- #1
PieceOfPi
- 186
- 0
Hi,
I will be starting my graduate study in mathematics in August 2011, and I was thinking of reviewing mathematics that I have learned while I was an undergraduate as soon as my summer vacation begins in June.
The topics that I am considering to review include algebra (abstract and linear), analysis (real & complex), topology, and geometry. Of course, if there are other subjects that I should review before beginning my study at the grad school, please let me know.
I am mostly interested in reviewing analysis, since I took both real and complex analysis sequences last year (I studied all the other topics that I mentioned above this year). For real analysis, my class Baby Rudin for single-variable stuff, and Spivak's Calculus on Manifolds for the multivariable calc. For complex analysis, my class used Brown/Churchill.
In the past, I asked a similar question, and one person recommended me Anthony Knapp's Basic Analysis for reviewing real analysis. While I have not studied from this book before, the topics covered in this book seems reasonable, and I also like the idea of having solutions to the exercises (great for self-study).
Let me know if you have any recommendation of books and topics to review over the summer.
I will be starting my graduate study in mathematics in August 2011, and I was thinking of reviewing mathematics that I have learned while I was an undergraduate as soon as my summer vacation begins in June.
The topics that I am considering to review include algebra (abstract and linear), analysis (real & complex), topology, and geometry. Of course, if there are other subjects that I should review before beginning my study at the grad school, please let me know.
I am mostly interested in reviewing analysis, since I took both real and complex analysis sequences last year (I studied all the other topics that I mentioned above this year). For real analysis, my class Baby Rudin for single-variable stuff, and Spivak's Calculus on Manifolds for the multivariable calc. For complex analysis, my class used Brown/Churchill.
In the past, I asked a similar question, and one person recommended me Anthony Knapp's Basic Analysis for reviewing real analysis. While I have not studied from this book before, the topics covered in this book seems reasonable, and I also like the idea of having solutions to the exercises (great for self-study).
Let me know if you have any recommendation of books and topics to review over the summer.