Introduction to Mathematical Analysis (MATH 571)

2021 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10.00
Turgay Bayraktar tbayraktar@sabanciuniv.edu,
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English
Doctoral, Master
--
Formal lecture,Interactive lecture
Interactive,Learner centered,Communicative
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CONTENT

The least upper bound property in R, equivalents and consequences. Metric spaces. Completeness, compactness, connectedness. Functions,continuity. Sequences and series of functions. Contraction mapping theorem and applications to calculus: Inverse and implicit function theorems.

OBJECTIVE

Learning the basics of mathematical analysis; i.e. basic theorems and basic techniques in analysis.

LEARNING OUTCOME

Comprehend the language of analysis

Read definitions, theorems, proofs.
Produce "own" proofs in simpler cases.
Comprehend the structure of real numbers and the Euclidean space.

Comprehend the topology of the Euclidean space.
Comprehend the notion and use the facts of continuity.

Comprehend the notion and use the facts of differentiability.
Comprehend the notion and use the inverse and implicit function theorems.
Comprehend the notion and use the facts of Riemann integrals.

ASSESSMENT METHODS and CRITERIA

  Percentage (%)
Final 30
Midterm 30
Exam 30
Other 10

RECOMENDED or REQUIRED READINGS

Textbook

Elementary Classical Analysis; Marsden & Hoffman, Freeman 1974.
QA300.M37.1993