DoctorJason Cosgrove

Mathematics, equipped with the powerful tools logic and reasoning, is the key ingredient that enriches all areas of education. A sound knowledge in mathematics not only opens up numerous career options, but also helps to understand the world in which one operates. The unit aims to provide the necessary basic knowledge that is essential to undertake tertiary studies, which require pre-tertiary background in mathematics and statistics. A brief look at basic concepts and notation of sets will lead us to the study of linear algebra and systems of linear equations related to graphs of linear functions. We will then study algebra with indices, logarithms and trigonometry. The concept of sequences and series will be introduced through arithmetic and geometric progressions. The unit will conclude with studies of probability and statistics. We look at dependent and independent events, conditional probability and probability tables. We will also discuss permutations and combinations. Finally, we will investigate collecting data, presenting categorical and discrete data, data distributions and correlations between variables.

This unit is designed to help you build the mathematical skills and confidence needed for university study. Mathematics plays an important role in many fields of study and helps you develop logical thinking, problem-solving, and analytical skills that are useful well beyond the classroom.You will learn the basic concepts of numbers and algebra, progressing to the study of functions, including trigonometric, exponential, and logarithmic functions. The unit introduces differentiation from first principles and shows how derivatives are used to solve real-world problems through graph sketching and optimisation. You will also learn the basics of integral calculus, with applications such as finding areas under curves. Throughout the unit, emphasis is placed on understanding concepts both visually and conceptually.Successful completion of Introduction to University Mathematics meets the prerequisite equivalent to pre-tertiary Mathematics Methods 4 (MTM514117) for selected University of Tasmania units and degree programs, including Mathematics 1A (KMA152) and Mathematics 1B (KMA154). The unit may also be taken as an elective to support study in science or other degree programs.

The applicability of calculus and linear algebra is so broad that fluency in it is essential for a successful career in a variety of areas including science and engineering. This unit is devoted to the conceptual and logical development of these two main areas of mathematics, gradually building the tools for solving innumerable problems of great practical importance. In calculus part of the unit, a brief look at the Real Number System and their properties will lead us to the study of Functions in general and the study of special functions such as trigonometric, exponential and logarithmic functions. The notion of limits will be utilized to define continuity and differentiability of functions, emphasizing the importance of understanding the material conceptually and graphically. This area will also help establish the technical skills necessary to solve problems arising in practical situations. One highlight of the unit will be the discussion of the Fundamental Theorem of Calculus, which unifies differential and integral calculus. An introduction to two and three dimensional vector spaces will be an essential part of the unit as the knowledge in that area is vital, particularly for studies in engineering and physics. This unit is a required unit in the Bachelor of Science mathematics major and Bachelor of Engineering students.