- Code MATH1115
- 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
- Ivo Vekemans
- Mode of delivery In Person
First Semester 2022
See Future Offerings
See https://www.anu.edu.au/covid-19-advice. In Sem 1 2022, this course is delivered on campus with adjustments for remote participants.
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.
Note: This is an Honours Pathway Course (HPC).
It involves extra material and emphasises the use and understanding of proof and abstract ideas to a deeper conceptual level than MATH1013.
Upon successful completion, students will have the knowledge and skills to:
- 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.
Secondary School Prerequisite: A satisfactory pass in the ACT Specialist Mathematics double major, NSW HSC Mathematics Extension 2 or equivalent. Students with excellent results in either the ACT Specialist Mathematics major-minor, NSW HSC Mathematics Extension 1, or equivalent, may be permitted to enrol.
- In-workshop assessment (0-5%) (0) [LO 1,2,3,4]
- Assignments and online quizzes (20-25%) (20) [LO 1,2,3,4]
- Tests during the semester (25-30%) (30) [LO 1,2,3,4]
- Final examination (40-50%) (50) [LO 1,2,3,4]
- The final weighting of the assessment will be determined in the class summary when published. (null) [LO null]
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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 22 hours of workshop time.
- Approximately 60 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.
• Elementary Linear Algebra: Applications Version (11th edition) by Howard Anton and Chris Rorres or Elementary Linear Algebra: Applications Version (12th edition) by Howard Anton, Chris Rorres and Anton Kaul.
Students are assumed to have taken the highest level of high school mathematics available. For ACT students this means a double major in specialist mathematics. For NSW students this means HSC Maths Extension 2. Other students should have equivalent background knowledge.
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
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Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.