MODULE SPECIFICATION KEY FACTS Module name Foundation Mathematics Module code AS0002 School Cass Business School Department or equivalent UG Programme UK credits 40 ECTS 20 Level 3 Delivery location (partnership programmes only) MODULE SUMMARY Module outline and aims The aim of this module is to consolidate your knowledge of mathematics and to introduce more advanced topics in the areas of calculus and linear algebra. The mathematical techniques taught in this module will be necessary for the understanding of modules throughout the degree. As the business world embraces the use of bigger data in all areas of operation, these techniques will also prove invaluable in your future employment. Content outline Elementary propositional logic, set theory, predicate logic. The natural numbers, integers, rational numbers and real numbers. Laws of indices, rational exponents. Permutations and combinations, expansion of (a+x)n for positive integral n. Expansion and factorization of algebraic expressions. Polynomials: division, the remainder theorem. Partial fractions. Summation of simple series: arithmetic and geometric progressions, sum of r(r+1), sum of r2, sum of r3. Simple inequalities and the modulus. Real-valued functions of one variable: graphical representation, trigonometric functions, exponential and logarithmic functions. Solution of equations: linear simultaneous equations, one linear and one quadratic equation, trigonometric equations. Two-dimensional coordinate geometry: distance between two points, gradient of a line, equation of a line, Cartesian and parametric equations of simple curves. Differentiation: rates of change, differentiation of polynomial, trigonometric,
exponential and logarithmic functions, differentiation of products, quotients and composites, differentiation of functions defined implicitly or parametrically. Applications to gradients, maxima and minima, equations of tangents and normals to curves. Integration: indefinite and definite integrals of polynomial, trigonometric and exponential functions, areas under curves, the methods of substitution and parts. Functions: inverse trigonometric, hyperbolic, inverse hyperbolic, including derivatives. Indeterminacy and limits. Differentiation: definition of derivative and standard results. Further examples on differentiation. Higher derivatives, Leibniz's theorem. Applications: local approximation, Taylor s theorem. Matrices: their algebra, row-reduction and row-equivalence, non-singular matrices, determinants, inverses by adjoints and by row-reduction. Solutions of sets of linear simultaneous equations. Complex numbers: their algebra, polar representation, the Argand diagram, their application in geometry and trigonometry. WHAT WILL I BE EXPECTED TO ACHIEVE? On successful completion of this module, you will be expected to be able to: Knowledge and understanding: Demonstrate an ability to carry out basic algebraic manipulation. Sketch elementary curves. Know how to manipulate and use matrix methods. Understand the basic idea of differential calculus and be able to differentiate elementary functions. Understand the basic idea of integration and be able to apply standard techniques for evaluating elementary integrals. Have a basic idea of the method of solution of differential equations. Be conversant with the definition and properties of the elementary functions. Skills: Differentiate and integrate elementary functions using standard results. Apply the basic skills to a wide range of problems. Manipulate and work with matrices. Differentiate compound functions using standard results. Values and attitudes: Appreciate the value of standard techniques in calculus and algebra. Understand the widespread use of these techniques in solving problems in the business world
HOW WILL I LEARN? A variety of learning and teaching methods will be used in this course. Lectures are used to introduce context, concepts and techniques. All new concepts and techniques will be illustrated with worked examples and you will also have the opportunity to work through examples and exercises with the support of the lecturer. It is strongly recommended that you attend ALL lectures. Key learning and teaching resources will be put on the module website on Moodle. In the independent study time you are encouraged to consolidate your knowledge in the particular topics covered by the lectures. You should also spend time working through sample exercises and questions to make sure that you are comfortable with all the techniques presented. As you will be frequently assessed on this module through class tests you will need to keep on top of the work as in mathematics new techniques extend previous techniques which you will have been expected to master. Teaching pattern: Teaching component Teaching type Contact (scheduled) Self-directed study (independent) Placement Lectures Lecture 120 280 400 Total student learning Totals 120 280 400 WHAT TYPES OF ASSESSMENT AND FEEDBACK CAN I EXPECT? Assessments This module is assessed by coursework divided into six sets covering different parts of the syllabus. Each coursework set will consist of a number of exercises and tests. The weighting of the individual assessments within each set will vary, and full details will be given at the start of the course. Each coursework set must be passed with an aggregate mark of 55% in addition to achieving the module pass mark. Assessment pattern: Assessment component Assessment type Weighting Minimum qualifying Pass/Fail?
1 2 3 4 5 6 mark Set exercise 0% 55% N/A Assessment criteria Assessment criteria are descriptions of the skills, knowledge or attributes you need to demonstrate in order to complete an assessment successfully and Grade-Related Criteria are descriptions of the skills, knowledge or attributes you need to demonstrate to achieve a certain grade or mark in an assessment. Assessment Criteria and Grade- Related Criteria for module assessments will be made available to you prior to an assessment taking place. More information will be available in the UG Assessment Handbook and from the module leader. Feedback on assessment Following an assessment, you will be given your marks and feedback in line with the University s Assessment Regulations and Policy. More information on the timing and type of feedback that will be provided for each assessment will be available from the module leader. Assessment Regulations The Pass mark for the module is 60%. Any minimum qualifying marks for specific assessments are listed in the table above. The weighting of the different components can also be found above. The Programme Specification contains information on what happens if you fail an assessment component or the module. INDICATIVE READING LIST Bostock, L. and Chandler, F.S. 2013. Core Maths Advanced Level. 3 rd ed. Oxford: Nelson Thornes. Bostock, L., Chandler, F.S. and Rourke, C.P. 1982. Further Pure Mathematics. Oxford: Nelson Thornes. Version: 1.0
Version date: April 2016 For use from: 2016-17 Appendix: see http://www.hesa.ac.uk/component/option,com_studrec/task,show_file/itemid,233/mnl,12 051/href,JACS3.html/ for the full list of JACS codes and descriptions CODES HESA Cost Centre Description Price Group 122 Mathematics C JACS Code Description Percentage (%) G100 The rigorous analysis of quantities, magnitudes, forms and their relationships, using symbolic logic and language, both in its own right and as applied to other disciplines 100%