Page 122 - Handbook Bachelor Degree of Science Academic Session 20202021

Faculty of Science Handbook, Academic Session 2020/2021

References: SIM3007 RING THEORY
1. Hoffman, K.M., & Kunze, R. (1971). Linear algebra (2
nd
ed.) Englewood Cliffs, NJ: Prentice-Hall. Ring, subrings and ideals, modules, internal direct sum,
2. Kwak, J.H., & Hong, S.P., (2004). Linear algebra (2 external direct product, nil and nilpotent ideals, prime and
nd
ed.). New York, NY: Birkhäuser Basel. maximal ideals, Jacobson and prime radicals, semiprimitive
3. Friedberg, S.H., Insel, A.J., & Spence, L.E. (2002). and semiprime rings, rings with chain condition, primitive
th
Linear algebra (4 ed.). Upper Saddle River, NJ: rings, group rings.
Prentice-Hall.
rd
4. Sheldon, A. (2015). Linear algebra done right (3 ed.). Assessment:
New York, NY: Springer International Publishing. Continuous Assessment: 40%
5. Yang, Y.S. (2015). A concise text on advanced linear Final Examination: 60%
algebra. Cambridge, NY: Cambridge University Press.
Medium of Instruction:
English
SIM3005 MATRIX THEORY
Soft Skills:
Rank and nullity of matrices. Inner product spaces, the CTPS3, LL2
Gram-Schmidt process, least squares problems, ortogonal
matrices. Diagonalization for real symmetric matrices, References:
quadratic forms, semi positive definite matrices. The singular 1. Cohn, P.M. (2001). Introduction to Ring Theory
value decomposition. Generalized inverses and linear (Springer Undergraduate Mathematics Series).
systems, Moore-Penrose inverses. Springer.
2. Herstein, I. N. (2005). Noncommutative rings (Carus
Assessment: Mathematical Monographs No. 15). Math. Assoc. of
Continuous Assessment: 40% America.
Final Examination: 60% 3. Beachy, J. A. (1999). Introductory lectures on rings and
modules (London Maths. Soc. Student Texts 47).
Medium of Instruction: Cambridge University Press.
nd
English 4. Lam, T.Y. (2010). Exercises in classical ring theory (2
ed.) (Problem Books in Mathematics). Springer.
Soft Skills:
CS3, CTPS3, LL2
SIM3008 GROUP THEORY
References:
1. Zhang, F.Z. (2011). Matrix theory: Basic results and The three isomorphism theorems. Cyclic groups. Direct
techniques (2 ed.). New York, NY: Springer-Verlag. product of groups. Introduction to the three Sylow’s
nd
2. Horn, R., & Johnson, C.R. (2013). Matrix analysis (2 Theorem. Classification of groups up to order 8. Finitely
nd
ed.). Cambridge, NY: Cambridge University Press. generated abelian groups. Nilpotent groups and Soluble
3. Steeb, W., & Hardy, Y. (2011). Matrix calculus and groups
Kronecker product (2 ed.). Singapore: World Scientific
nd
Publishing. Assessment:
4. Bapat, R.B. (2012). Linear algebra and linear Models Continuous Assessment: 40%
rd
(3 ed.). London, UK: Springer-Verlag. Final Examination: 60%
5. Zhan, X.Z. (2013). Matrix theory. Providence, RI:
American Mathematical Society. Medium of Instruction:
English

SIM3006 ALGEBRA II Soft Skills:
CTPS3, LL2
Groups-Isomorphism theorems. Permutation groups. Group
actions, p-groups. References:
1. Ledermann, W., Weir, A. J., & Jeffery, A. (1997).
nd
Rings-Maximal and prime ideals. Polynomial rings. Field Introduction to group theory (2 ed.). Addison Wesley
extensions. Finite fields. Pub. Co.
2. Rotman, J. J. (2014). An Introduction to the theory of
Assessment: groups (4th ed.). New Work: Springer-Verlag.
Continuous Assessment: 40% 3. Gallian, A. J. (2017). Contemporary abstract algebra
th
Final Examination: 60% (9 ed.). Brooks Cole.

Medium of Instruction:
English SIM3009 DIFFERENTIAL GEOMETRY

Soft Skills: Vector algebra on Euclidean space. Lines and planes.
CTPS3, LL2 Change of coordinates. Differential geometry of curves.
Frenet Equations. Local theory of surfaces in Euclidean
References: space. First and second fundamental forms. Gaussian
1. Durbin, J. R. (2009). Modern algebra: An Introduction curvatures and mean curvatures. Geodesics. Gauss-Bonnet
th
(6 ed.). John Wiley. Theorem.
2. Fraleigh, J. B. (2003). A first course in abstract algebra
th
(7 ed.). Addison-Wesley. Assessment:
th
3. Gallian, J. (2012). Contemporary abstract algebra (8 Continuous Assessment: 40%
ed.). Brooks/Cole Cengage Learning. Final Examination: 60%
4. Hungerford, T.W. (2014). Abstract algebra: An
Introduction (3 ed.). Brooks/Cole Cengage Learning.
rd
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