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Main
UQU Programs
Mathematics

Introduction to Real Analysis

MTH2301
3 hours English

Introduction to Real Analysis

Introduction to Real Analysis
MTH1101 Calculus 1
3 hours No requisites
1 Mathematical Induction, finite and infinite sets, countable sets
2 The algebraic and order properties of real numbers, rational and irrational numbers
3 Inequalities, absolute value and the real line
4 The Completeness Property of real numbers, applications of the Supremum Property, The Archimedean Property, The Density Theorem
5 Sequences and their limits, limit theorems
6 Monotone sequences, Euler's Number
7 Subsequences and the Bolzano- Weierstrass Theorem, limit superior and limit inferior, The Cauchy Criterion
8 Introduction to infinite series, tests for absolute convergence
9 Others: Revision and activities, Exam, quizzes
1.1 Mapped to: K1

Understand basic properties of real numbers.

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

Identify properties of convergent sequences, Cauchy sequences, monotone sequences and subsequences

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

Prove algebraic order properties and completeness properties of real numbers

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

Apply theorems to analyze real sequences and determine their limit

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

Use appropriate convergence tests for series

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

Working effectively in groups, 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%