- Code MATH1116
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career UGRD
- Dr Griffith Ware
- Mode of delivery In Person
Second Semester 2020
See Future Offerings
All activities that form part of this course will be delivered remotely in Sem 2 2020.
This course continues on from MATH1115, providing an in-depth development of 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 - short introduction to metric spaces in the context of the calculus of functions of several variables, generalisation of the real analysis theory studied in MATH1115 to multivariable functions including limits and continuity, double integrals, Fubini's theorem, integrability of continuous functions, partial derivatives, gradients and directional derivatives, differentiation of multivariable functions, extreme values, vector functions, curves and parametrisations, infinite series, convergence tests, power series, Taylor series;
Linear Algebra – subspaces, span, linear independence, bases and dimension, linear maps, duality, eigenvalues and eigenvectors, inner product spaces, Gram-Schmidt orthogonalisation, operators on inner product spaces, the spectral theorem in finite dimensions, singular value decomposition.
Note: This is an Honours Pathway Course. It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1014.
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of analysis and linear algebra and their role in modern mathematics and applied contexts.
- Demonstrate accurate and efficient use of analysis and linear algebra techniques.
- Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts and theorems from analysis and linear algebra.
- Apply problem-solving using analysis and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
- In-workshop assessment (0-5%) (0) [LO 1,2,3,4]
- Assignments and online quizzes (25-30%) (30) [LO 1,2,3,4]
- Tests during the semester (25-35%) (30) [LO 1,2,3,4]
- Final examination (35-45%) (40) [LO 1,2,3,4]
- The final weighting of the assessment will be determined in the class summary when published. (null) [LO null]
In response to COVID-19: Please note that Semester 2 Class Summary information (available under the classes tab) is as up to date as possible. Changes to Class Summaries not captured by this publication will be available to enrolled students via Wattle.
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The expected workload will consist of approximately 130 hours throughout the semester including:
- Face-to face component which may consist of 4 x 1 hour lecturer per week (48 hours) as well as 20 hours of workshop time.
- Approximately 62 hours of self-study per semester which will include preparation for lectures, quizzes and other assessment tasks.
There are no course-specific inherent requirements.
Requisite and Incompatibility
Essential Calculus (2nd edition) by James Stewart.
Linear Algebra Done Right (3rd edition) by Sheldon Axler.
Tuition fees are for the academic year indicated at the top of the page.
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- Student Contribution Band:
- Unit value:
- 6 units
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Offerings, Dates and Class Summary Links
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Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.