Singapore University of Social Sciences

Calculus and Algebra

Applications Open: 01 April 2019

Applications Close: 16 June 2019

Next Available Intake: July 2019

Schemes: Lifelong Learning Credit (L2C)

Language: English

Duration: 6 months

Fees: $1312 View More Details on Fees

Area of Interest: Science & Technology


Synopsis

This course extends the calculus introduced in MTH103, and introduces a number of abstract algebraic structures. Complex numbers, congruences and some basic group theory are introduced. Various methods of proof, such as mathematical induction, are discussed. The aim is to prepare students for higher level mathematics.

Level: 1
Credit Units: 5
Presentation Pattern: Every semester
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.

Topics

  • Differentiation from First Principles
  • Taylor's Theorem
  • Integration using Substitution, by Parts and Completing the Square
  • Separable First Order Differential Equations
  • Complex Numbers
  • Nth Roots
  • Congruence Relations
  • Cryptography
  • Groups
  • Isomorphisms
  • Methods of Proof
  • Proof by Induction

Learning Outcome

  • Use all the general rules of differential calculus, including optimization problems, Taylor series and Newton–Raphson method.
  • Demonstrate integration by substitution, integration by parts and integration by completing the square.
  • Identify complex numbers in Cartesian, exponential and trigonometric form.
  • Apply some basic notions of number theory, including congruence, divisibility tests, modular inverses and cryptography.
  • Show basic properties of a group.
  • Identify group features and isomorphisms between isomorphic groups.
  • Demonstrate various types of formal proof and methods.
  • Define a range of mathematical techniques to solve a variety of quantitative problems.
  • Solve problems individually and/or as part of a group.
  • Solve a number of problem sets within strict deadlines.
  • Use Mathcad to solve problems related to calculus and algebra.
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