Page 109 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

SIM3013 PROBABILISTIC METHODS IN Final Examination: 50%
COMBINATORICS
Medium of Instruction:
The probabilistic method and its applications in Bahasa Malaysia/English
combinatorics. The topics are selected from: The basic
probabilistic methods applied on graphs, tournaments, and Humanity Skill:
set systems; the use of linearity of expectation for CT 3, LL 2
Hamiltonian paths and splitting graphs; alterations for lower
bound of Ramsey numbers, independent sets, packing and References:
recolouring; the second moment methods; random graphs 1. Engineering with Excel by Ronald W. Larsen, Upper
– threshold functions, subgraphs, clique number and Saddle River, NJ : PearsonPrentice Hall, 2011
chromatic number; the Lovász Local Lemma and its 2. Excel for Engineers and Scientists by S. C. Bloch and
applications. Sylvan Charles Bloch, John Wiley & Sons 2003
3. Excel for Scientists and Engineers: Numerical
Assessment: Methods by E. Joseph Billo, Wiley-Interscience; 2007.
Continuous Assessment: 40% 4. A guide to Microsoft Excel for scientists and engineers
Final Examination: 60% by Bernard V. Liengme, London : Arnold, 1997.

Medium of Instruction:
English SIN1003 MATHEMATICAL METHODS I

Humanity Skill: First order ODE: Definitions, solution concepts, valid
CT3, LL2 solution intervals. Solutions to variable separable
equations, linear equations, Bernoulli, exact and non-exact,
References: homogeneous equations. Some applications of first order
ODE.
1. Alon, N and Spencer, J. (2008). The Probabilistic
rd
Method, Wiley (3 edition). Linear ODE with second and higher order: Definitions,
2. Janson, S., Luczak, T. and Rucinski, A. (2000). solution concepts, linear independence, Wronskian.
Random Graphs, Wiley. Solution to homogeneous and non-homogeneous
3. Matousek, J. and Nesetril, J. (1998). Invitation to equations. Method of undetermined coefficient, Variation of
Discrete Mathematics, Oxford University Press. parameters, Series solution of ordinary differential
4. Molloy, M. and Reed, B. (2002). Graph Colouring and equations, Frobenius’s method, Legendre and Bessel’s
the Probabilistic Method, Springer. equations. Some applications of second order ODE.
5. Lovász, L., Ruzsa, I. and Sós, Vera T. (Eds.)
(2013). Erdös Centennial, Springer. Assessment
Continuous Assessment: 40%
Final Examination: 60%
SIN1001 INTRODUCTORY TO COMPUTER
Medium of Instruction:
MATLAB - Matlab environment, matrices, constants and English
variables, operation, built-in functions, output format, plot
graphs, expressions and data logic, branches and loops, Humanity Skill:
scripting, user-defined functions. Application of selected CS2, CT 3, LL 2
mathematical problems.
References:
Assessment 1. Problem solving, Abstraction and Design Using C++ F.
Continuous Assessment: 50% L. Friedman and Elliot B Koffman, Addison-Wesley
Final Examination: 50% (1997).
2. A Survey of Computational Physics: Introductory
Medium of Instruction: Computational Science. Rubin H. Landau (Princeton
Bahasa Malaysia/English Press) 2011.
3. Numerical Recipes W. H. Press 2007.
Humanity Skill: 4. Numerical Analysis: Mathematics of Scientific
rd
CT 3, LL 2 Computing, 3 Edition David R. Kincaid and E.
Ward Cheney (2002).
References:
1. Matlab Programming for Engineers by Stephen
J.Chapman, Thomson, 2004. SIN2001 MATHEMATICAL METHODS II
2. Engineering computation with MATLAB by David M.
Smith, Boston : Addison/Wesley, 2010. Computer arithmetic: floating-point numbers, round off
3. Essentials of MATLAB programming by Stephen J. error, machine precision, overflow/underflow, numerical
Chapman, Stamford, CT : CENGAGE Learning, 2009. cancellation, truncation error.
4. Mastering MATLAB 7 by Duane Hanselman and
Bruce Littlefield, Pearson Education; 2005. Taylor polynomial and limits.

Interpolation: Lagrange interpolation, Divided differences,
SIN1002 INTRODUCTION TO SPREADSHEET Hermite interpolation, cubic spline interpolation

Basics of Spreadsheet, entering labels, numbers and Roots of nonlinear equation: bisection method, fixed-point
formulae. Absolute & relative addressing, Excel functions. iteration, Newton – Raphson method, secant method.
Graph plotting, use of solvers. Applications to some Numerical differentiation: Forward, backward and central
selected mathematical problems finite difference.
Assessment
Continuous Assessment: 50%

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