Page 47 - handbook 20162017

Faculty of Science Handbook, Session 2016/2017

Medium of Instruction: SIM3011 COMPLEX ANALYSIS
English
Taylor and Laurent series. Singularities and zeroes.
Humanity Skill: Residue Theory. Evaluation of certain Integrals. Arguments
CT3, LL2 Principle, Rouche’s theorem. Maximum Modulus Principle.
Infinite Products. Entire Functions.
References:
1. Ledermann, W., Weir, A. J. & Jeffery, A. (1997). Assessment:
Introduction to Group Theory, Addison Wesley Pub. Continuous Assessment: 40%
Co. (2 edition). Final Examination: 60%
nd
2. Rotman, J. J. (2014). An Introduction to the Theory of
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Groups, Springer-Verlag, New York (4 edition). Medium of Instruction:
3. Gallian, A. J. (2012). Contemporary Abstract Algebra, English
th
Brooks Cole (8 edition).
Humanity Skill:
CT3, LL2
SIM3009 DIFFERENTIAL GEOMETRY
References:
Vector algebra on Euclidean space. Lines and planes. 1. John H. Mathews & Russell W. Howell (2012),
Change of coordinates. Differential geometry of curves. Complex Analysis: for Mathematics and Engineering,
Frenet Equations. Local theory of surfaces in Euclidean Jones & Bartlett Pub. Inc (6 edition).
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space. First and second fundamental forms. Gaussian 2. Saff, E. B. & Snider, A. D. (2003). Fundamental of
curvatures and mean curvatures. Geodesics. Gauss- Complex Analysis, Pearson Education Inc.
Bonnet Theorem. 3. Ali, Rosihan M. and Ravichandran, V. (2008). Complex
Analysis, Penerbit USM.
Assessment: 4. Markushevich, A. I. (1985). Theory of Functions of
Continuous Assessment: 40% Complex Variables, Chelsea Publ. Co.
Final Examination: 60% 5. Brown, J. & Churchill, R.V. (2013). Complex Variables
& Applications, McGraw Hill (9 edition).
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Medium of Instruction:
English
SIM3012 REAL ANALYSIS
Humanity Skill:
CS3, CT3, LL2 Riemann integral. Integrable functions. Properties of the
Riemann integral. Integration in relation to differentiation.
References: Differentiation of integrals. Improper integrals. Sequences
1. Lipschutz, M. (1969), Schaum’s Outline of Differential and series of functions. Pointwise and uniform
Geometry, McGraw-Hill. convergence. Properties of uniform convergence. Superior
2. Oprea, J. (2004). Differential Geometry and Its limit and inferior limit. Power series, radius of
Applications, Prentice Hall (2 edition). convergence. Taylor series.
nd
3. Kuhnel, W. (2005), Differential Geometry: Curves,
Surfaces, Manifolds, Amer. Math. Soc. (2 edition). Assessment:
nd
4. Abate, M. and Tovena, F. (2012). Curves and Continuous Assessment: 40%
Surfaces, Springer. Final Examination: 60%
5. Pressley, A.N. (2010). Elementary Differential Medium of Instruction:
Geometry, Springer. English

SIM3010 TOPOLOGY Humanity Skill:
CS3, CT3, LL2
Topological Spaces. Continuity, connectedness and References:
compactness. Separation axioms and countability. Metric
spaces. Product spaces. 1. Witold A.J. Kosmala (2004). A Friendly Introduction to
Analysis, Single and Multivariable, Pearson
nd
International (2 edition).
Assessment: 2. Schroder, B. S (2008). Mathematical Analysis: A
Continuous Assessment: 40% Concise Introduction, John-Wiley.
Final Examination: 60%
3. Richardson, L. F. (2008). Advanced Calculus: An
Medium of Instruction: 4. Introduction To Linear Analysis, John-Wiley.
Lay, S.R. (2014). Analysis with an introduction to
English proof, Pearson (5 edition).
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5. Pedersen, S. (2015). From Calculus to Analysis,
Humanity Skill:
CT3, LL2 Springer.
References: SIM3013 PROBABILISTIC METHODS IN
1. Armstrong, M.A. (2010). Basic Topology, COMBINATORICS
Undergraduate Texts in Mathematics, Springer.
2. Munkres, J. (2000). Topology, Second edition,
Prentice Hall Inc. The probabilistic method and its applications in
3. McCluskey, A. and B. McMaster, B. (2014). combinatorics. The topics are selected from: The basic
probabilistic methods applied on graphs, tournaments, and
Undergraduate Topology: A Working Textbook, Oxford set systems; the use of linearity of expectation for
University Press.
Hamiltonian paths and splitting graphs; alterations for lower
bound of Ramsey numbers, independent sets, packing and
recolouring; the second moment methods; random graphs

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