BST Discrete Mathematics PDF

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KYU/A/ASA/02

SCHOOL: PURE AND APPLIED SCIENCES COURSE OUTLINE DEPARTMENT: PURE AND APPLIED SCIENCES PROGRAMME: STATISTICS AND MATHEMATICS AND COMPUTER SCIENCE YEAR: I SEMESTER: I UNIT CODE: SMA 2100

UNIT TITLE: DISCRETE MATHEMATICS

LECTURE HOURS: 45

PRE-REQUISITES: None

LECTURER: Kinyanjui J.N LECTURER CONTACTS: EMAIL: [email protected]

1.0 COURSE PURPOSE At the end of the course, the learner should be proficient in handling the basics of set theory, rules of logic, functions and mathematical induction. 2.0 LEARNING OUTCOMES At the end of this course, the learners should be able to: i. Appreciate the Algebra of Logic, including truth tables, implication and equivalence. ii. Appreciate the language of sets, and apply set theory in solving problems involving vehn diagrams. iii. Apply the properties of functions. iv. Be able to recognize the different sets of numbers. v. Apply the methods of proof to prove mathematical statements

3.0COURSE OUTLINE WEE TOPIC K 1-4 Sets

5 5-8

Cat 1 Logic

SUB-TOPIC  Elements, Specification, finite and infinite  Universal, Empty and disjoint, subsets  Vehn diagram, union , intersection  Compliment, difference, number of elements  Principle of inclusion and exclusion  Variables, open sentences, truth sets  Propositions, truth values, logical equivalence, truth tables, negation  Conjunction, disjunction, tautology.

REMARKS

9-10

Functions

10

Cat2

11-13

Methods of Proofs

14

Numbers

15-16

Examinations

 Contradiction, implication, contrapositive , converse, inverse  Existential and Universal quantifiers, negation with quantifiers  Domain, codomain, images, range, pre image, specification and composition  Bracket, absolute value and inverse  Injections, surjections and bijections  Sum, difference, product and quotient, increasing and decreasing functions

Direct, Contrapositive Contradiction, counter example Principle of Mathematical induction Real, natural, prime, integer, rational and irrational.  Laws of arithmetic including comparison with laws of set theory and logic.  Evenness and oddness, denseness, real number lines, intervals and inequalities     

4.0TEACHING METHODOLOGIES Lectures and tutorials; group discussion; demonstration; Individual presentations. 5.0 INSTRUCTIONAL MATERIALS AND EQUIPMENT Audio Visual aids; Computers; Overhead projector and LCD, Whiteboard, flip charts.

6.0 COURSE EVALUATION Cat 1= 10% Cat 2= 10%

Other Assesments=10% Examinations = 70% Total = 100% Pass Mark 40% 7.0 COURSE TEXTBOOKS Elias Zakon. Basic Concepts of Mathematics, The Trillia Group, 2001, ISBN: 9781931705004 L. Bostock and S. Chandler. Core Mathematics for Advanced Level (3rd Edition). Stanley Thornes (Publishers) Ltd. 2000, ISBN: 978-0748755097 Kenneth Rossen, Discrete Mathematics and its Applications (2011) McGram-Hill ISBN-13: 978-0073383095 Hungerford, T.W.; Mercer, R., College algebra, (Saunders College Publishing), 1991, ISBN: 978-0030595219 Booth, D.J., Foundation Mathematics, (Addison Wesley), 1991, ISBN: 978-0201416985 8.0 REFERENCE TEXTBOOKS Newmark, J; Lake, F., Mathematics as a second language, (Addison Wesley), 1988, ISBN: 9780201192971 Niven, I.; Zuckerman, H.S., An introduction to the theory of numbers, (Wiley), 1980, ISBN: 978-0471625469 Stewart, I.; Tall, D., The foundations of mathematics, (Oxford University Press), 1977, ISBN: 9780198531654.

9.0 COURSE JOURNALS Discrete Mathematics Journal – Elsevier ISSN: 0012-365X Discrete Applied Mathematics Journal – Elsevier, ISSN:0166-218X SIAM Journal on Discrete Mathematics, David P. Williamson, ISSN: 0895-4801, 1988

10.0

REFERENCE JOURNALS

Journal of Discrete Mathematics, ISSN: 2090-9837 Open journal of Discrete Mathematics, ISSN: 2161-7643 Japanese Journal of Mathematics, ISSN: 1861-3624...