MATHS 1010 - Applications of Quantitative Methods in Finance I
North Terrace Campus - Semester 2 - 2014
General Course Information
Course Code MATHS 1010 Course Applications of Quantitative Methods in Finance I Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 5.5 hours per week Prerequisites MATHS 1009 Incompatible MATHS 1011, MATHS 1012, MATHS 1013 Restrictions Not available to BMaSc, BMaCompSc, BCompSc Course Description Together with MATHS 1009 Introduction to Financial Mathematics I, this course provides an introduction to the basic mathematical concepts and techniques used in finance and business and includes topics from calculus, linear algebra and probability, emphasising their inter-relationships and applications to the financial area; introduces students to the use of computers in mathematics; develops problem solving skills with a particular emphasis on financial and business applications.
Topics covered are: Calculus: differential and integral calculus with applications; functions of two real variables. Probability: basic concepts, conditional probability; probability distributions and expected value with applications to business and finance.
Course Coordinator: Dr Adrian Koerber
The full timetable of all activities for this course can be accessed from Course Planner.
Course Learning OutcomesOn successful completion of this course students will be able to:
- Demonstrate understanding of basic concepts in calculus, relating to differentiation, integration and differential equations.
- Demonstrate understanding of basic concepts in probability, relating to conditonal probability, markov chains, and probability distributions.
- Demonstrate understanding of concepts in two variable calculus.
- Employ methods related to these concepts in a variety of financial applications.
- Apply logical thinking to problem solving in context.
- Use appropriate technology to aid problem solving.
- Demonstrate skills in writing mathematics.
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Knowledge and understanding of the content and techniques of a chosen discipline at advanced levels that are internationally recognised. all The ability to locate, analyse, evaluate and synthesise information from a wide variety of sources in a planned and timely manner. 4,5 An ability to apply effective, creative and innovative solutions, both independently and cooperatively, to current and future problems. 1,2,3,4,5,6 A proficiency in the appropriate use of contemporary technologies. 6 A commitment to continuous learning and the capacity to maintain intellectual curiosity throughout life. all
- Applications of Quantitative Methods in Finance I: Student Summary Notes.
- Introduction to Financial Mathematics I: Student Summary Notes.
- Harshbarger, R.J. & Reynolds, J.J., Mathematical Applications for the Management, Life and Social Sciences 9th ed. (Houghton-Mifflin).
- Lial, M.L. & Hungerford, T.W., Mathematics with Applications 8th ed. (Addison-Wesley).
Online LearningThis course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lectures to guide students through the material, tutorial classes to provide students with class/small group/individual assistance, and a sequence of written and online assignments to provide formative assessment opportunities for students to practice techniques and develop their understanding of the course.
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 48 72 Tutorials 11 22 Computer Labs 3 3 Assignments 11 53 Mid Semester Test 1 6 Total 156
Learning Activities SummaryThe two topics of calculus and probability detailed below are taught in parallel, with two lectures a week on each. The tutorials are a combination of the two topics, pertaining to the previous week's lectures. (The section on two-variable calculus is actually taught at the end of the probability stream.)
- The Derivative (8 lectures)
- Rates of change, the derivative.
- Rules for differentiation.
- Critical points, concavity.
- Applications of the Derivative (4 lectures)
- Marginal cost/revenue/profit.
- Min/max problems.
- Integration (9 lectures)
- Upper and lower sums.
- Definite integral, Fundamental Theorem of Calculus.
- Techniques for integration.
- Trapezoidal rule.
- Differential Equations (2 lectures)
- Introduction and seperable DEs.
- Probability (6 lectures)
- Sample spaces, odds, unions, intersections.
- Conditional probability.
- Bayes' Formula, Law of Total Probablity.
- Markov Chains (3 lectures)
- Introduction to random processes.
- Transition matrices, steady state.
- Probability Distributions (6 lectures)
- The binomial distribution.
- Expected value and variance of a probability distribution.
- The normal distribution.
- Functions of two variables, partial derivatives.
- Critical points and classification.
- Lagrange multipliers.
Tutorial 1: Sets, Venn diagrams, simple probability. Rate of change, derivative.
Tutorial 2: Conditional probability. Derivatives and applications.
Tutorial 3: Probability tree diagrams, Bayes' Theorem. Differentiation rules.
Tutorial 4: Markov chains. Chain rule, implicit differentiation.
Tutorial 5: Binomial probability. Critical points of functions.
Tutorial 6: Expectation, payoff matrix. Applications of calculus.
Tutorial 7: Normal distribution. Estimation of area under a curve.
Tutorial 8: Functions of 2 variables. Fundamental Theorem of Calculus. Definite integrals.
Tutorial 9: Partial derivatives. Integration techniques.
Tutorial 10: Critical points of a function of 2 variables. First order differential equations.
Tutorial 11: Lagrange multipliers. Improper integrals.
Tutorial 12: Applications of functions of 2 variables. Numerical integration.
(Note: This tutorial is not an actual class, but is a set of typical problems with solutions provided.)
Note: Precise tutorial content may vary due to the vagaries of public holidays.
Week 6: Probability simulation.
Week 10: 3-D surfaces.
Week 12: Evaluation of integrals.
- The Derivative (8 lectures)
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Task Task Type Weighting Learning Outcomes Assignments Formative 15% all Mid Semester Test Summative and Formative 15% 1,2,3,4,5 Exam Summative 70% 1,2,3,4,5,7
Assessment Related RequirementsAn aggregate score of 50% is required to pass the course. Furthermore students must achieve at least 45% on the final examination to pass the course.
Assessment item Distributed Due date Weighting Assignment 1 week 1 week 3 1.4% Assignment 2 week 2 week 4 1.4% Assignment 3 week 3 week 5 1.4% Assignment 4 week 4 week 6 1.4% Assignment 5 week 5 week 7 1.4% Assignment 6 week 6 week 8 1.4% Assignment 7 week 7 week 9 1.4% Assignment 8 week 8 week 10 1.4% Assignment 9 week 9 week 11 1.4% Assignment 10 week 10 week 12 1.4% Assignment 11 week 11 week 13 1.4% Mid Semester Test week 8 15%
- All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
- Late assignments will not be accepted without a medical certificate.
- Written assignments will have a one week turn-around time for feedback to students.
Grades for your performance in this course will be awarded in accordance with the following scheme:
M10 (Coursework Mark Scheme) Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
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