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Main
UQU Programs
Mathematics

Real Analysis 1

MTH3302
3 hours English

Real Analysis 1

Real Analysis 1
MTH2301 Introduction to Real Analysis
3 hours One requisite
1 Metric Spaces: Definition, Examples
2 Open, closed balls and open, closed sets (theorems-examples) / the distance between two sets, diameter of set, bounded set, neighborhood of a point (theorems- examples)
3 Interior, closure of a set and limit point (theorems-examples) / Dense and nowhere dense subsets
4 Sequences in metric space - Complete metric space – Separable spaces (theorems-examples)
5 Continuous and uniformly continuous functions in metric space (theorems-examples) / Contraction mapping - Fixed point - Banach fixed point theorem
6 Compactness in metric space (theorems-examples)
7 Connectedness in metric space (theorems-examples)
8 Others: Revision and activities, Exam, quizzes
1.1 Mapped to: K1

Develop knowledge on the concept of a metric space and show familiarity with a different example of metric spaces.

Teaching Strategy Lectures
Assessment Methods Homework Exam-Quiz
1.2 Mapped to: K1

Demonstrate understanding of the distance function (open, closed ball, open, closed sets, interior, closure, limit point).

Teaching Strategy Lectures
Assessment Methods Homework Exam-Quiz
2.1 Mapped to: S5

Apply mathematical reasoning to analyze the continuous and the uniformly continuous functions in metric spaces

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
2.2 Mapped to: S5

Apply logical reasoning to develop mathematical proofs of Heine-Borel theorem, Banach fixed point theorem and others.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
2.3 Mapped to: S6

Demonstrate the ability to develop solutions for specific and advanced theoretical problems to recognize between the convergence sequence and the Cauchy sequence in metric spaces and determine the complete metric space.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
2.4 Mapped to: S7

Use appropriate mathematical formulas and techniques to solve problem in compactness, and connectedness for metric spaces.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
3.1 Mapped to: V1

Show the ability to work independently and within groups.

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
3.2 Mapped to: V2

Demonstrating communication skills and time management

Teaching Strategy Lectures and individual or group work
Assessment Methods Homework Exam-Quiz
Assessment
Weight
Midterm Exam
30%
Homework, Quizzes and Assignments
20%
Final Exam
50%
Total
100%