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Faculty of Science Handbook, Session 2017/2018

operators, unitary operators, self-adjoint operators and Medium of Instruction:
positive definite operators. Dual spaces, bilinear forms. English
Diagonalization of symmetric bilinear forms, real quadratic
forms. Triangularization theorem, primary decomposition Humanity Skill:
theorem, Jordan canonical forms. CT3, LL2
Assessment: References:
Continuous Assessment: 40% 1. Durbin, J. R. (2009). Modern Algebra, An Introduction,
th
Final Examination: 60% John Wiley (6 edition.).
2. Fraleigh, J. B. (2003). A First Course in Abstract
Medium of Instruction: Algebra, Addison-Wesley (7 edition).
th
English 3. Gallian, J. (2012). Contemporary Abstract Algebra,
th
Brooks/Cole Cengage Learning (8 edition).
Humanity Skill: 4. Hungerford, T.W. (2014). Abstract Algebra: An
CS3, CT3, LL2 Introduction, Brooks/Cole Cengage Learning (3rd
edition).
References:
1. Kenneth Hoffman, Ray Kunze (1971), Linear Algebra,
Pearson Prentice Hall, Inc. SIM3007 RING THEORY
2. Jin Ho Kwak, Sungpyo Hong (2004), Linear Algebra,
Brikhauser,. (2 edition.). Ring, subrings and ideals, modules, internal direct sum,
nd
3. Stephen H. Friedberg, Arnold J. Insel & Lawrence E. external direct product, nil and nilpotent ideals, prime and
Spence (2003) Linear Algebra, Pearson Education maximal ideals, Jacobson and prime radicals, semiprimitive
th
International (4 edition.). and semiprime rings, rings with chain condition, primitive
4. Axler, S. (2015). Linear Algebra Done Right, Springer rings, group rings.
(3 edition).
rd
5. Yang, Y. (2015). A Concise Text on Advanced Linear Assessment:
Algebra, Cambridge University Press. Continuous Assessment: 40%
Final Examination: 60%
SIM3005 MATRIX THEORY Medium of Instruction:
English
Rank and nullity of matrices. Inner product spaces, the
Gram-Schmidt process, least squares problems, ortogonal Humanity Skill:
matrices. Diagonalization for real symmetric matrices, CT3, LL2
quadratic forms, semi positive definite matrices. The
singular value decomposition. Generalized inverses and References:
linear systems, Moore-Penrose inverses. 1. Cohn, P.M. (2001). Introduction to Ring Theory,
Springer Undergraduate Mathematics Series,
Assessment: 2. Herstein, I. N. (2005), Noncommutative Rings, Carus
Continuous Assessment: 40% Mathematical Monographs No. 15, Math. Assoc. of
Final Examination: 60% America.
3. Beachy, J. A. (1999), Introductory Lectures on Rings
Medium of Instruction: and Modules, London Maths. Soc. Student Texts 47,
English Cambridge University Press.
4. Lam, T.Y. (2010). Exercises in Classical Ring Theory
Humanity Skill: (Problem Books in Mathematics), Springer, Second
CS3, CT3, LL2 Edition.
References:
1. Anton, H. & Busby, R. C. (2002). Contemporary Linear SIM3008 GROUP THEORY
Algebra, Wiley Publishers.
2. Horn, R. A. & Johnson, C. R. (1985). Matrix Analysis, The three isomorphism theorems. Cyclic groups. Direct
Cambridge University Press. product of groups. Introduction to the three Sylow’s
3. Zhang, F. (2011). Matrix Theory – Basic Results and Theorem. Classification of groups up to order 8. Finitely
nd
Techniques, Springer (2 edition). generated abelian groups. Nilpotent groups and Soluble
4. Zhan, X. (2013). Matrix Theory, American groups
Mathematical Society.
5. Bapat, R. B. (2012), Linear Algebra and Linear Assessment:
nd
Models, Springer (3 edition). Continuous Assessment: 40%
Final Examination: 60%
SIM3006 ALGEBRA II Medium of Instruction:
English
Groups-Isomorphism theorems. Permutation groups. Group
actions, p-groups. Humanity Skill:
CT3, LL2
Rings-Maximal and prime ideals. Polynomial rings. Field
extensions. Finite fields. References:
1. Ledermann, W., Weir, A. J. & Jeffery, A. (1997).
Assessment: Introduction to Group Theory, Addison Wesley Pub.
nd
Continuous Assessment: 40% Co. (2 edition).
Final Examination: 60% 2. Rotman, J. J. (2014). An Introduction to the Theory of
th
Groups, Springer-Verlag, New York (4 edition).

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