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sparkster
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I'm taking a class in differential geometry in the fall and I wanted to be sure to be well prepared. Are there any basics that I might need to bone up on before showing up?
He's teaching the class and using his own book. Some texts I've had in the past have been next to useless so sometimes I'll buy a backup. If you liked his other book, then the diff geo one will probably be pretty good too.mathwonk said:no, but i liked millmans book on non eucliden geometry. i.e. he is smart and writes well.
Yeah, he's the guy; he's new to the university. I think the class text is "Elements of Differential Geometry" but I'll ask him about the short version. I usually like to have a couple of texts for classes like this.mathwonk said:If this class is being taught by Richard S Millman, I think it should be excellent. In my view the world's best differential geometry book is by spivak, especially volume 2. vol 1 is a big load of abstract background on manifolds, and makes it hard, or at least long, to get to vol 2.
it is probably important to also have a short version, like maybe millman and parker, or manfred docarmo, or the notes by Ted Shifrin from University of Georgia.
ex-xian said:Yeah, he's the guy; he's new to the university. I think the class text is "Elements of Differential Geometry" but I'll ask him about the short version. I usually like to have a couple of texts for classes like this.
Oh, I see. I've not gotten the book yet, so I didn't know how long or short it was.mathwonk said:actually i meant millman and parker IS the short version, compared to spivaks 5 volumes.
I had heard that was a former university president, but I didn't know much else about him. I do know that's really excited about the class; I went to his office to ask a few questions about it and got an impromtu lesson on lie algebra. After your posts I'm looking forward to the class even more. Thanks!check out your new prof's bio on the web. he's a big time university professor, teacher, author and administrator, even former univ president. and he has participated in a lot of high level instructional activity, as well as written intelligent books which treat a subject thoughtfully, not ones designed to make the most money possible by talking down to the audience.
so if this diff geom book is like his geometry book, it will have a good pedagogical point of view, as well as significant mathematical underpinnings. You never know what someone's classroom style will be like, but I would welcome the chance to learn the subject from him myself.
That depends on how quickly you can pick up ideas. You should learn what you need to know in class if the teacher and material is good. Pick up a text on differential geometry and learn it over the summer. That's what I used to do and it worked out well for me. Differential Geometry, by Erwin Kreyszig is pretty good.ex-xian said:I'm taking a class in differential geometry in the fall and I wanted to be sure to be well prepared. Are there any basics that I might need to bone up on before showing up?
I'd like to hear more about this text.ex-xian said:Yeah, he's the guy; he's new to the university. I think the class text is "Elements of Differential Geometry" but I'll ask him about the short version. I usually like to have a couple of texts for classes like this.
The math library had a copy of schaum's outlines for differential geometry. I'm working my way through it.pmb_phy said:That depends on how quickly you can pick up ideas. You should learn what you need to know in class if the teacher and material is good. Pick up a text on differential geometry and learn it over the summer. That's what I used to do and it worked out well for me. Differential Geometry, by Erwin Kreyszig is pretty good.
Pete
I'll let you know when I pick it up.I'd like to hear more about this text.
mathwonk said:another excellent book, unfortunately out of print for years, is by noel j. hicks, something like "notes on differential geometry".
Differential geometry is a branch of mathematics that studies the properties of curved surfaces and spaces using the concepts of calculus and linear algebra. It is used in various fields such as physics, engineering, and computer graphics.
Before taking a differential geometry class, it is important to have a strong understanding of linear algebra, calculus, and multivariable calculus. Knowledge of vector calculus and basic topology can also be helpful.
To prepare for a differential geometry class, it is recommended to review fundamental concepts in linear algebra and calculus, as well as practice solving problems involving curves and surfaces. Familiarizing yourself with basic notation and terminology used in differential geometry can also be beneficial.
Differential geometry has many practical applications, including in physics, engineering, and computer graphics. It is used to study and model the behavior of curved objects and surfaces, such as the motion of planets, the design of bridges, and the creation of 3D graphics in video games and movies.
Yes, there are many online resources available to help you prepare for a differential geometry class. Some popular options include online lectures, textbooks, and practice problems. You can also find helpful videos and tutorials on websites such as Khan Academy and Coursera.