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Faculty of Science Handbook, Session 2017/2018

3. Gallian, A. J. (2012). Contemporary Abstract Algebra, Medium of Instruction:
th
Brooks Cole (8 edition). English
Humanity Skill:
SIM3009 DIFFERENTIAL GEOMETRY CT3, LL2
Vector algebra on Euclidean space. Lines and planes. References:
Change of coordinates. Differential geometry of curves. 1. John H. Mathews & Russell W. Howell (2012),
Frenet Equations. Local theory of surfaces in Euclidean Complex Analysis: for Mathematics and Engineering,
th
space. First and second fundamental forms. Gaussian Jones & Bartlett Pub. Inc (6 edition).
curvatures and mean curvatures. Geodesics. Gauss- 2. Saff, E. B. & Snider, A. D. (2003). Fundamental of
Bonnet Theorem. Complex Analysis, Pearson Education Inc.
3. Ali, Rosihan M. and Ravichandran, V. (2008). Complex
Assessment: Analysis, Penerbit USM.
Continuous Assessment: 40% 4. Markushevich, A. I. (1985). Theory of Functions of
Final Examination: 60% Complex Variables, Chelsea Publ. Co.
5. Brown, J. & Churchill, R.V. (2013). Complex Variables
Medium of Instruction: & Applications, McGraw Hill (9 edition).
th
English
Humanity Skill: SIM3012 REAL ANALYSIS
CS3, CT3, LL2
Riemann integral. Integrable functions. Properties of the
References: Riemann integral. Integration in relation to differentiation.
1. Lipschutz, M. (1969), Schaum’s Outline of Differential Differentiation of integrals. Improper integrals. Sequences
Geometry, McGraw-Hill. and series of functions. Pointwise and uniform
2. Oprea, J. (2004). Differential Geometry and Its convergence. Properties of uniform convergence. Superior
nd
Applications, Prentice Hall (2 edition). limit and inferior limit. Power series, radius of
3. Kuhnel, W. (2005), Differential Geometry: Curves, convergence. Taylor series.
nd
Surfaces, Manifolds, Amer. Math. Soc. (2 edition).
4. Abate, M. and Tovena, F. (2012). Curves and Assessment:
Surfaces, Springer. Continuous Assessment: 40%
5. Pressley, A.N. (2010). Elementary Differential Final Examination: 60%
Geometry, Springer. Medium of Instruction:
English
SIM3010 TOPOLOGY
Humanity Skill:
Topological Spaces. Continuity, connectedness and CS3, CT3, LL2
compactness. Separation axioms and countability. Metric References:
spaces. Product spaces. 1. Witold A.J. Kosmala (2004). A Friendly Introduction to
Assessment: Analysis, Single and Multivariable, Pearson
nd
Continuous Assessment: 40% 2. International (2 edition).
Schroder, B. S (2008). Mathematical Analysis: A
Final Examination: 60% Concise Introduction, John-Wiley.
3. Richardson, L. F. (2008). Advanced Calculus: An
Medium of Instruction:
English Introduction To Linear Analysis, John-Wiley.
4. Lay, S.R. (2014). Analysis with an introduction to
th
proof, Pearson (5 edition).
Humanity Skill: 5. Pedersen, S. (2015). From Calculus to Analysis,
CT3, LL2
Springer.
References:
1. Armstrong, M.A. (2010). Basic Topology, SIM3013 PROBABILISTIC METHODS IN
Undergraduate Texts in Mathematics, Springer. COMBINATORICS
2. Munkres, J. (2000). Topology, Second edition,
Prentice Hall Inc.
3. McCluskey, A. and B. McMaster, B. (2014). The probabilistic method and its applications in
Undergraduate Topology: A Working Textbook, Oxford combinatorics. The topics are selected from: The basic
probabilistic methods applied on graphs, tournaments, and
University Press. set systems; the use of linearity of expectation for
Hamiltonian paths and splitting graphs; alterations for lower
SIM3011 COMPLEX ANALYSIS bound of Ramsey numbers, independent sets, packing and
recolouring; the second moment methods; random graphs
– threshold functions, subgraphs, clique number and
Taylor and Laurent series. Singularities and zeroes. chromatic number; the Lovász Local Lemma and its
Residue Theory. Evaluation of certain Integrals. Arguments applications.
Principle, Rouche’s theorem. Maximum Modulus Principle.
Infinite Products. Entire Functions.
Assessment:
Continuous Assessment: 40%
Assessment: Final Examination: 60%
Continuous Assessment: 40%
Final Examination: 60%
Medium of Instruction:
English

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