The objectives of this course are to introduce basic notions in mathematics and to develop thinking skills in terms of ideas and criticism. Illustrated by simple examples and with wonderful developments, the course is especially designed to inspire students to apply imagination and creativity in understanding mathematics. Major topics to be covered: How do we think of Mathematics? Basic models of mathematics: Definition, Theorem, Proof, Speculation, Idea-criticism (each with elementary examples). Major Facilities for Mathematical Thinking: Human Language; Vision, Spatial Sense and Motion Sense; Logic and Deduction; Intuition, Association and Metaphor; Stimulus Response; Process and Time. Critical Reasoning ? Conjectures and Refutations. Post Critical Facets: Fact? Knowledge- Personal Use of Imagination; Connoisseurship, Conviviality, Serendipity. Selected topics on Mathematics in Information Technology and Life Sciences. Target: Students with 'O' Level Mathematics.