Real Analysis I

Applications Open: 01 October 2022

Applications Close: 30 November 2022

Next Available Intake: January 2023

Course Types: Modular Undergraduate Course

Language: English

Duration: 6 months

Fees: $1378 View More Details on Fees

Area of Interest: Science & Technology

Schemes: Alumni Continuing Education (ACE), Lifelong Learning Credit (L2C)

Funding: To be confirmed

School/Department: School of Science & Technology

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Synopsis

MTH312 Real Analysis I will introduce students to the notions of convergence and techniques of mathematical analysis. The course develops concepts of limits and continuity rigorously. Mathematical rigor will be emphasized for this course. Students will be exposed to and be expected to acquire the skills to read and write mathematical proofs

Level: 3
Credit Units: 5
Presentation Pattern: Every January

Topics

Completeness Axiom
Convergent Sequences
Monotone Convergence Theorem
Subsequences
Bolzano-Weierstrass Theorem
Cauchy Sequences
Upper and Lower Limits
Limits of Functions
Continuous Functions
Intermediate Value Theorem
Extreme Value Theorem
Inverse Functions

Learning Outcome

Show the validity of given mathematical statements in real analysis.
Give examples of mathematical statements in real analysis.
Apply epsilon-delta arguments to prove mathematical statements in real analysis.
Use the Monotone Convergence Theorem and/or Bolzano-Weierstrass Theorem to prove mathematical statements in real analysis.
Compute the limit supremum, limit infimum or limit of a sequence.
Determine whether given function(s) are continuous and/or uniformly continuous.

Part-time Programmes / CET Courses

Singapore University of Social Sciences

Real Analysis I

Real Analysis I (MTH312)

Synopsis

Topics

Learning Outcome