Page 108 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

SIM3008 GROUP THEORY References:
1. Armstrong, M.A. (2010). Basic Topology,
The three isomorphism theorems. Cyclic groups. Direct Undergraduate Texts in Mathematics, Springer.
product of groups. Introduction to the three Sylow’s 2. Munkres, J. (2000). Topology, Second edition,
Theorem. Classification of groups up to order 8. Finitely Prentice Hall Inc.
generated abelian groups. Nilpotent groups and Soluble 3. McCluskey, A. and B. McMaster, B. (2014).
groups Undergraduate Topology: A Working Textbook, Oxford
University Press.
Assessment:
Continuous Assessment: 40%
Final Examination: 60% SIM3011 COMPLEX ANALYSIS

Medium of Instruction: Taylor and Laurent series. Singularities and zeroes.
English Residue Theory. Evaluation of certain Integrals. Arguments
Principle, Rouche’s theorem. Maximum Modulus Principle.
Humanity Skill: Infinite Products. Entire Functions.
CT3, LL2
Assessment:
References: Continuous Assessment: 40%
1. Ledermann, W., Weir, A. J. & Jeffery, A. (1997). Final Examination: 60%
Introduction to Group Theory, Addison Wesley Pub.
nd
Co. (2 edition). Medium of Instruction:
2. Rotman, J. J. (2014). An Introduction to the Theory of English
th
Groups, Springer-Verlag, New York (4 edition).
3. Gallian, A. J. (2012). Contemporary Abstract Algebra, Humanity Skill:
th
Brooks Cole (8 edition). CT3, LL2

References:
SIM3009 DIFFERENTIAL GEOMETRY 1. John H. Mathews & Russell W. Howell (2012),
Complex Analysis: for Mathematics and Engineering,
th
Vector algebra on Euclidean space. Lines and planes. Jones & Bartlett Pub. Inc (6 edition).
Change of coordinates. Differential geometry of curves. 2. Saff, E. B. & Snider, A. D. (2003). Fundamental of
Frenet Equations. Local theory of surfaces in Euclidean Complex Analysis, Pearson Education Inc.
space. First and second fundamental forms. Gaussian 3. Ali, Rosihan M. and Ravichandran, V. (2008). Complex
curvatures and mean curvatures. Geodesics. Gauss- Analysis, Penerbit USM.
Bonnet Theorem. 4. Markushevich, A. I. (1985). Theory of Functions of
Complex Variables, Chelsea Publ. Co.
Assessment: 5. Brown, J. & Churchill, R.V. (2013). Complex Variables
th
Continuous Assessment: 40% & Applications, McGraw Hill (9 edition).
Final Examination: 60%

Medium of Instruction: SIM3012 REAL ANALYSIS
English
Riemann integral. Integrable functions. Properties of the
Humanity Skill: Riemann integral. Integration in relation to differentiation.
CS3, CT3, LL2 Differentiation of integrals. Improper integrals. Sequences
and series of functions. Pointwise and uniform
References: convergence. Properties of uniform convergence. Superior
1. Lipschutz, M. (1969), Schaum’s Outline of Differential limit and inferior limit. Power series, radius of
Geometry, McGraw-Hill. convergence. Taylor series.
2. Oprea, J. (2004). Differential Geometry and Its
nd
Applications, Prentice Hall (2 edition). Assessment:
3. Kuhnel, W. (2005), Differential Geometry: Curves, Continuous Assessment: 40%
nd
Surfaces, Manifolds, Amer. Math. Soc. (2 edition). Final Examination: 60%
4. Abate, M. and Tovena, F. (2012). Curves and
Surfaces, Springer. Medium of Instruction:
5. Pressley, A.N. (2010). Elementary Differential English
Geometry, Springer.
Humanity Skill:
CS3, CT3, LL2

SIM3010 TOPOLOGY References:
1. Witold A.J. Kosmala (2004). A Friendly Introduction to
Topological Spaces. Continuity, connectedness and
compactness. Separation axioms and countability. Metric Analysis, Single and Multivariable, Pearson
nd
International (2 edition).
spaces. Product spaces. 2. Schroder, B. S (2008). Mathematical Analysis: A
Concise Introduction, John-Wiley.
Assessment: 3. Richardson, L. F. (2008). Advanced Calculus: An
Continuous Assessment: 40%
Introduction To Linear Analysis, John-Wiley.
Final Examination: 60% 4. Lay, S.R. (2014). Analysis with an introduction to
proof, Pearson (5 edition).
th
Medium of Instruction: 5. Pedersen, S. (2015). From Calculus to Analysis,
English
Springer.
Humanity Skill:
CT3, LL2
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