## 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 Applications of Quantitative Methods in Finance I School of Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 5.5 hours per week Y MATHS 1009 ECON 1005, ECON 1010, MATHS 1011, MATHS 1012, MATHS 1013 Not available to BMaSc, BMaCompSc, BCompSc students 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 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.

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.

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.
• 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.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
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: