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# CHANCELLOR Sir George Alleyne OCC, MD, FRCP, FACP (Hon), Hon. DSC (UWI) - page 113 / 136

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The

FA C U L T Y Faculty

BOOKLET 2004 – 2005 of Science & Agriculture

MATH 2150 (M 25B) INTRODUCTION TO STATISTICS (4 credits)

MATH 2170 (M 24A) INTRODUCTION TO COMBINATORICS (4 credits)

Prerequisite:MATH 2140 (M 25A) or Permission of the Head of Department

Syllabus: Theory of Estimation: Ideas of point estimation; mean-squared error; interval estimation; method of maximum likelihood; Cramer-Rao Inequality.Hypothesis Testing: Type I and Type II errors; tests concerning means, variances and proportions; Goodness of fit Tests; non-parametric tests.Ideas of Regres- sion Analysis including simple linear Regression in detail; Ex- perimental Design and the Analysis of Variance (Completely Randomised Design, Block Designs, Latin Squares, Factional

Prerequisite: MATH 1140 (M 12A) Syllabus: Permutations and Combinations. The Inclusion - Exclusion Principle. Linear equations with unit coefficients; Recurrence relations; Generating functions; Geometry of the plane; Colouring problems; Combinatorial probability. Partitions of

integer; Random walks; Designs. Examination: One 2-hour written paper Coursework Examination

75% 25%

Designs). Examination: One 2-hour paper Coursework

60% 40%

MATH 2180 (M 24B) INTRODUCTION TO OPTIMISATION (4 credits)

# MATH 2160 (M 21B) ANALYSIS & MATHEMATICAL METHODS II (4 credits)

Prerequisites: MATH 1140 and MATH 1150 (M 12A and M 12B) Syllabus: The Laplace transform and applications to differential and in- tegral equations. Ordinary linear differential equations, Wronskian, linear independence. Existence and uniqueness (no proofs). Classification of points of second-order differential equations. Series solutions about ordinary and regular singu- lar points. Fourier series. Solution of the two-dimensional heat, wave and Laplace equation using the separation of variables technique. Functions of a single complex variable, continuity, differentiability, analyticity and the Cauchy-Riemann equations; power series and contour integrals, Cauchy’s theorem and in- tegral formulae. Singularities and their classification. Residue theorem and its application to the evaluation of definite inte-

Prerequisite: MATH 1140 (M 12A) Syllabus: Graphs and Digraphs; Ranking; Shortest Path; Communica- tion Networks; Convex sets; Linear programming; Simplex

Method; Theory of games. Examination: One 2-hour written paper Coursework Examination

75% 25%

grals. Examination: One 2-hour written paper Coursework

70% 30%

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