Module FOUN0257: Further Maths for Finance

Department: Foundation Year

FOUN0257: Further Maths for Finance

Prerequisites

• None.

Corequisites

• None.

Excluded Combination of Modules

• Further Maths for Marketing & Management (FOUN0267)

Aims

• To improve confidence in algebraic manipulation through the study of mathematical techniques and development of investigative skills.
• to introduce and develop understanding of a range of standard techniques for integration to include trigometric and logarithmic functions.
• to provide the opportunity for students to engage in logical reasoning, algorithmic thinking and applications.
• to introduce and develop a knowledge of matrices and their applications.
• to introduce and develop knowledge of complex numbers.
• to introduce and develop the concept of linear programming

Content

• complex numbers: +, -, x, /, complex conjugate, Argand diagrams.
• Matrices 2x2 and nxm, addition, subtraction and multiplication, determinant, transpose and inverse. Applications to simultaneous equations.
• Linear Programming
• Sequences and series, arithmetic, geometric, use of sigma notation.
• Evaluation of integrals by using standard forms, substitution or partial fractions.
• Spanning trees (Prim's and Kruska's algorithm and travelling salesperson problem).

Learning Outcomes

• Differentiate and integrate a number of different types of functions (SK1)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SK2)
• Solve a range of predictable problems in discrete mathematics (SK3).

• By the end of the module the student will have acquired the skills to be able to:
• recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts (SS1)
• confidently manipulate a range of algebraic expressions and use a range of techniques in a variety of contexts and as required in problems appropriate to the syllabus (SS2)
• understand and use complex numbers in a range of situations as appropriate to the syllabus. (SS3)
• use matrices in a number of mathematical situations. (SS4)
• reduce problems to a series of equations and inequalities and solve using linear programming techniques. (SS5)
• apply mathematics to a variety of problems (SS6).

• By the end of the module the student will:
• be able to apply number in the tackling of numerical problems (KS1)
• be able to demonstrate problem solving skills (KS2)
• In-class Test covers some of SK1-SK2, SS1-SS6, KS1-KS2
• Examination covers SK1-SK3, SS1-SS6, KS1-KS2
• Portfolio covers some of SK1-SK3, SS1-SS6, KS1-KS2,

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Theory, initial concepts and techniques will be introduced during lectures.
• Much of the learning, understanding and consolidation will take place through the use of structured worksheets during tutorials and students' own time.
• Small coursework tasks testing, developing or consolidating the previous weeks work will be set usually on a weekly basis. These tutor marked tasks allow rapid feedback and build confidence. Whilst the marks accumulate towards the overall portfolio mark, the tasks also perform a formative role enabling students to reflect on their own performance, identify areas of weakness, and practice some of the skills and techniques which will be required in the longer in-class tests and exam. Additionally, they ensure that students master specific skills to an appropriate level prior to their requirement in more complex tasks. As an example, an early task on differentiation might require students to differentiate 4 functions. Tutor feedback from this tasks ensures that students are ready to build on these skills when moving on to integration.
• Ability to recall, select and use knowledge will be tested by a short class test and invigilated end of module exam in addition to the portfolio of tasks. The class test which will be given in 4 separate 15-minute sub-tests, will focus on selected subsets of content. In addition to their summative role, these tests also serve a formative function helping to prepare students for their end of module exam which will test a wider area of content.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Self-testing units on a weekly basis in the form of worksheets with answers and/or DUO quizzes. Portfolio tasks with a rapid marking turnaround fulfill a formative as well as a summative role (see Section 14.). Students have access to 2 or more mock papers and answers to help prepare for the exam.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University