Hobart
This unit has been discontinued.
Introduction
Successful completion of this unit supports your development of Mathematics core knowledge and skills. Through the development of this knowledge and skills you will have the necessary mathematics content and understanding of the nature of Mathematics for contributing to your development as a mathematics teachers.
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 its properties will lead us to the study of real valued functions on  in general and the study of special functions such as trigonometric, exponential and logarithmic functions. The notion of limits will be utilised to define continuity and differentiability of functions, emphasising 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. The concept of Complex Numbers will also be introduced together with their fundamental operations, basic knowledge of which is essential for the units involved in Real and Complex Analysis and Differential equations. The Euclidean spaces Â2 and Â3 are introduced which then is followed by an introduction to 2 and 3 dimensional vector spaces arising from Â2 and Â3.
Summary 2020
| Unit name | Mathematics 1A |
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| Unit code | KMA552 |
| Credit points | 12.5 |
| Faculty/School | College of Sciences and Engineering School of Natural Sciences |
| Discipline | Mathematics |
| Coordinator | H. Kumudini Dharmadasa |
| Available as student elective? | No |
| Breadth Unit? | No |
Availability
Note
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* The Final WW Date is the final date from which you can withdraw from the unit without academic penalty, however you will still incur a financial liability (see withdrawal dates explained for more information).
Learning Outcomes
1. Demonstrate a coherent understanding of the mathematics at first year undergraduate level by acquiring the ability to construct logical, clearly presented and justified arguments incorporating deductive reasoning (Assessed by ATs 1, 2, 3 and 4)
2. Exhibit depth and breadth of knowledge of the principles and concepts in this area of mathematics In particular, you will be able to:
a) Use the notion of a function conceptually and graphically to investigate, interpret or manipulate results, as the need arises
b) Use conceptual understanding of
(i) Limits
(ii) Continuity
(iii) Differentiability and
(iv) Integrability
Of functions together with the associated technical skills to build mathematical models to physical problems and arrive at solutions which are logically sound
c) Move beyond the real number system and enjoy properties of complex numbers together with their algebraic manipulations
d) Use techniques of linear algebra, in particular, matrix algebra, to solve and represent solutions to systems of linear equations
e) Appreciate the applicability of Euclidean vector spaces and their geometry to solve simple geometrical problems
f) Understand the abstract concept of a vector space and its applicability to other areas of mathematics
g) Understand rigorous mathematical proofs of standard theorems, lemmas or corollaries that you will encounter in your future studies in mathematics (Assessed by ATs 1, 2, 3 and 4)
3. Demonstrate strength of inquiry and problem solving capabilities through formulating and modelling practical and abstract problems arising in this level of mathematics, and interpreting results critically (Assessed by AT 1 and 4)
4. Develop communication skills to present mathematical information using logical reasoning (Assessed by ATs 1, 2, 3 and 4)
5. Demonstrate responsibility of learning through proving
a) Ability to self-direct learning to extend their existing knowledge and that of others
b) Ability to work effectively and responsibly in an individual or team context (Assessed by ATs 1, 2, 3 and 4)
6. Critically reflect upon the nature of Mathematics. (Assessed by AT 5)
Fees
Requisites
Prerequisites
MTM415117 Mathematics Methods (or higher) or (KMA003)
Mutual Exclusions
You cannot enrol in this unit as well as the following:
KMA152 or JEE103
Teaching
| Teaching Pattern | 4 x 50 minute lectures weekly, 1 X 60 minute tutorial weekly |
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| Assessment | Assessment Task 1: Weekly assignments: 15% |
| Timetable | View the lecture timetable | View the full unit timetable |
Textbooks
| Required | Students are required to obtain access to Pearson Link on MyLO page for the unit through which the on-line text for the Unit is available. This process will be detailed during the Introductory lecture as well as through Announcements on MyLO. |
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The University reserves the right to amend or remove courses and unit availabilities, as appropriate.