Naive Lie Theory is an undergraduate text in Mathematics by well-renown Professor John Stillwell, a professor at University San Franscisco, California. I've met Professor Stillwell in 2004 during the TSL Expository Lecture Series III, 2004. Professor Stillwell is one of the invited speaker for the lecture series. I also used one of his famous book, Geometry of Surfaces, 1995 (Springer) during my master research.
Currently I'm using Naive Lie Theory to further upgrade my understanding due to Lie Groups and Lie algebra. As beforehand I'm using a book by Professor Brian C. Hall, "Lie Groups, Lie Algebras and Representations" for my informal reading course with my supervisor. Lie groups (group theory) is one of the tools needed to pursue my future research despite of other methods such as functional analysis, differential geometry and quantum mechanics.
I recommend the reader who have a similar interest as I am to consider the Naive Lie Theory as the next best companion. I like the way Professor Stillwell organized the contents of the book. One must have thankful to be able to find a crash course on groups and their basic important properties.
The book was divided into nine chapters that include, geometry of complex numbers and quarternions, groups, generalized rotation groups, the exponential map, the tangent space, structure of Lie algebras, the matrix logarithm, topology and simply connected Lie groups. Details work are shown in almost of every topics. The best thing is at the end of every chapters there is a discussion that introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.
As catchy as the title, the author used a naive approach that will be usefull to those senior undergraduates or early graduates level as myself.
Note: Some of the exercises is similar as the one Prof. Hall presented in his book. Lie Groups, Lie Algebras and Representations, Graduate Text in Mathematics (GTM), No. 222.
Currently I'm using Naive Lie Theory to further upgrade my understanding due to Lie Groups and Lie algebra. As beforehand I'm using a book by Professor Brian C. Hall, "Lie Groups, Lie Algebras and Representations" for my informal reading course with my supervisor. Lie groups (group theory) is one of the tools needed to pursue my future research despite of other methods such as functional analysis, differential geometry and quantum mechanics.
I recommend the reader who have a similar interest as I am to consider the Naive Lie Theory as the next best companion. I like the way Professor Stillwell organized the contents of the book. One must have thankful to be able to find a crash course on groups and their basic important properties.
The book was divided into nine chapters that include, geometry of complex numbers and quarternions, groups, generalized rotation groups, the exponential map, the tangent space, structure of Lie algebras, the matrix logarithm, topology and simply connected Lie groups. Details work are shown in almost of every topics. The best thing is at the end of every chapters there is a discussion that introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history.
As catchy as the title, the author used a naive approach that will be usefull to those senior undergraduates or early graduates level as myself.
Note: Some of the exercises is similar as the one Prof. Hall presented in his book. Lie Groups, Lie Algebras and Representations, Graduate Text in Mathematics (GTM), No. 222.
