Page 123 - Handbook Bachelor Degree of Science Academic Session 20202021

Faculty of Science Handbook, Academic Session 2020/2021

Medium of Instruction: SIM3012 REAL ANALYSIS
English
Soft Skills: Riemann integral. Integrable functions. Properties of the
CS3, CTPS3, LL2 Riemann integral. Integration in relation to differentiation.
Differentiation of integrals. Improper integrals. Sequences
References: and series of functions. Pointwise and uniform convergence.
1. Lipschutz, M. (1969). Schaum’s outline of differential Properties of uniform convergence. Superior limit and
geometry. McGraw-Hill. inferior limit. Power series, radius of convergence. Taylor
2. Oprea, J. (2004). Differential geometry and its series.
nd
applications (2 ed.). Prentice Hall.
3. Kuhnel, W. (2005). Differential geometry: curves, Assessment:
surfaces, manifolds (2 ed.). Amer. Math. Soc. Continuous Assessment: 40%
nd
4. Abate, M., & Tovena, F. (2012). Curves and Surfaces. Final Examination: 60%
Springer.
5. Pressley, A.N. (2010). Elementary differential Medium of Instruction:
English
geometry. Springer.
Soft Skills:

SIM3010 TOPOLOGY CS3, CTPS3, LL2
References:
Topological Spaces. Continuity, connectedness and 1. Witold A.J. Kosmala (2004). A friendly introduction to
compactness. Separation axioms and countability. Metric nd
spaces. Product spaces. analysis: Single and multivariable (2 ed.). Pearson
International.
2. Schroder, B. S (2008). Mathematical analysis: A
Assessment: concise introduction. John-Wiley.
Continuous Assessment: 40% 3. Richardson, L. F. (2008). Advanced calculus: An
Final Examination: 60% introduction to linear analysis. John-Wiley.

Medium of Instruction: 4. Lay, S.R. (2014). Analysis with an introduction to proof
(5 ed.). Pearson.
th
English 5. Pedersen, S. (2015). From calculus to analysis.
Springer.
Soft Skills:
CTPS3, LL2
SIM3013 PROBABILISTIC METHODS IN
References: COMBINATORICS
1. Armstrong, M.A. (2010). Basic topology
(Undergraduate Texts in Mathematics). Springer. The probabilistic method and its applications in
2. Munkres, J. (2000). Topology (2 ed.). Prentice Hall
nd
Inc. combinatorics. The topics are selected from: The basic
3. McCluskey, A., & McMaster, B. (2014). Undergraduate probabilistic methods applied on graphs, tournaments, and
set systems; the use of linearity of expectation for
topology: A working textbook. Oxford University Press. Hamiltonian paths and splitting graphs; alterations for lower

bound of Ramsey numbers, independent sets, packing and
SIM3011 COMPLEX ANALYSIS recolouring; the second moment methods; random graphs –
threshold functions, subgraphs, clique number and
chromatic number; the Lovász Local Lemma and its
Taylor and Laurent series. Singularities and zeroes. Residue applications.
Theory. Evaluation of certain Integrals. Arguments Principle,
Rouche’s theorem. Maximum Modulus Principle. Infinite
Products. Entire Functions. Assessment: 40%
Continuous Assessment:
Final Examination: 60%
Assessment:
Continuous Assessment: 40% Medium of Instruction:
Final Examination: 60%
English

Medium of Instruction: Soft Skills:
English CTPS3, LL2

Soft Skills:
CTPS3, LL2 References:
1.
Alon, N, & Spencer, J. (2008). The probabilistic method
(3 ed.). Wiley.
rd
References: 2. Janson, S., Luczak, T., & Rucinski, A. (2000). Random
1. John H. Mathews, & Russell W. Howell (2012). Complex
th
analysis for mathematics and engineering (6 ed.). graphs. Wiley.
Jones & Bartlett Pub. Inc. 3. Matousek, J., & Nesetril, J. (1998). Invitation to discrete
2. Saff, E. B., & Snider, A. D. (2003). Fundamental of 4. mathematics. Oxford University Press.
Molloy, M., & Reed, B. (2002). Graph colouring and the
complex analysis. Pearson Education Inc. probabilistic method. Springer.
3. Ali, Rosihan M., & Ravichandran, V. (2008). Complex 5. Lovász, L., Ruzsa, I., & Sós, Vera T. (Eds.).
Analysis. Penerbit USM.
4. Markushevich, A. I. (1985). Theory of functions of (2013). Erdös Centennial. Springer.
complex variables. Chelsea Publ. Co.
5. Brown, J., & Churchill, R.V. (2013). Complex variables &
applications (9 ed.). McGraw Hill.
th

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