Singapore University of Social Sciences

Analysis I: Limits, Sequences and Series

Applications Open: 01 October 2019

Applications Close: 30 November 2019

Next Available Intake: January 2020

Schemes: Lifelong Learning Credit (L2C)

Language: English

Duration: 6 months

Fees: To be confirmed

Area of Interest: Science & Technology


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 Discrete Mathematics, Calculus and Statistics, Further Discrete Mathematics and Further Calculus and Algebra

Level: 2
Credit Units: 5
Presentation Pattern: Every January
E-Learning: BLENDED - Learning is done MAINLY online using interactive study materials in MyUniSIM. Students receive guidance and support from online instructors via discussion forums and emails. This is supplemented with SOME face-to-face sessions. If the course has an exam component, this will be administered on-campus.


  • 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.
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