MATHS 1010 - Applications of Quantitative Methods in Finance I

North Terrace Campus - Semester 2 - 2019

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.

  • General Course Information
    Course Details
    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 1011, MATHS 1012, MATHS 1013
    Restrictions Not available to BMaSc, BMaCompSc, 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 Staff

    Course Coordinator: Dr Adrian Koerber

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    On successful completion of this course students will be able to:
    1. Demonstrate understanding of basic concepts in calculus, relating to differentiation, integration and differential equations.
    2. Demonstrate understanding of basic concepts in probability, relating to conditonal probability, markov chains, and probability distributions.
    3. Demonstrate understanding of concepts in two variable calculus.
    4. Employ methods related to these concepts in a variety of financial applications.
    5. Apply logical thinking to problem solving in context.
    6. Use appropriate technology to aid problem solving.
    7. 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
    4,5,6
  • Learning Resources
    Recommended Resources
    1. Harshbarger, R.J. & Reynolds, J.J., Mathematical Applications for the Management, Life and Social Sciences 12th ed. (Cengage Learning).
    Online Learning
    This 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 Modes
    This 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.
    Workload

    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 Summary
    The 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.)

    Lecture Outline

    Calculus
    • 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
    • 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.
    Calculus of Two Variables (8 lectures)
    • Functions of two variables, partial derivatives.
    • Critical points and classification.
    • Lagrange multipliers.
    Tutorial Outline

    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.

  • Assessment

    The University's policy on Assessment for Coursework Programs is based on the following four principles:

    1. Assessment must encourage and reinforce learning.
    2. Assessment must enable robust and fair judgements about student performance.
    3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
    4. Assessment must maintain academic standards.

    Assessment Summary
    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 Requirements
    An 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 Detail
    Assessment itemDistributedDue dateWeighting
    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%
    Submission
    1. All written assignments are to be e-submitted following the instructions on MyUni.
    2. Late assignments will not be accepted without a medical certificate.
    3. Written assignments will have a one week turn-around time for feedback to students.
    See MyUni for more comprehensive details regarding assignment submission, our late policy etc.
    Course Grading

    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:
    https://www.adelaide.edu.au/student/exams/modified-arrangements-for-coursework-assessment/replacement-examinations-and-additional-assessment
  • Student Feedback

    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.

  • Student Support
  • Policies & Guidelines
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