MATHS 1010 - Applications of Quantitative Methods in Finance I
North Terrace Campus - Semester 2 - 2020
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 Available for Study Abroad and Exchange Y Prerequisites MATHS 1009 Incompatible ECON 1005, ECON 1010, MATHS 1004, MATHS 1011, MATHS 1012, MATHS 1013 Restrictions Not available to BMaSc, BMthASc (Adv), BMaCompSc or BCompSc students 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, highlighting the inter-relationships of the mathematics and developing problem solving skills with a particular emphasis on financial and business applications.
Topics covered are: differential and integral calculus with applications; separable differential equations; functions of two real variables; Lagrange multipliers; sample spaces, conditional probability; an introduction to Markov chains; probability distributions (binomial, normal) and expected value.
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) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
Required ResourcesOutline lecture notes for use in the lectures will be provided via MyUni.
- Harshbarger, R.J. & Reynolds, J.J., Mathematical Applications for the Management, Life and Social Sciences 12th ed. (Cengage Learning).
This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes and videos, assignment and tutorial questions, and worked solutions. Students should make appropriate use of these resources. MyUni can be accessed here: https://myuni.adelaide.edu.au/
Students are also reminded that they need to check their University email on a daily basis. Sometimes important and time-critical information might be sent by email and students are expected to have read it. Any problems with accessing or managing student email accounts should be directed to Technology Services.
Learning & Teaching Activities
Learning & Teaching ModesThis course relies on lecture videos to guide students through the material, tutorial classes to provide students with small group and individual assistance, and a sequence of written and online assignments to provide formative assessment opportunities for students to practise techniques and develop their understanding of the course.
We provide additional support via discussions on MyUni and via "drop-in" help.
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 Assignments 11 55 Mid Semester Test 1 7 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 separable 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.
- 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 Written Assignments Formative and Summative 35% all Mid Semester Test Summative and Formative 25% 1,2,3,4 Final Exam Summative 40% 1,2,3,4,5,6
Assessment DetailPrecise details of the nature and timing of all assessment components will be provided on the MyUni site for this course.
SubmissionSee MyUni for comprehensive details regarding assignment submission, our late policy etc.
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.Replacement and Additional Assessment Examinations (R/AA Exams)
Students are encouraged to read the University's R/AA exam information on the University’s Examinations webpage here:
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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