Page 107 - handbook 20152016

Faculty of Science Handbook, Session 2015/2016

References:
Medium of Instruction: 1. Anton, H. & Busby, R. C. (2002). Contemporary Linear
English Algebra, Wiley Publishers.
2. Horn, R. A. & Johnson, C. R. (1985). Matrix Analysis,
Humanity Skill: Cambridge University Press.
CS3, CT5, LL2 3. Zhang, F. (2011). Matrix Theory – Basic Results and
nd
Techniques, Springer (2 edition).
References: 4. Zhan, X. (2013). Matrix Theory, American
1. Burton, D. (2010). Elementary Number Theory, Mathematical Society.
th
McGraw Hill Publ. Co. (7 edition). 5. Bapat, R. B. (2012), Linear Algebra and Linear
nd
2. Rosen, K. H. (2010) Elementary Number Theory and Models, Springer (3 edition).
th
Its Applications, Pearson Addison Wesley (6 edition).
3. Davenport, H. (2008). The Higher Arithmetic,
th
Cambridge University Press (8 edition). SIM3006 ALGEBRA II
4. Baker, A. (1985). A Concise Introduction to the Theory
of Numbers, Cambridge University Press. Groups-Isomorphism theorems. Permutation groups. Group
5. Baker, A. (2012). A Comprehensive Course in Number actions, p-groups.

Theory, Cambridge University Press.
Rings-Maximal and prime ideals. Polynomial rings. Field
extensions. Finite fields.

SIM3004 ADVANCED LINEAR ALGEBRA Assessment:

Inner product spaces, the Gram-Schmidt orthogonalization Continuous Assessment: 40%
process and orthogonal complements. Orthogonal Final Examination: 60%

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
theorem, Jordan canonical forms. Humanity Skill:
CT3, LL2

Assessment: References:
Continuous Assessment: 40% 1. Durbin, J. R. (2009). Modern Algebra, An Introduction,
Final Examination: 60% th
2. John Wiley (6 edition.).
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,
Brooks/Cole Cengage Learning (8 edition).
th
Humanity Skill:
CS3, CT3, LL2 4. Hungerford, T.W. (2014). Abstract Algebra: An
Introduction, Brooks/Cole Cengage Learning (3rd
edition).
References:
1. Kenneth Hoffman, Ray Kunze (1971), Linear Algebra,
Pearson Prentice Hall, Inc.
2. Jin Ho Kwak, Sungpyo Hong (2004), Linear Algebra, SIM3007 RING THEORY

nd
Brikhauser,. (2 edition.). Ring, subrings and ideals, modules, internal direct sum,
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.).
4. Axler, S. (2015). Linear Algebra Done Right, Springer and semiprime rings, rings with chain condition, primitive
rings, group rings.
rd
(3 edition).
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
matrices. Diagonalization for real symmetric matrices, Humanity Skill:
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,

Assessment: 2. Springer Undergraduate Mathematics Series,
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:
English and Modules, London Maths. Soc. Student Texts 47,
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.

100