Introduction to Mathematics (MAST10012)
Undergraduate level 1Points: 12.5Dual-Delivery (Parkville)
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Semester 1 - Dual-Delivery
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Students will strengthen and develop algebraic and conceptual skills, building a firm mathematical base for MAST10005 Calculus 1.
Fundamental concepts about number systems and set theory will be followed by introductory counting principles and techniques. These will be applied to the laws of probability, leading to the study of discrete and continuous random variables. Basic ideas about functions and their inverses will be introduced using examples such as the logarithmic, exponential and trigonometric functions. Differential and integral calculus will be studied with applications to graph sketching and optimization problems. Students will also learn integration techniques, with applications to areas between curves.
Intended learning outcomes
On completion of this subject, students should be able to:
- Understand fundamental concepts of number systems and counting techniques and be able to use logic and set notation;
- Understand the concept of a mathematical function, domain, range and inverse function;
- Be able to apply transformations and the ideas of sum, difference, product and composite functions to graphing polynomial, exponential, logarithmic and circular functions;
- Understand the derivative as a limit and use the product, quotient and chain rules of differentiation with polynomial, circular, exponential and logarithmic functions and apply these techniques to graph sketching and optimisation problems;
- Understand the process of integration as anti-differentiation and be able to find definite and indefinite integrals of polynomials, exponential and circular functions with application to calculating the area of a region under a curve and between curves;
- Understand the fundamental concepts of probability and be able to calculate probabilities for discrete and continuous random variables, including binomial and normal probabilities.
In addition to learning specific mathematical skills, students will have the opportunity to develop generic skills that will assist them in any career path. These include:
- Problem-solving skills: the ability to engage with unfamiliar problems and identify relevant solution strategies;
- Analytical skills: the ability to construct and express logical arguments and to work in abstract or general terms to increase the clarity and efficiency of analysis;
- Collaborative skills: the ability to work in a team;
- Time management skills: the ability to meet regular deadlines while balancing competing commitments.
Last updated: 30 March 2023