Page 141 - buku panduan 20192020

Faculty of Science Handbook, Session 2019/2020

3. Friedberg, S.H., Insel, A.J., & Spence, L.E. (2002). maximal ideals, Jacobson and prime radicals, semiprimitive
Linear algebra (4 ed.). Upper Saddle River, NJ: and semiprime rings, rings with chain condition, primitive
th
Prentice-Hall. rings, group rings.
rd
4. Sheldon, A. (2015). Linear algebra done right (3
ed.). New York, NY: Springer International Publishing. Assessment:
5. Yang, Y.S. (2015). A concise text on advanced linear Continuous Assessment: 40%
algebra. Cambridge, NY: Cambridge University Press. Final Examination: 60%

Medium of Instruction:
SIM3005 MATRIX THEORY English

Rank and nullity of matrices. Inner product spaces, the Soft Skills:
Gram-Schmidt process, least squares problems, ortogonal CTPS3, LL2
matrices. Diagonalization for real symmetric matrices,
quadratic forms, semi positive definite matrices. The References:
singular value decomposition. Generalized inverses and 1. Cohn, P.M. (2001). Introduction to Ring Theory
linear systems, Moore-Penrose inverses. (Springer Undergraduate Mathematics Series).
Springer.
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
Soft Skills: (2 ed.) (Problem Books in Mathematics). Springer.
nd
CS3, CTPS3, LL2

References: SIM3008 GROUP THEORY
1. Zhang, F.Z. (2011). Matrix theory: Basic results and
nd
techniques (2 ed.). New York, NY: Springer-Verlag. The three isomorphism theorems. Cyclic groups. Direct
nd
2. Horn, R., & Johnson, C.R. (2013). Matrix analysis (2 product of groups. Introduction to the three Sylow’s
ed.). Cambridge, NY: Cambridge University Press. Theorem. Classification of groups up to order 8. Finitely
3. Steeb, W., & Hardy, Y. (2011). Matrix calculus and generated abelian groups. Nilpotent groups and Soluble
nd
Kronecker product (2 ed.). Singapore: World groups
Scientific Publishing.
4. Bapat, R.B. (2012). Linear algebra and linear Models Assessment:
(3 ed.). London, UK: Springer-Verlag. Continuous Assessment: 40%
rd
5. Zhan, X.Z. (2013). Matrix theory. Providence, RI: Final Examination: 60%
American Mathematical Society.
Medium of Instruction:
English
SIM3006 ALGEBRA II
Soft Skills:
Groups-Isomorphism theorems. Permutation groups. Group CTPS3, LL2
actions, p-groups.
References:
Rings-Maximal and prime ideals. Polynomial rings. Field 1. Ledermann, W., Weir, A. J., & Jeffery, A. (1997).
nd
extensions. Finite fields. Introduction to group theory (2 ed.). Addison Wesley
Pub. Co.
Assessment: 2. Rotman, J. J. (2014). An Introduction to the theory of
Continuous Assessment: 40% groups (4th ed.). New Work: Springer-Verlag.
Final Examination: 60% 3. Gallian, A. J. (2017). Contemporary abstract algebra
th
(9 ed.). Brooks Cole.
Medium of Instruction:
English
SIM3009 DIFFERENTIAL GEOMETRY
Soft Skills:
CTPS3, LL2 Vector algebra on Euclidean space. Lines and planes.
Change of coordinates. Differential geometry of curves.
References: Frenet Equations. Local theory of surfaces in Euclidean
1. Durbin, J. R. (2009). Modern algebra: An Introduction space. First and second fundamental forms. Gaussian
th
(6 ed.). John Wiley. curvatures and mean curvatures. Geodesics. Gauss-
2. Fraleigh, J. B. (2003). A first course in abstract Bonnet Theorem.
th
algebra (7 ed.). Addison-Wesley.
3. Gallian, J. (2012). Contemporary abstract algebra (8 Assessment:
th
ed.). Brooks/Cole Cengage Learning. Continuous Assessment: 40%
4. Hungerford, T.W. (2014). Abstract algebra: An Final Examination: 60%
rd
Introduction (3 ed.). Brooks/Cole Cengage Learning.
Medium of Instruction:
English
SIM3007 RING THEORY Soft Skills:
CS3, CTPS3, LL2
Ring, subrings and ideals, modules, internal direct sum,
external direct product, nil and nilpotent ideals, prime and
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