# Singapore University of Social Sciences

## Analysis I: Limits, Sequences and Series (MTH205)

Applications Open: 01 October 2020

Applications Close: 30 November 2020

Next Available Intake: January 2021

Language: English

Duration: 6 months

Fees: \$1378 View More Details on Fees

Area of Interest: Science & Technology

Schemes: Lifelong Learning Credit (L2C)

Funding: To be confirmed

### Synopsis

MTH205 introduces the analysis of pure mathematics. Topics include sequences, series, limits and continuity of functions. Students should have a sound knowledge of mathematics, as developed in MTH101 Discrete Mathematics or MTH105 Fundamentals of Mathematics, differential Calculus as developed in MTH103 Calculus and Statistics or MTH107 Calculus I and integral Calculus as developed in MTH104 Calculus and Algebra or MTH108 Calculus II.

Level: 2
Credit Units: 5
Presentation Pattern: Every January

### Topics

• Numbers and bounds
• Inequalities
• Null sequences
• Convergent sequences, properties of convergent sequences
• Divergent sequences, monotone convergence theorem
• Series
• Convergent series test
• Continuity in terms of sequences
• Inverse of continuous functions
• Expontential functions

### Learning Outcome

• Employ various number types and relate these to equations and functions.
• Identify convergence properties of infinite sequences.
• Infer properties of divergent sequences.
• Outline convergence properties of infinite series.
• Use the continuity of functions.
• Contrast properties and consequences of continuity.
• Apply a range of mathematical techniques to solve a variety of quantitative problems.
• Analyze and solve problems individually and/or as part of a group.
• Solve a number of problem sets within strict deadlines.
• Solve abstract mathematical problems using logical and systematic thinking.