Module FOUD0651: Maths Applications for Economics and Computing

Department: Foundation Year (Durham)

FOUD0651: Maths Applications for Economics and Computing

Prerequisites

• Core Foundation Maths for Scientists and Core Foundation Maths for Business and Economics

Corequisites

• None

Excluded Combination of Modules

• Maths Applications Advanced

Aims

• To provide the opportunity for students to engage in logical reasoning, algorithmic thinking and applications
• To introduce the concept of linear programming
• To extend knowledge of Cartesian coordinates in two dimensions to include equations of circles and lines.
• To introduce functions and relations
• To extend understanding of a range of standard techniques for differentiation and integration.
• To introduce and develop a knowledge of first order differential equations and its’ applications
• To introduce and develop knowledge of complex numbers and polar coordinates.
• To introduce and develop a knowledge of matrices and their applications.
• To develop a knowledge of vectors and their applications in two and three dimensions

Content

• Bipartate Graphs and matchings
• Shortest paths in networks (Dijkstra's algorithm)
• Spanning trees (Prim's and Kruska's algorithm and travelling salesperson problem)
• Minimum tour (postman problem)
• Critical Path Analysis
• Linear Programming
• Set, functions and types, domain, range and inverse functions.
• Trigonometrical functions of angles and graphs.
• Cartesian equations of straight lines, perpendicular lines and circles.
• Differentiation of functions defined parametrically and implicitly.
• Applications of first order differential equations.
• Matrices (n x m): addition, subtraction, multiplication, determinant, transpose, inverse. Applications to simultaneous equations.
• Complex numbers: +, -, x, /, complex conjugate, polar form, Argand diagrams, De Moivre's theorem.
• Vectors in two dimensions including: use of column and unit vectors, addition, subtraction and multiplication by scalar. Scalar (dot) and vector (cross) product and their applications.

Learning Outcomes

• By the end of the module students will be able to:
• Solve a range of predictable problems in Discrete Mathematics. (SSK1)
• Give standard Cartesian equations for circles and lines. (SSK2)
• Understand set, and define various types of functions and relations including trigonometry functions. (SSK 3)
• Understand parametric and implicit functions and first order differential equations. (SSK4)
• State the rules for addition, subtraction and multiplication of complex numbers and understand polar coordinates. (SSK5)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SSK6)
• Understand vectors and rules of application in two and three dimensions. (SSK7)

• By the end of the module the student will have acquired the skills to be able to:
• Reduce problems to a series of equations and inequalities and solve using linear programming techniques. (SSS1)
• Apply mathematics to a variety of problems (SSS2)
• Confidently manipulate a range of Cartesian and vector equations in two and three dimensions. (SSS3)
• Confidently manipulate various functions and solving equations. (SSS4)
• Recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.(SSS5)
• Understand and use first order differential equations in a range of situations as appropriate to the syllabus. (SSS6)
• Use complex numbers in a range of situations as appropriate to the syllabus. (SSS7)
• Use matrices in a number of mathematical situations. (SSS8)

• By the end of the module students will be able to:
• Apply number in the tackling of numerical problems (KS1)
• Effectively use algebra in mathematical modelling (KS2)
• Demonstrate problem solving skills (KS3)

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 seminars, tutorials and students' own time.
• In class tests, developing or consolidating the previous weeks’ work will be set which will contribute towards final the module mark. These tests 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 final exam.
• Ability to recall, select and use knowledge and manipulative skills will be tested by: tasks set by the tutor on a weekly basis, mid-module invigilated tests and an end of module exam.
• Test 1 covers SSK1. SSK2, SSS1, SSS2, SSS3, KS1, KS2, KS3
• Test 2 covers SSK3, SSK4, SSK5, SSS4, SSS5, SSS6, SSS7, KS1, KS2, KS3
• Examination covers SSK 2-7, SSS 3-8, KS1, KS2, KS3
• Portfolio covers SSK1-5, SSS1-8, KS1, KS2, KS3

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Students will be given 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 summative role (See Section 14). Students have access to two or more mock papers and answers to help prepare for the class tests and 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