School Of Mathematics And Statistics University Of St .

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University of St Andrews - School of Mathematics and StatisticsThis is a list of the 1000-level and 2000-level modules that were available to students during the2019-2020 academic year. The School's sub-honours courses remain broadly the same fromyear to year, but this list of module offerings is for illustration purposes only and does notconstitute a guarantee of the specific modules, module content or timetabling to be offered infuture years.1000-level modulesMT1001MT1002MT1003MT1007MT1010Introductory MathematicsMathematicsPure and Applied MathematicsStatistics in PracticeTopics in Mathematics: Problem-solving TechniquesID1003 Great Ideas 1MT1901 Topics in Contemporary Mathematics (Evening degree programme only)MT1001 Introductory Timetable9.00 amDescriptionThis module is designed to give students a secure base in elementary calculusto allow them to tackle the mathematics needed in other sciences. Studentswishing to do more mathematics will be given a good foundation from whichthey can proceed to MT1002. Some of the work covered is a revision andreinforcement of material in the Scottish Highers and many A-Level syllabuses.1

PrerequisitesHigher or A-Level Mathematics (A/S level Mathematics with approval of Head ofSchool).Antirequisites MT1003, MT2501-MT5999Lectures andtutorials5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 -11).AssessmentWritten Examination 90% (2-hour final exam 70%, 2 class tests 10%each), Coursework 10%ModulecoordinatorDr C V TranLecturerDr V Archontis, Dr P Pagano, Dr C V Tran, Dr S YardleySyllabusBasic properties of real numbers (real numbers, intervals, inequalities)Algebraic equations (including quadratic equations)Sequences and series (definitions, arithmetic and geometric series, binomial series)Functions (domain and range, odd and even, one to one, function composition, inversefunctions)Exponential and logarithm (including expressions in different bases, solving equationsinvolving exp and log)Trigonometry (basic functions, inverse functions, trigonometric identities, solving trigonometricequations)Curve sketchingGeometry: straight lines and circlesLimits and continuityDifferentiation (introduction, derivatives of elementary functions, rules for calculatingderivatives)Integration (introduction, connection with differentiation, techniques of integration)MT1002 /20Timetable9.00 amThis module is designed to introduce students to the ideas, methods andtechniques which they will need for applying mathematics in the physicalsciences or for taking the study of mathematics further. It aims to extend and2

DescriptionPrerequisitesenhance their skills in algebraic manipulation and in differential and integralcalculus, to develop their geometric insight and their understanding of limitingprocesses, and to introduce them to complex numbers and matrices.MT1001 or B at Advanced Higher Mathematics or B at A-Level Mathematics orequivalent qualificationAntirequisitesLectures andtutorials5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11).AssessmentWritten Examination 90% (2-hour final exam 70%, 2 class tests 10%each), Coursework 10%ModulecoordinatorDr A Wilmot-Smith (S1); Dr T Coleman (S2)LecturerDr T Coleman, Prof C E Parnell, Dr M Todd, Dr A Wilmot-Smith (S1); Dr TColeman, Dr A P Naughton, Dr A Wilmot-Smith (S2)SyllabusRevision of integration techniques, hyperbolic functions and applications to integration;Limits of functions, l’Hospital’s rule;Complex numbers: their arithmetic, Argand diagram, modulus-argument form, de Moivre’stheorem, powers and roots, geometric and trigonometric applications;Differential equations: first order separable, first order linear, second order with constantcoefficients both homogeneous and inhomogeneous;Matrices, determinants and linear equations: basic matrix operations, inverses including byrow operations, determinants and their properties, solutions of systems of linear equations,including degenerate cases;Vectors: Vector operations, including scalar and vector product, geometrical applicationsincluding equations of lines and planes;Proof: the need for precision in mathematics, basic types of proof, including induction;Sequences and series: convergence of sequences, convergence of series, geometric series,tests for convergence, power series, Taylor-Maclaurin series, including standard examples(exp, sine, etc.).Reading listE. Kreyszig, Advanced Engineering Mathematics (John Wiley, 2011). [This book covers muchmore material than just this module and will be useful for many level 2 modules.]Robert A. Adams, Calculus - A Complete Course (6th Edition) (Prentice Hall, 2006).E. W. Swokowski, M. Olinick, D. Pence, Calculus (6th Edition) (Addison Wesley, 2003). [Thisbook is out of print, but is in the library and may be available second-hand.]K. E. Hirst Numbers, Sequences and Series, (Edward Arnold, 1995).K. E .Hirst Vectors in 2 and 3 Dimensions, (Edward Arnold, 1995).3

MT1003 Pure and Applied Timetable9.00 amDescriptionThe aim of this module is to provide students with a taste of both pure andapplied mathematics, to give them insight into areas available for study in lateryears and to provide them with the opportunity to broaden their isitesLectures andtutorials5 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11).AssessmentWritten Examination 90% (2-hour final exam 70%, 2 class tests 10%each), Coursework 10%ModulecoordinatorDr H CammackLecturerDr C Bleak, Dr H CammackSyllabusFunctions and Relations.Natural numbers and integers. Elementary number theory.Rational numbers, irrational numbers, real numbers.Groups. Permutations and geometric symmetries,subgroups.Graphs. Hamiltonian and Eulerian paths, planarity, trees.Discrete and continuous descriptions.Simple continuous mathematical models applied to mechanical, thermal and biologicalproblems. Autonomous systems.Solution of difference equations with applications to economics and population dynamics.The logistic and related equations. Chaos.Difference equations as iterative methods for solving algebraic equations.Numerical solution of initial value problems using simple difference schemes.Reading listAdvanced Engineering Mathematics E Kreyszig; Wiley; 20014

Calculus, R A Adams; Pearson; 2002.Calculus (6th Edition) E W Swokowski, M Olinick, D Pence; PWS; 1994.MT1007 Statistics in etable11.00 amDescriptionThis module provides an introduction to statistical reasoning, elementary butpowerful statistical methodologies, and real world applications of statistics. Casestudies, such as building an optimal stock portfolio, and data vignettes are usedthroughout the module to motivate and demonstrate the principles. Students gethands-on experience exploring data for patterns and interesting anomalies aswell as experience using modern statistical software to fit statistical models todata.PrerequisitesAn A grade at GCSE or an A grade National 5 Mathematics or a C grade at ASlevel Mathematics or a C grade at Higher Mathematics.AntirequisitesLectures andtutorials4 lectures (weeks 1 - 10), 1 tutorial and 1 laboratory (weeks 2 - 11).Assessment2-hour Written Examination 50%, Coursework 50%ModulecoordinatorDr M L BurtLecturerDr M L Burt, Dr C G PaxtonMT1010 Topics in Mathematics: Problem-solving imetable10.00 am Mon (odd weeks), Wed and Fri5

DescriptionThis module introduces some important basic concepts in mathematics and alsoexplores problem-solving in the context of these topics. It is intended tostrengthen the mathematical skills of an undergraduate entering on the FastTrack route into the MMath degree programme.PrerequisitesAdmission onto the Fast Track MMath degree programmeAntirequisitesLectures andtutorials1.5-hour lecture, 1 practical and 1 tutorial (x 10 weeks)Assessment1.5-hour Written Examination 50%, Coursework 50%ModulecoordinatorDr J N ReinaudLecturerDr T Coleman, Dr V M Popov, Dr J N ReinaudThis module is taken only by students on the Fast Track route through the MMath degreeprogramme.SyllabusThe syllabus splits into five blocks, each consisting of two weeks, covering: properties of integers, the Euclidean Algorithm;Polynomials, their roots and divisibility properties;Sequences and convergence (iterative schemes, Newton's Method, Euler Algorithm);Euclidean geometry (possible topics including conic sections, equations of parabolae,ellipses, etc.);5. Combinatorics and probability.Block 5 will tie in with the material that students are covering during the semester in MT2504.Reading listDavid M. Burton, Elementary Number Theory, Allyn & Bacon, 1976Erwin Kreyszig, Advanced Engineering Mathematics, Wiley, 2011Earl W. Smokowski, Michael Olinick & Dennis Pence, Calculus, PWS Pub. Co., 1994Sheldon Ross, A First Course in Probability, Pearson, 2014ID1003 Great Ideas 1Credits20.0Semester1Academicyear2019/206

Timetable1.00 pm Mon, 1.00 pm Tue, 1.00 pm ThuThe aim of this module is to trace some of the major intellectual and societalthreads in the development of modern civilisation: the 'canon' of modernthought. The module is in three sections.Part 1 is "Arguments and Facts" and explores the fundamentals of logic,analysis and reasoning.DescriptionPart 2. "Rhetoric, Debate and Understanding" will explore how argument can beused to cajole, convert, persuade and entertain and emphasise the importancein understanding another person's position.Part 3 "Applying Analysis" takes the learning and skills of the previous sectionsand applies them to some of the great texts and artworks of western civilisation.PrerequisitesAntirequisitesLectures andtutorials2 to 3 lectures and 1 tutorial.Assessment2-hour Written Examination 50%, Coursework 50%ModulecoordinatorDr C PaxtonLecturerTeam taughtMT1901 Topics in Contemporary tableNext available TBDDescriptionThis module will introduce areas of contemporary mathematics and statistics ata basic level. Topics may include chaos and fractals, the golden ratio,mathematical modelling of populations and analysis of the resulting equations.The statistical component will consider how to graph data, and will introduceprobability, odds and betting, basic descriptive statistics and uncertainty andrisk. The topics will be illustrated by simple examples and day-to-day situations.7

PrerequisitesEntry to the Evening Degree programme. Basic algebraic manipulation, but notany knowledge of calculus, will be assumed. (Maths Standard Grade (Creditlevel) or Maths GCSE (Higher tier) would provide sufficient algebraicbackground.)AntirequisitesLectures andtutorials1 x 3-hour session (lecture plus tutorial).AssessmentCoursework 100%ModulecoordinatorTBCLecturerTBCThis module runs in alternate years.SyllabusRecurrence relations and applications, Fibonacci numbers;Newton’s mathematics;Fractals, chaos, Julia sets and the Mandelbrot set;Modern statistics, looking at data, basic probability;Statistical inference and hypothesis testing.Assumed knowledgeBasic algebraic manipulation, but not any knowledge of calculus, will be assumed. (MathsStandard Grade (Credit level) or Maths GCSE (Higher tier) would provide sufficient algebraicbackground.) This material will be reviewed in the first session.Reading listStephen B. Maurer & Anthony Ralston, Discrete Algorithmic Mathematics (Addison-Wesley,1991) [Chapter 5, p366-437].Richard Johnsonbaugh, Discrete Mathematics (Pearson, 2005) [Chapter 7.1-7.2, pp279-304].Kenneth H. Rosen, Discrete Mathematics and Its Applications, (McGraw-Hill, 1999) [Chapter5.1-5.2, pp308-332].Louis Trenchard More, Isaac Newton (Scribners 1934).Kenneth Falconer, Fractals – A Very Short Introduction (Oxford UP, 2013).H.-O. Peitgen, H Jürgens & D Saupe, Chaos and Fractals (Springer-Verlag, 1992).Ian Stewart, Does God Play Dice? (Penguin, 1990).M. Blastland & A. Dilnot, The Tiger that Isn't: Seeing Through a World of Numbers (ProfileBooks, 2007).D. Huff, How to Lie with Statistics (Penguin, 1991).David Salsburg, The Lady Tasting Tea?: how statistics revolutionized science in the twentiethcentury (Henry Holt, 2002).8

University of St Andrews - School of Mathematics and StatisticsThis is a list of the 2000-level modules that were available to students during the 2019-2020academic year. The School's sub-honours courses remain broadly the same from year to year, butthis list of module offerings is for illustration purposes only and does not constitute a guarantee ofthe specific modules, module content or timetabling to be offered in future years.2000-level T2508MT2901Linear MathematicsAnalysisMultivariate CalculusCombinatorics and ProbabilityAbstract AlgebraVector CalculusMathematical ModellingStatistical InferenceMathematical concepts through historyID2003 Science MethodsID2005 Scientific ThinkingMT2501 Linear /20Timetable12.00 noon Mon (odd weeks), Wed and Fri [Semester 1]; 11.00 am on Mon(even weeks), Tue and Thu [Semester 2]This module extends the knowledge and skills that students have gainedconcerning matrices and systems of linear equations. It introduces the basic9

DescriptionPrerequisitestheory of vector spaces, linear independence, linear transformations anddiagonalization. These concepts are used throughout the mathematical sciencesand physics. It is recommended that students in the Faculties of Arts andDivinity take an even number of the 15-credit 2000-level MT modules.MT1002, or A at Advanced Higher Mathematics, or A at A-level FurtherMathematics, or A at both A-level Mathematics and A-level PhysicsAntirequisites MT2001Lectures andtutorials2.5-hours lectures (x 10 weeks), 1 tutorial (x 4 weeks), 1 examples class (x 6week)Assessment2-hour Written Examination 70%, Coursework (including class test) 30%ModulecoordinatorProf N Ruskuc (S1), Dr A Wilmot-Smith (S2)LecturerProf N Ruskuc (S1), Dr A Wilmot-Smith (S2)Continuous assessmentClass test (50 minute): 15%Coursework problem sets: 15%SyllabusMatrices and determinants: basic revision of matrices & relevant fields (especially complexnumbers); revision of e.r.o.’s; system of linear equations; determinants and their basicproperties; matrix inverses; solutions of systems of linear equations.Vector spaces: Definition of vector spaces; examples of vector spaces (with emphasis ongeometrical intuition); basic properties of vector spaces; subspaces.Linear independence and bases: spanning sets; linear independence, bases, dimension.Linear transformations: definition of linear transformation and examples (including trace), thematrix of a linear transformation; rank and nullity (including proof of Rank-Nullity Theorem);the rank of a matrix and reduced echelon form; rank and the matrix of a lineartransformation.Eigenvalues, eigenvectors and diagonalization: eigenvalues and eigenvectors; change ofbasis; powers of matrices, symmetric matrices and quadratic forms.Reading listT.S. Blyth & E.F. Robertson, Basic Linear Algebra, Springer, 2002.R.B.J.T. Allenby, Linear Algebra, Edward Arnold, 1995.Richard Kaye & Robert Wilson, Linear Algebra, OUP, 1998.MT2502 Analysis10

.00 am Mon (even weeks), Tue and ThuDescriptionThe main purpose of this module is to introduce the key concepts of realanalysis: limit, continuity and differentiation. Emphasis will be placed on therigourous development of the material, giving precise definitions of the conceptsinvolved and exploring the proofs of important theorems. This module forms theprerequisite for all later modules in mathematical analysis. It is recommendedthat students in the Faculties of Arts and Divinity take an even number of the15-credit 2000-level MT modules.PrerequisitesMT1002 or A at Advanced Higher Mathematics or A at A-level FurtherMathematicsAntirequisites MT2002Lectures andtutorials2.5 hours lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examplesclass (x 5 weeks)Assessment2-hour Written Examination 70%, Coursework (including 1 class test) 30%ModulecoordinatorDr J M FraserLecturerDr J M FraserContinuous assessmentClass tests (50 minute): 15%Fortnightly assessed tutorial questions: 5 x 3% 15%SyllabusThe rationals and the reals: maximum & minimum, supremum & infimum, completeness.Sequences, series and convergence: the Bolzano-Weierstrass Theorem, tests forconvergence - the ratio test, the root test, the comparison test, Cauchy sequences.Continuous functions: algebraic properties of continuous functions, the Intermediate ValueTheorem.Differentiable functions: the chain rule, Rolle’s Theorem, the Mean Value Theorem, Taylorpolynomials.These topics will be introduced from a rigorous point of view, giving precise definitions, applyingan ε-δ approach and giving examples.11

Reading listJohn M. Howie, Real Analysis, Springer, 2001, Chapters 1-4.Robert G. Bartle & Donald R. Sherbert, Introduction to Real Analysis, Wiley, 1992, Chapters2-6.Kenneth Ross, Elementary Analysis, Spring, 1980, some parts of Chapters 1-6.MT2503 Multivariate etable12 noon Mon (even weeks), Tue and ThuDescriptionThis module extends the basic calculus in a single variable to the setting of realfunctions of several variables. It introduces techniques and concepts that areused throughout the mathematical sciences and physics: partial derivatives,double and triple integrals, surface sketching, cylindrical and sphericalcoordinates. It is recommended that students in the Faculties of Arts andDivinity take an even number of the 15-credit 2000-level MT modules.PrerequisitesMT1002, or A at Advanced Higher Mathematics, or A at A-level FurtherMathematics, or A at both A-level Mathematics and A-level Physics, or Corequisite MT1010Antirequisites MT2001Lectures andtutorials23 hours of lectures, 1-hour tutorial (x 4 weeks), 1-hour examples class (x 4weeks)Assessment2-hour Written Examination 70%, Coursework 30% (including 1 class test)ModulecoordinatorDr A P NaughtonLecturerProf A W Hood, Dr A P NaughtonContinuous assessment50-minute class test: 15%Projects involving computer-based work: 15%SyllabusRevision of basic differentiation rules: product rule, quotient rule, chain rule. Hyperbolic12

functions & inverse hyperbolic function: graphs, derivatives, integrals & identities.Power series, including Taylor series about an arbitrary point. Limits, continuity &differentiability of functions on one variable (definitions). l’Hopital’s Rule.Revision of vectors and dot product. Functions of several variables, representation assurfaces, surface sketching, and limits of functions of several variables, continuity anddifferentiability for functions of two variables.Partial derivatives, chain rule for functions of n-variables.Implicit differentiation and contours, higher order partial derivatives, derivatives in ndimensions, tangent planesTaylor series for functions of two variables. Maxima and minima.Directional derivative and gradient. Lagrange multipliers.Revision of integration for functions of one-variable. Double integrals. Spherical andcylindrical coordinates. Triple integrals.Reading listEarl W. Swokowski, Michael Olinick & Dennis Pence, Calculus, 6th ed., PWS Pub. Co.,1994.Wilfred Kaplan, Advanced Calculus, 3rd ed., Addison-Wesley, 1984.Erwin Kreyszig, Advanced Engineering Mathematics, 10th ed., Wiley, 2011.Alan Jeffrey, Advanced Engineering Mathematics, Harcourt Academic, 2002.Robert Adams & Christopher Essex, Calculus, 8th ed, Pearson 2013.MT2504 Combinatorics and Timetable4pm Mon (odd weeks), Thu and FriDescriptionThis modul

Advanced Engineering Mathematics E Kreyszig; Wiley; 2001 4. Calculus, R A Adams; Pearson; 2002. Calculus (6th Edition) E W Swokowski, M Olinick, D Pence; PWS; 1994. MT1007 Statistics in Practice Credits 20.0 Semester 2 Academic year 2019/20 Timetable 11.00 am Description This module provides an introduction to statistical reasoning, elementary but powerful statistical methodologies, and real .

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