Module FOUD0651: Calculus and Further Maths with Statistics and Decision Maths

Department: Foundation Year (Durham)

FOUD0651: Calculus and Further Maths with Statistics and Decision Maths

Prerequisites

• Any Core Foundation Maths or equivalent modules

Corequisites

• None

Excluded Combination of Modules

• FOUD0638, FOUD0551, FOUD0301

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 to include equations of circles and lines.
• To extend understanding of a range of standard techniques for differentiation and integration.
• To introduce and develop a knowledge of first and second order differential equations and their applications
• To introduce and develop knowledge of complex numbers and polar coordinates.
• To introduce and develop a knowledge of matrices and their applications.
• To improve confidence in algebraic manipulation

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
• Trigonometrical functions of angles and graphs.
• Series expansions
• Cartesian equations of straight lines, perpendicular lines and circles.
• Consolidation of Integration by parts and integration by substitution
• Differentiation of functions defined parametrically and implicitly.
• First order differential equations and applications including separating variables.
• Second 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.
• mean, mode, median and standard deviation
• Normal Distribution and significance
• Linear Regression

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 parametric and implicit functions and first and second order differential equations. (SSK3)
• State the rules for addition, subtraction and multiplication of complex numbers and understand polar coordinates. (SSK4)
• State the rules for addition, subtraction and multiplication of matrices and for finding inverses. (SSK5)

• 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 equations (SSS3)
• Select and use statistical techniques as required in problems appropriate to the syllabus. (SSS4)
• Recall, select and use knowledge of appropriate integration and differentiation techniques as needed in a variety of contexts.(SSS5)
• Understand and use first and second order differential equations in a range of situations as appropriate to the syllabus. (SSS6)
• Understand and 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)
• Demonstrate problem solving skills (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 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 SSK2, SSS2, SSS3, SSS4 KS1, KS2,
• Test 2 covers SSK1, SSK2, SSS1, SSS2, SSS3, KS1, KS2,
• Examination covers SSK 2-5, SSS2, SSS3, SSS5-8, KS1, KS2,
• Portfolio covers SSK1-5, SSS1-8, KS1, KS2,
• In addition to obtaining an overall weighted mark of 50% or above, students must obtain a mark of 50% or above for the following element/s - Test 2 & Exam

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