# Singapore University of Social Sciences

## Fundamentals of Mathematics (MTH105)

### Synopsis

MTH105 Fundamentals of Mathematics will introduce students to the language, notions and methods upon which a sound education in mathematics at the university level is built. Students will be exposed to the language of mathematical logic, the idea of rigorous mathematical proofs and fundamental mathematical concepts such as sets, relations and functions.

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

### Topics

• Predicates
• Quantified Statements
• Direct Proof
• Counterexamples
• Algorithms
• Sets
• Set Theoretic Operations
• Mathematical Induction
• Relations
• Equivalence Relations
• Functions

### Learning Outcome

• Show certain mathematical statements by rigorous mathematical arguments.
• Give counterexamples to disprove certain mathematical statements.
• Use mathematical induction or well ordering principle to prove mathematical statements.
• Describe equivalence classes of a given equivalence relation.
• Employ truth tables to determine whether given arguments are valid.
• Determine whether given functions are injective and/or surjective.