Page 82 - Handbook Bachelor Degree of Science Academic Session 20212022

Faculty of Science Handbook, Academic Session 2021/2022

References:
SIM3008 GROUP THEORY
1. John H. Mathews and Russell W. Howell. (2012).
Complex Analysis: for Mathematics and Engineering,
The three isomorphism theorems. Cyclic groups. Direct 6 ed. Jones & Bartlett Pub. Inc.
th
product of groups. Introduction to the three Sylow’s
E.B. Saff, A.D. Snider. (2003). Fundamental of
Theorem. Classification of groups up to order 8. Finitely 2. Complex Analysis, Pearson Education Inc.
generated abelian groups. Permutation groups.
3. Rosihan M. Ali and V. Ravichandran. (2007).
Complex Analysis, Universiti Sains Malaysia Press.
Assessment: 4. A. I. Markushevich. (1985). Theory of functions of
Continuous Assessment: 40%
Final Examination: 60% complex variables, Chelsea Publ. Co.
5. Nakhle H. Asmar and Laukas Grafakos. (2018).
Complex Analysis with Applications (Undergraduate
References: Texts in Mathematics), Springer.
1. Hall, M., The theory of Groups. Dover Publications;
Reprint edition, New York, 2018.
2. Barnard, T., Neill, H., Discovering Group Theory: A
Transition to Advanced Mathematics, Taylor & SIM3012 REAL ANALYSIS
Francis Ltd, London, 2016. Infinite series, convergence. Tests of convergence. Absolute
3. Rotman, J.J., An introduction to the theory of groups,
4th edition. Springer-Verlag, New York, 1999. and conditional convergence. Rearrangement of series.
Pointwise and uniform convergence. Properties of uniform
convergence. Superior limit and inferior limit. Power series,
radius of convergence. Taylor series. Riemann integral.
SIM3009 DIFFERENTIAL GEOMETRY
Integrable functions. Properties of the Riemann integral.
Integration in relation to differentiation. Differentiation of
Vector algebra on Euclidean space. Lines and planes.
Change of coordinates. Differential geometry of curves. integrals. Improper integrals. Sequences and series of
functions.
Frenet Equations. Local theory of surfaces in Euclidean
space. First and second fundamental forms. Gaussian Assessment:
curvatures and mean curvatures. Geodesics. Gauss-Bonnet
Theorem. Continuous Assessment: 40%
Final Examination: 60%
Assessment: References:
Continuous Assessment: 40% 1. W.P. Ziemer, Modern Real Analysis, Springer 2017.
Final Examination: 60%
2. Witold A.J. Kosmala, A friendly introduction to
analysis, 2nd Edition, Pearson International 2004.
References: 3. B.S, Schroder, Mathematical Analysis: A concise
1. M. Lipschutz, Schaum’s Outline of differential introduction, John-Wiley 2008.
geometry, McGraw-Hill, 1969.
2. M. Umehara; K. Yamada, Differential Geometry of 4. L.F. Richardson, Advanced Calculus: An introduction
Curves and Surfaces, World Scientific, 2017. to linear analysis, John-Wiley 2008.
3. K. Tapp, Differential Geometry of Curves and 5. D.S. Kurtz and C.W. Swartz, Theories of Integration,
World Scientific 2004.
Surfaces, Springer, 2016.
SIM3020 INDUSTRIAL TRAINING
SIM3010 TOPOLOGY
Candidates are required to spend a minimum 16 weeks
Topological Spaces. Continuity, connectedness and working with selected companies in selected areas of
compactness. Separation axioms and countability. Metric industry.
spaces. Product spaces.
Assessment: Assessment:
Continuous Assessment: 40% Continuous Assessment: 100%
Final Examination: 60%
References:
References: Universiti Malaya Guidebook for Industrial Training
1. Armstrong, M.A. (2010). Basic topology
(Undergraduate Texts in Mathematics). Springer.
2. Munkres, J. (2000). Topology (2 ed.). Prentice Hall SIM3021 MATHEMATICAL SCIENCE PROJECT
nd
Inc.
3. McCluskey, A., & McMaster, B. (2014). Undergraduate Subject to supervising lecturer.
topology: A working textbook. Oxford University Press.
Assessment:
Continuous Assessment: 100%
SIM3011 COMPLEX ANALYSIS
References:
Infinite series expansions: convergence and divergence and Refer to supervising lecturer.
region of convergence. Taylor and Laurent theorems.
Classification of isolated singularities. Zeroes and Poles.
Calculus of residues; calculation of definite integrals.
Residue Theory. Evaluation of certain Integrals. Arguments
Principle, Rouche’s Theorem. Maximum Modulus Principle.
Conformal Mappings.
Assessment:
Continuous Assessment: 40%
Final Examination: 60%
81