Page 76 - Handbook Bachelor Degree of Science Academic Session 20212022

Faculty of Science Handbook, Academic Session 2021/2022

Assessment:
BACHELOR OF SCIENCE PROGRAMS
Continuous Assessment: 40%
Final Examination: 60%
Please refer to Program Structure for courses.
References:
FURTHER DEGREE 1. Susanna S. Epp, Discrete Mathematics with
th
applications, 5 edition, Cengage Learning, 2019.
Apart from teaching and supervising at the bachelor’s level, 2. Douglas E. Ensley, J. Winston Crawley, Discrete
the staff members of the institute also supervise research Mathematics, John Wiley and Sons. 2006.
projects that lead to Master’s and doctorate degrees in the nd
three branches of mathematics. 3. K. Devlin, Sets, Functions and Logic, 2 edition,
Chapman & Hall, 1992.
4. H. Anton, C. Rorres, Elementary Linear Algebra with
JOB OPPORTUNITIES Applications, 11 edition, Wiley High Education Inc.,
th
2014.
The learning of mathematics will help increase one's skills in th
problem solving and analysis. It trains one’s mind to 5. Larson, D.C. Falvo, Elementary Linear Algebra, 7
edition, Brooks/Cole Thomson Learning, 2012.
manipulate information, to form accurate, complicated and
abstract ideas and to enable one to discern complicated
arguments. The training to think quantitatively, logically and
analytically in problem solving may prove valuable in one's SIM1002 CALCULUS I
chosen career.
Functions and their graphs, combining functions,
trigonometric functions. Rate of change and tangent lines to
Since the use of mathematics is all encompassing in human curves, limits of functions and limit laws, the precise
endeavour, a graduate’s career opportunities are almost
limitless and not only confined to teaching and research. definition of a limit, one-sided limits, continuity, limits
Many graduates from this Institute have been employed in involving infinity and asymptotes of graphs. Tangent lines
and the derivative at a point, the derivative as a function,
the financial sectors (banking, accountancy and insurance differentiation rules, derivatives of trigonometric functions,
for instance), management, business, industry and the chain rule, implicit differentiation. Extreme values of
computing sectors.
functions, the mean value theorem, monotonic functions and
the first derivative test, concavity and curve sketching,
antiderivatives. Sigma notation and limits of finite sums, the
SYNOPSIS OF COURSES
definite integral, the fundamental theorem of calculus,
indefinite integrals and the substitution method, the definite
SIX1016 STATISTICS (FACULTY OF SCIENCE)
integrals substitution and the area between curves,
logarithms functions, exponential functions, indeterminate
Introduction to statistics; Experimental and observational forms and L’hopital’s Rule.
studies; Display and organisation of data; Descriptive
statistics; Population and samples; Sampling methods;
Basic probability theory; Useful probability distributions: Assessment:
binomial, Poisson and normal; Sampling distributions; Continuous Assessment: 40%
Central Limit Theorem; Point estimation and confidence Final Examination: 60%
interval; Hypothesis testing for mean and proportion in one References:
and two populations; Chi-square tests; Simple linear 1. Joel R. Hass, Christopher E. Heil, Maurice D. Weir,
regression and correlation analysis.
Thomas' Calculus, 14th edition, Pearson Education, Inc.
2019.
Assessment: 2. J. Stewart, Calculus, 8th. edition, Cengage Learning,
Continuous Assessment: 100%
2016.
3. Robert A. Adams, Christopher Essex, Calculus: A
References: th
1. McClave, J.T. & Sincich, T.T. (2016). Statistics (13th complete course, 8 edition with MyMathLab, Pearson
ed.). Upper Saddle River, NJ: Pearson. Education, 2013.
2. Mann, P. S. (2010). Introductory Statistics (7th ed.). 4. R.T. Smith, R.B. Minton, Calculus, 4th ed., McGraw-Hill,
2012.
New York: Wiley.
3. Freedman, D., Pisani, R. & Purves, R. (2007). Statistics
(4th ed.). New York: W.W. Norton.
SIM1003 CALCULUS II
Inverses trigonometric functions, hyperbolic functions,
SIM1001 BASIC MATHEMATICS
inverses hyperbolic functions. Basic integration formulas,
integration by parts, trigonometric integrals, trigonometric
Introductory logic. Mathematical statements. Quantifiers. substitutions, integration of rational functions by partial
Rules of inference. Mathematical induction, binomial fractions, improper Integrals. Sequence, infinite series, the
theorem. Sets, Cartesian products, equivalence relations, integral test, comparison tests, absolute convergence, the
functions, bijections, inverse functions. Integers, rational
numbers, real numbers. Complex numbers. De Moivre’s ratio and root tests, alternating series test, conditional
theorem and roots of unity. Polynomials and equations. convergence, power series, Taylor and Maclaurin series.
Calculus with parametric curves, polar coordinates. Three-
Remainder theorem, fundamental theorem of algebra, dimensional coordinate systems, vectors, the dot product,
conjugate roots.
the cross product, triple product, lines and planes, cylinder
and quadric surfaces. Vector-valued functions, space curves,
Systems of linear equations, row reduction, echelon forms.
Matrix operations, algebraic properties of matrices, inverses, derivatives and integrals of vector functions.
elementary matrices, linear independence and Assessment:
homogeneous linear systems, matrices with special forms.
Determinants, cofactor expansion, properties of Continuous Assessment: 40%
determinants, Cramer’s rule, eigenvalues, eigenvectors, and Final Examination: 60%
diagonalization.
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