MATHS 1009 - Introduction to Financial Mathematics I

North Terrace Campus - Semester 1 - 2019

Together with MATHS 1010 Applications of Quantitative Methods in Finance 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: polynomial, exponential and logarithmic functions; limits, sequences, interest rates and annuities; linear equations, matrices and determinants; Leontief economic models; optimisation (linear programming).

• General Course Information
Course Details
Course Code MATHS 1009 Introduction to Financial Mathematics I School of Mathematical Sciences Semester 1 Undergraduate North Terrace Campus 3 Up to 5.5 hours per week Y ECON 1005, ECON 1010, MATHS 1011, MATHS 1012, MATHS 1013 SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) Not available to BMaSc, BMaCompSc, BCompSc students Together with MATHS 1010 Applications of Quantitative Methods in Finance 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: polynomial, exponential and logarithmic functions; limits, sequences, interest rates and annuities; linear equations, matrices and determinants; Leontief economic models; optimisation (linear programming).
Course Staff

Course Coordinator: Dr Stuart Johnson

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 linear algebra, relating to linear equations, matrices, and optimization.
2. Demonstrate understanding of concepts relating to functions and annuities.
3. Employ methods related to these concepts in a variety of financial applications.
4. Apply logical thinking to problem solving in context.
5. Use appropriate technology to aid problem solving.
6. 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
3,4,5
• Learning Resources
Required Resources
Outline lecture notes for use in the lectures will be provided via MyUni.
Recommended Resources
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 extensively and exclusively for providing electronic resources, such as lecture notes, 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 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 algebra and functions & annuities 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.

Lecture Outline

Algebra

• Linear Equations and Matrices (9 lectures)
• Algebra of matrices and vectors.
• Systems of linear equations, elementary row operations, Gauss-Jordan elimination.
• Inverse of a matrix and applications to solution of systems of equations.
• Leontief Economic Models (6 lectures)
• Leontief open and closed economic model. Determinants.
• Optimization (8 lectures)
• Linear inequalities, linear programming problems, geometric and algebraic solution.
• Simplex algorithm.
Functions & Annuities
• Functions (11 lectures)
• Linear and quadratic functions with applications. Domain, graph and composition of functions.
• Simple rational functions, modulus, piecewise defined functions.
• Exponential and logarithmic functions.
• Limits and continuity.
• Financial Mathematics (12 lectures)
• Arithmetic and geometric sequences.
• Simple and compound interest.
• Present and future values.
• Continuous compounding.
• Annuities, loans and amortization.
Tutorial Outline

Tutorial 1: Matrices, matrix operations and applications. Linear functions, composition of functions.

Tutorial 2: Systems of linear equations in matrix form. Polynomial and piecewise-defined functions.

Tutorial 3: Gauss-Jordan elimination. Rational and exponential functions.

Tutorial 4: General solution of a linear system. Exponentials, logarithms and applications.

Tutorial 5: Inverse matrices. Leontief models. Compound interest.

Tutorial 6: Determinants. Rational functions, continuity.

Tutorial 7: Closed Leontief models.Comparison of interest rates.

Tutorial 8: Linear optimization. Geometric sequences.

Tutorial 9: Linear optimization. Present and future value.

Tutorial 10: Simplex algorithm. Annuities.

Tutorial 11: Simplex algorithm. Amortization schedules.

Tutorial 12: Formulation of linear programming problems. Loans and amortization.
(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 Exam Summative 70% 1,2,3,4,6
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 1.36%
Assignment 2 week 2 week 4 1.36%
Assignment 3 week 3 week 5 1.36%
Assignment 4 week 4 week 6 1.36%
Assignment 5 week 5 week 7 1.36%
Assignment 6 week 6 week 8 1.36%
Assignment 7 week 7 week 9 1.36%
Assignment 8 week 8 week 10 1.36%
Assignment 9 week 9 week 11 1.36%
Assignment 10 week 10 week 12 1.36%
Assignment 11 week 11 week 13 1.36%
Mid Semester Test week 7 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:

In this course Additional (Academic) exams will be granted to those students who have obtained a final mark
of 40–49%.
• 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
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

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