Page 79 - Handbook Bachelor Degree of Science Academic Session 20212022

Faculty of Science Handbook, Academic Session 2021/2022

SIM2016 COMPLEX VARIABLES
SIM2013 INTRODUCTION TO COMBINATORICS

Ordered and equivalence relations, binomial and multinomial Complex numbers, complex functions, limits, continuity.
theorems, recurrence relations, principle of inclusion and Differentiable and analytic functions, Cauchy-Riemann
exclusion, generating functions, Latin squares, magic equations, harmonic functions. Sequences and series of
complex numbers, convergence tests, power series.
squares, basic properties of graphs, circuits and cycles in Elementary functions: the complex exponential function,
graphs, trees and their applications. complex logarithms, complex exponents, trigonometry

Assessment: functions. Complex integrals, contour integrals, the Cauchy-
Continuous Assessment: 40% Goursat theorem, the fundamental theorems of integration,
Cauchy’s integral formula, Cauchy’s integral formula for
Final Examination: 60% derivatives and Morera’s theorem.

References:
1. M. J. Erickson, Introduction to Combinatorics, 2 Assessment:
nd
Edition, Wiley, 2013. Continuous Assessment: 40%
2. R. A. Brualdi, Introductory Combinatorics (Classic Final Examination: 60%
Version), 5 Edition, Pearson, 2017. References:
th
3. C.C. Chen & K.M. Koh, Principles and Techniques in
Combinatorics, World Scientific, 1992. 1. Mathews, J.H., Howell, R.W. (2012). Complex
th
4. L. Lovasz, J. Pelikan & K. Vesztergombi, Discrete analysis: for mathematics and engineering (6 ed.).
Sudbury: Jones & Bartlett Learning.
Mathematics: Elementary and Beyond, Springer, 2003. 2. Saff, E.B., Snider, A.D. (2018). Fundamental of
5. J. Matousek & J. Nesetril, Invitation to Discrete complex analysis: with applications to engineering and
nd
Mathematics, 2 Edition, Oxford University Press, rd
2008. science (3 ed.). New York: Pearson.
3. Churchill, R.V., Brown, J.W. (2014). Complex
variables and applications (9 ed.). New York:
th
McGraw-Hill Education.
SIM2014 ALGEBRA I 4. Howie, J.M. (2003). Complex analysis. London:

Group Theory - abstract groups, subgroups, cyclic and Springer-Verlag.
dihedral groups; order of an element and of a subgroup, 5. Asmar, N.H., Grafakos, L. (2018). Complex analysis
with applications. Switzerland AG: Springer-Verlag.
Lagrange’s theorem; cosets, normal subgroups and factor
groups; group homomorphisms.

Ring Theory – rings, integral domains and fields; subrings, SIM2017 GEOMETRY
ideals and quotient rings; ring homomorphisms; polynomial Euclidean Geometry, congruence, parallelism, similarity,
rings, the Division algorithm and Euclidean algorithm in isometry, Incidence geometry of the hyperbolic plane,
polynomial rings.
motions of the sphere.
Assessment: Assessment:
Continuous Assessment: 40% Continuous Assessment: 40%
Final Examination: 60%
Final Examination: 60%

References:
th
1. Gilbert, L., Gilbert, J. Elements of Modern Algebra, 8 References:
edition, Brooks Cole, 2014. 1. P. Ryan, Euclidean and non-Euclidean geometry,
Cambridge Univ. Press, 2012.
th
2. Fraleigh, J.B. First Course in Abstract Algebra, 8 2. H. P. Manning, Non-Euclidean geometry,
edition, Pearson eText, 2019. Independently Publ. 2019.
3. Judson, T.W. Abstract Algebra, Theory and 3. M. Henle, Modern Geometries: Non-Euclidean,
Applications, Open Source, 2019.
nd
Projective, and Discrete Geometry, 2 ed., Pearson,
2001.
SIM2015 INTRODUCTION TO ANALYSIS 4. J. Kappraff, A Participatory Approach to Modern
Geometry, World Scientific, 2014.
Sequences. Topology of the real line. Compactness.
Properties of continuous functions. Uniform continuity. SIM2018 PARTIAL DIFFERENTIAL EQUATIONS
Derivative of a function. Properties of differentiable
functions. Mean Value Theorems. Higher order derivatives.
L’Hospital’s Rules. Fourier series, introduction to partial differential equations,
method of characteristics, separation of variables, Laplace
Assessment: transform method.
Continuous Assessment: 40% Assessment:
Final Examination: 60%
Continuous Assessment: 40%
References: Final Examination: 60%
th
1. S. R. Lay, Analysis with an introduction to proof, 5 References:
ed., Pearson, 2014. 1. W. E. Boyce, R. C. Prima & D. B. Meade, Elementary
2. S. M. Oon, A First Course in Real Analysis, Universiti
Malaya Press, 2017 Differential Equations and Boundary Value Problems,
th
3. W. Kosmala, A Friendly Introduction to Analysis, 2nd 11 edition, John Wiley & Sons, 2017.
ed., Pearson, 2004. 2. N. H. Asmar, Partial Differential Equations with Fourier
rd
4. R. Haggarty, Fundamentals of Mathematical Analysis. Series and Boundary Value Problems, 3 edition,
Dover, 2017.
2nd ed., Addison-Wesley Publ. Co., 1993.
5. R. G. Bartle & D. R. Sherbert, Introduction to Real 3. D. G. Zill & M. R. Cullen, Differential Equations with
Analysis, 4 ed., John Wiley & Sons Inc., 2011. Boundary-Value Problems, 7th Edition, Brooks/Cole,
th
2005.
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