Page 46 - handbook 20162017

Faculty of Science Handbook, Session 2016/2017

4. Baker, A. (1985). A Concise Introduction to the Theory SIM3006 ALGEBRA II
of Numbers, Cambridge University Press.
5. Baker, A. (2012). A Comprehensive Course in Number Groups-Isomorphism theorems. Permutation groups. Group
Theory, Cambridge University Press. actions, p-groups.
Rings-Maximal and prime ideals. Polynomial rings. Field
SIM3004 ADVANCED LINEAR ALGEBRA extensions. Finite fields.
Inner product spaces, the Gram-Schmidt orthogonalization Assessment:
process and orthogonal complements. Orthogonal Continuous Assessment: 40%
operators, unitary operators, self-adjoint operators and Final Examination: 60%
positive definite operators. Dual spaces, bilinear forms.
Diagonalization of symmetric bilinear forms, real quadratic Medium of Instruction:
forms. Triangularization theorem, primary decomposition English
theorem, Jordan canonical forms.
Humanity Skill:
Assessment: CT3, LL2
Continuous Assessment: 40%
Final Examination: 60% References:
1. Durbin, J. R. (2009). Modern Algebra, An Introduction,
th
Medium of Instruction: John Wiley (6 edition.).
English 2. Fraleigh, J. B. (2003). A First Course in Abstract
Algebra, Addison-Wesley (7 edition).
th
Humanity Skill: 3. Gallian, J. (2012). Contemporary Abstract Algebra,
th
CS3, CT3, LL2 Brooks/Cole Cengage Learning (8 edition).
4. Hungerford, T.W. (2014). Abstract Algebra: An
References: Introduction, Brooks/Cole Cengage Learning (3rd
1. Kenneth Hoffman, Ray Kunze (1971), Linear Algebra, edition).
Pearson Prentice Hall, Inc.
2. Jin Ho Kwak, Sungpyo Hong (2004), Linear Algebra,
Brikhauser,. (2 edition.). SIM3007 RING THEORY
nd
3. Stephen H. Friedberg, Arnold J. Insel & Lawrence E.
Spence (2003) Linear Algebra, Pearson Education Ring, subrings and ideals, modules, internal direct sum,
International (4 edition.). external direct product, nil and nilpotent ideals, prime and
th
4. Axler, S. (2015). Linear Algebra Done Right, Springer maximal ideals, Jacobson and prime radicals, semiprimitive
rd
(3 edition). and semiprime rings, rings with chain condition, primitive
5. Yang, Y. (2015). A Concise Text on Advanced Linear rings, group rings.
Algebra, Cambridge University Press.
Assessment:
Continuous Assessment: 40%
SIM3005 MATRIX THEORY Final Examination: 60%
Rank and nullity of matrices. Inner product spaces, the Medium of Instruction:
Gram-Schmidt process, least squares problems, ortogonal English
matrices. Diagonalization for real symmetric matrices,
quadratic forms, semi positive definite matrices. The Humanity Skill:
singular value decomposition. Generalized inverses and CT3, LL2
linear systems, Moore-Penrose inverses.
References:
Assessment: 1. Cohn, P.M. (2001). Introduction to Ring Theory,
Continuous Assessment: 40% Springer Undergraduate Mathematics Series,
Final Examination: 60% 2. Herstein, I. N. (2005), Noncommutative Rings, Carus
Mathematical Monographs No. 15, Math. Assoc. of
Medium of Instruction: America.
English 3. Beachy, J. A. (1999), Introductory Lectures on Rings
and Modules, London Maths. Soc. Student Texts 47,
Humanity Skill: Cambridge University Press.
CS3, CT3, LL2 4. Lam, T.Y. (2010). Exercises in Classical Ring Theory
(Problem Books in Mathematics), Springer, Second
References: Edition.
1. Anton, H. & Busby, R. C. (2002). Contemporary Linear
Algebra, Wiley Publishers.
2. Horn, R. A. & Johnson, C. R. (1985). Matrix Analysis, SIM3008 GROUP THEORY
Cambridge University Press.
3. Zhang, F. (2011). Matrix Theory – Basic Results and The three isomorphism theorems. Cyclic groups. Direct
nd
Techniques, Springer (2 edition). product of groups. Introduction to the three Sylow’s
4. Zhan, X. (2013). Matrix Theory, American Theorem. Classification of groups up to order 8. Finitely
Mathematical Society. generated abelian groups. Nilpotent groups and Soluble
5. Bapat, R. B. (2012), Linear Algebra and Linear groups
nd
Models, Springer (3 edition).
Assessment:
Continuous Assessment: 40%
Final Examination: 60%

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