Foundation Mathematics 2 (MAST10015)

This is the second in a sequence of two subjects (Foundation Mathematics 1 and Foundation Mathematics 2) providing students in the Diploma of Science with a broad foundation in mathematics. The knowledge and skills developed prepares students for continuing studies in the Bachelor of Science, or for skilled work and further learning after graduating with the Diploma of Science. 

The content consists of differential and integral calculus, probability and combinatorics, as well as discrete and continuous probability distributions and statistical inference, and includes problem solving in these areas.  While developing knowledge and understanding in these topics, students will also strengthen their skills in data analysis, mathematical logic and reasoning, communication, and active, collaborative learning. 

Real-world applications are included throughout, emphasising connections to the sciences and Indigenous ways of knowing. 

Intended learning outcomes

On completion of the subject students should have:

• an understanding of the derivative of a function as a rate of change, and its definition from first principles, and the ability to differentiate polynomials and exponential, logarithmic and trigonometric functions, and combinations of these using the product, quotient and chain rules
• the ability to use differential calculus to explore the nature of functions, including finding and classifying stationary points and solving application problems
• the ability to use basic integral calculus to perform antidifferentiation, and find the area beneath a curve and between two curves
• an understanding of core concepts in probability and combinatorics, and visul ways to present probabilities
• an understanding of the concept and uses of probability distributions, including discrete probability distributions (eg. the binomial), and continuous probability distributions (eg. the normal), and the ability to compute probabilities and measures of centre and spread for these distributions
• an understanding of the concept of statistical inference, including the definition and distribution of sample statistics, and the ability to compute confidence intervals for population parameters
• the ability to use differential and integral calculus and probability theory to solve problems motivated by real world applications
• a familiarity with language and conventions used in mathematical and statistical writing and reasoning, and the ability to communicate mathematics and statistics clearly and logically; this requires writing and manipulating mathematical and statistical equations in real time in collaboration with others, and to identify and evaluate mathematical and statistical reasoning in a group context

Generic skills

• problem-solving skills: the ability to engage with unfamiliar problems in a variety of contexts and identify relevant solution strategies
• numeracy skills: the ability to understand and work with numerical and symbolic representation of ideas
• analytical skills: the ability to construct clear and logical arguments, and effectively justify reasoning
• conceptual skills: the ability to see connections across topics, to help organise thinking and frame big picture views
• collaborative skills: the ability to work in a team, and actively participate and engage collaboratively in a task
• time-management and organisational skills: the ability to meet regular deadlines while balancing competing commitments
• capacity for learning in a higher education environment: the ability to engage productively in active learning