CECS Professional Skills Mapping

MATH1115 — Advanced Mathematics and Applications 1

Note: information provided here is indicative only. For full and current course information view the official page on P&C.

code:	MATH1115
name:	Advanced Mathematics and Applications 1
unit value:	6
description:	This course begins an in-depth study of the fundamental concepts of calculus and linear algebra, with a particular emphasis on the underlying foundations of mathematics. The use and understanding of proof and abstract ideas will allow students to develop analytical skills which will form a base for further study in fundamental mathematics, as well as providing a foundation for a wide range of quantitative areas such as actuarial studies, computer science, economics, engineering, physics and statistics. Topics to be covered include: Calculus/Analysis - suprema and infima of sets of real numbers, completeness, Riemann-Darboux definition of integration, introductory formal logic, axioms for the real numbers, sequences, convergence, limits, continuity, related real analysis theorems including the monotone convergence theorem for sequences of real numbers and the Bolzano-Weierstrass theorem, existence of extrema, differentiation, applications of derivatives, proof of the fundamental theorem of calculus, Taylor polynomials, l'Hospital's rules, inverse functions; Linear Algebra - solving linear equations, matrix equations, linear independence, matrix transformations, matrix operations, matrix inverses, abstract vector spaces, subspaces, dimension and rank, determinants, Cramer's rule, complex numbers.
P&C:	https://programsandcourses.anu.edu.au/course/MATH1115
course learning outcomes:	Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. Demonstrate accurate and efficient use of calculus and linear algebra techniques. Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from calculus and linear algebra. Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
assessment:	Workshop presentation (5%) Assignments and online quizzes (25%) Tests during the semester (30%) Final examination (40%)

Mapped learning outcomes

learning outcome	1. KNOWLEDGE AND SKILL BASE						2. ENGINEERING APPLICATION ABILITY				3. PROFESSIONAL AND PERSONAL ATTRIBUTES						assessment tasks
learning outcome	1.1	1.2	1.3	1.4	1.5	1.6	2.1	2.2	2.3	2.4	3.1	3.2	3.3	3.4	3.5	3.6	1	2	3	4
Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts.	✓	✓															✓	✓	✓	✓
Demonstrate accurate and efficient use of calculus and linear algebra techniques.	✓	✓												✓			✓	✓	✓	✓
Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from calculus and linear algebra.	✓	✓	✓												✓		✓	✓	✓	✓
Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.	✓	✓	✓														✓	✓	✓	✓

Course contribution towards the Engineers Australia Stage 1 Competency Standard

This table depicts the relative contribution of this course towards the Engineers Australia Stage 1 Competency Standard. Note that this illustration is indicative only, and may not take into account any recent changes to the course. You are advised to review the official course page on P&C for current information..

1. KNOWLEDGE AND SKILL BASE
1.1
1.2
1.3
1.4
1.5
1.6
2. ENGINEERING APPLICATION ABILITY
2.1
2.2
2.3
2.4
3. PROFESSIONAL AND PERSONAL ATTRIBUTES
3.1
3.2
3.3
3.4
3.5
3.6

Engineers Australia Stage 1 Competency Standard — summary

1. KNOWLEDGE AND SKILL BASE
✓	1.1	Comprehensive, theory based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the engineering discipline.
✓	1.2	Conceptual understanding of the, mathematics, numerical analysis, statistics, and computer and information sciences which underpin the engineering discipline.
✓	1.3	In depth understanding of specialist bodies of knowledge within the engineering discipline.
	1.4	Discernment of knowledge development and research directions within the engineering discipline.
	1.5	Knowledge of contextual factors impacting the engineering discipline.
	1.6	Understanding of the scope, principles, norms, accountabilities and bounds of contemporary engineering practice in the engineering discipline.
2. ENGINEERING APPLICATION ABILITY
	2.1	Application of established engineering methods to complex engineering problem solving.
	2.2	Fluent application of engineering techniques, tools and resources.
	2.3	Application of systematic engineering synthesis and design processes.
	2.4	Application of systematic approaches to the conduct and management of engineering projects.
3. PROFESSIONAL AND PERSONAL ATTRIBUTES
	3.1	Ethical conduct and professional accountability.
	3.2	Effective oral and written communication in professional and lay domains.
	3.3	Creative, innovative and pro-active demeanour.
✓	3.4	Professional use and management of information.
✓	3.5	Orderly management of self, and professional conduct.
	3.6	Effective team membership and team leadership.

Updated: 18 February 2021/ Responsible Officer: Dean, CECS/ Page Contact: CECS Academic Education Services