The course begins with an introduction to basic logical structures and techniques of proof. The ideas introduced here, especially the crucial "forward-backward method" of constructing proofs, are all emphasized and used explicitly throughout. The rest of Part 1 includes discussions of the concept of cardinality, the algebraic and order structure of the real and rational number systems. Part 2 is an in-depth examination of the completeness of the real number system in its various guises and a complete construction of the real number system, as well as a discussion of the topological structure of the real number system. It is here also that the discussion of proofs becomes most focused. Part 3 deal with the uniform convergence of the continuous functions and approximation of continuous functions by polynomials..
13:00-14:00 MWF in HB 423
Zhiyong Gao
Office: HB 428; Office hours: To be
announced
Email: gao@rice.edu
Telephone: ext 3281
This is a new course. Here is the catalogue description.:
Math
300 Topics
in Undergraduate Mathematics
Treatment of topics in undergraduate mathematics with an emphasis on writing of
clear, cogent
complete mathematical proofs. Topics vary by year. May be repeated for credit with permission of department.