Course Objectives:
The objectives are to give students a holistic view of the science discipline in terms of its nature, concepts and impact on civilization and society; to equip students with basic skills of logical and quantitative reasoning; and to introduce to students mathematical and statistical methods for science studies and research.
Course Contents & Topics:
The course comprises two parts.
Part I: The nature and methodology of science
- Demarcation between science and non-science
- Shared features of the sciences
- Scientific method
- The role of mathematics in the historical development of science
-
Part II: Quantitative reasoning
a. Mathematics with topics selected from
- Foundation of mathematics
- Mathematics and advancement of science - an introduction
- Mathematical modelling - an introduction
- Guesstimation
- Difference equations
- Linear algebra and matrices
- Calculus and differential equations, and/or
- Fractals and Chaos
b. Statistics
- Probability rules
- Probabilistic methods
- Statistical inference
- Confidence intervals estimation
- Hypothesis testing
- Decision making with statistics
- Statistical modelling, and use and misuse of statistics
