Course Information

Course Name	Turkish	İleri Matematik
	English	Advanced Mathematics
Course Code	MAT 272E	Credit	Lecture (hour/week)	Recitation (hour/week)	Laboratory (hour/week)
Semester	-	3	4	-	-
Course Language		English
Course Coordinator		İbrahim Kırat
Course Objectives		To teach the student the techniques and methods of Mathematical Analysis and to allow the student to develop a certain level of proficiency in these methods. To teach students to use the basic concepts they learned in Calculus classes in a mathematically rigourous way.
Course Description		Sequences and Series of Real Numbers and Convergence. Finite Dimensional Real Vector Spaces. Young’s, Hölder’s and Minkowski’s Inequalities. Metric Spaces. Sequences in Metric Spaces. Convergence and Boundedness. Cauchy Sequences and Completeness. Topology of Metric Spaces: Open and Closed Sets. Compactness. Heine-Borel Theorem. Real Valued Continuous Functions on Metric Spaces and Their Metric Structure. Continuity and Uniform Continuity. Lipschitz Continuity. Total Derivative. C^k[a,b] and ell^p spaces. Sequences and Series of Real Valued Functions on Metric Spaces. Pointwise and Uniform Convergence. Cauchy Criterion for Uniform Convergence. Weierstrass M-test. The Stone-Weierstrass Theorem. Hilbert Spaces.
Course Outcomes
Pre-requisite(s)
Required Facilities
Other
Textbook		1. W. R. Parzynski and P. W. Zipse, Introduction to Mathematical Analysis, McGraw-Hill Book Company, 1987. 2. Erwin O. Kreyszig, Introductory Functional Analysis with Applications, Wiley; 1-st edition, 1989.
Other References		3. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976 4. Micheal O. Searcoid, Metric Spaces, Springer, 2007. 5. Robert G. Bartle and Donald R. Sherbert, Introduction to Real Analysis, John Wiley & Sons; 3-rd edition, 2000.

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