Hi Friends,
This would be my first scribbling on this site. My wish is to provide some assistance to those who want to learn string theory. Since I have been in this situation in the past, I think I can offer some advice from my humble experiences.
Before proceeding I wish to make some remarks:
1. Whenever you learn a topic in theoretical physics, especially if it is in those frontier areas, try to learn first the computational techniques for its own sake. Once you have done with this (or parallely alongside the process), read about the original papers on the topics which will give you not only the context of the calculations but some physical insights into the subject.
2. There are usually two extreme class of learners. Of which first needs everything to be mathematically rigorous and can accept abstract things even without supply of physical examples. Latter class needs always some physical explanation to accept an idea and are not keen on being mathematically rigor. My presentation here will be intermediate between these two.
3. Never rush through any of fundamentals while starting as a beginner. Always take your time to allow the concept or the idea to settle down. Try to apply the newly learned concept to known examples or even better to your own created examples to obtain different perspective on them.
I will divide my article into a series of articles dealing with separate topics.
- Learn the Math First
It is always better to master the necessary math before jumping into sea of subject. It's easier to lose your way, especially if it is a newer one, with out the necessary navigational tools. On your first reading trying to master math along with physics will block understanding of either and will lead you to a confused state of mind. Once you have mastered the math, learning physics will be relatively plus you get the advantage of understanding the math at a physical level.Note : I assume that you have just passed High school, so that I can include a broad class of people. If you are at a higher level just ignore whatever you know and proceed from your level (or better can provide some comments or advice on any improvements).
I will provide you with some list of books I found useful on these topics.
Calculus & Differential Equations
1. Piskunov ; Differential and Integral calculus.( 2 Volumes)
Covers differential and integral calculus along with some vector calculus and probability theory. Good to learn how to do calculations without losing the grasp on theory.
(It went out of print after MIR publishers went down, but some regional publishers have made them available in market.)
2. V. I. Smirnov: A course on Higher mathematics ( Volume 1 and 2 )
A typical Russian classic written by a renowned mathematician imparting all his wealth of knowledge and skill into these books . A must read.
Before proceeding I wish to make some remarks:
1. Whenever you learn a topic in theoretical physics, especially if it is in those frontier areas, try to learn first the computational techniques for its own sake. Once you have done with this (or parallely alongside the process), read about the original papers on the topics which will give you not only the context of the calculations but some physical insights into the subject.
2. There are usually two extreme class of learners. Of which first needs everything to be mathematically rigorous and can accept abstract things even without supply of physical examples. Latter class needs always some physical explanation to accept an idea and are not keen on being mathematically rigor. My presentation here will be intermediate between these two.
3. Never rush through any of fundamentals while starting as a beginner. Always take your time to allow the concept or the idea to settle down. Try to apply the newly learned concept to known examples or even better to your own created examples to obtain different perspective on them.
I will divide my article into a series of articles dealing with separate topics.
- Learn the Math First
I will provide you with some list of books I found useful on these topics.
Calculus & Differential Equations
1. Piskunov ; Differential and Integral calculus.( 2 Volumes)
Covers differential and integral calculus along with some vector calculus and probability theory. Good to learn how to do calculations without losing the grasp on theory.
(It went out of print after MIR publishers went down, but some regional publishers have made them available in market.)
3. R. Courant; Differential and Integral Calculus (Volume 1 and 2).
A German Classic. Both selection and presentation of topics are excellent. (This doesn't cover any differential equations)
4. I.G. Petrovsky; Lectures on Partial Differential Equations
Another Russian Classic.
Although all these books are very old, they present the subject in the clean and complete manner. So once you worked out through any of these, you may never have to look back. Regarding the selection of books, you can browse through these and select the one which suits your temperament and this applies to the rest of subjects also.
Linear Algebra and Group Theory
1. V. I. Smirnov: A course on Higher mathematics ( Volume 3, Part 1) (Recommended)
(Republished by Dover books under the title : Linear Algebra and Group Theory)
Excellent algebraic exposition on the topic. A must read.
2. Halmos; Finite Dimensional Vector space (Recommended)
Superb book written in an excellent manner by a brilliant teacher and mathematician.
3. A.P. Balachandran, S G Jo & G Marmo ; Group Theory and Hopf Algebra: Lectures for Physicists
3. A.P. Balachandran, S G Jo & G Marmo ; Group Theory and Hopf Algebra: Lectures for Physicists
No comments:
Post a Comment