Differential geometry is pervasive in physics and engineering, and has made its presence known in areas such as computer graphics and robotics. In this regard, the authors of this book have given students a fine book, and they emphasize right at the beginning that an undergraduate introduction to differential geometry is necessary in today’s curriculum, and that such a course can be given for students with a background in calculus and linear algebra.


They also do not hesitate to use diagrams, without sacrificing mathematical rigour. Too often books in differential geometry omit the use of diagrams, holding to the opinion that to do so would be a detriment to mathematical rigour.

Much is to be gained by the reading and studying of this book, and after finishing it one will be on the right track to begin a study of modern differential geometry.

This book I also purchased as a resource for studying differential geometry. It’s a little bit better than the one by Thorpe, but not by much. I’m ,illman self-learning type of guy, with an MS in physics. Too many questions arise to gelmetry this book for the self-learner.

There are problems, and a FEW examples. There are many differential geometry books out there. Some are very rigorous others not.

This book walks the road in the middle. The book requires some very basic knowledge of linear algebra and some multivariate calculus knowledge. So basically every undergrad in the sciences should find this book easy to understand, and a good introduction to differential geometry. I had the class from Prof.

Elements of Differential Geometry (Millman-Parker)

I still have my signed! I am now a professor of EE and a large research university and this is still a subject that I love. Credit that to the Book and Prof. After reviewing a few dozen books in the subject, this is without any doubt one of the best. It it written with rare clarity, and gives enough motivation and examples to understand the more abstract and difficult aspects of the field. The book is intended for advanced undergraduate with good understanding of linear algebra and calculus III and should be read prior to an abstract course in differential geometry such as is covered in the books of Warner and Hicks.

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