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SST 102: Discrete Mathematics Notes

Institution: University

Course: Bachelor of Computer Science

Content Category: Lecture Notes

Posted By: davidkariuki1010

Document Type: DOCX

Number of Pages: 3

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Summary

KENYATTA UNIVERSITY
DIGITAL SCHOOL OF VIRTUA L AND OPEN LEARNING
IN COLLABORATION WITH
SCHOOL OF PURE AND APPLIED SCIENCES
DEPARTMENT OF MATHEMATICS AND ACTUARIAL SCIENCE,

SST102 DISCRETE MATHEMATICS

-

INTRODUCTION
Welcome to this module. Here you will learn basic concepts of mathematical structures that are countable or otherwise distinct and are separable. In contrast to real numbers that have the property of varying smoothly the objects studied in discrete mathematics such as integers, graphs and statements in logic do not vary smoothly in this way but have distinct separated values. Discrete mathematics therefore excludes topics in continuous mathematics such as calculus and analysis. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer algorithms, programming languages, cryptography, automated theorem proving and software development.

DISCRETE MATHEMATICS FLOW CHART
WEEK LESSON
WEEK 0 INTRODUCTION (YOUR CONTEXT, YOUR GOALS, THOUGHTS ABOUT MATHEMATICS)
WEEK 1 THE NOTION OF A SET
WEEK 2 SET OPERATIONS
WEEK 3 RELATIONS
WEEK 4 PARTIAL ORDERINGS
WEEK 5 LATTICES
WEEK 6 BASIC DEFINITIONS AND CONCEPTS OF GROUPS, RINGS AND FIELDS
WEEK 7 BOOLEAN ALGEBRA
WEEK 8 DUALITY
WEEK 9 TRUTH VALUES AND TRUTH TABLES
WEEK 10 TAUTOLOGY
WEEK 11 GRAPHS
WEEK 12 ADJACENCY MATRICES
WEEK 13 & 14 EXAMINATION

OVERVIEW OF THE MODULE

Introduction (Your Context, Your Goals)
This lesson is intended to help you acclimatize learning and create a community of learners who will motivate each other during the course. You will be required to introduce yourself to your lecturer and colleagues either physically during a face to face session or even online before other academic interaction start. This will be at the discretion of individual universities and lecturers. It will be important to also state your context and goals as well as what you think about Mathematics. You can also share any experience that you may have regarding Mathematics.

LESSON ONE introduces the basic language and notation of sets.
LESSON TWO explores the standard set operations including union of sets, intersection of sets, difference between sets and Venn diagrams.
LESSON THREE considers the relations between objects of the same set or between objects of two or more sets.
LESSON FOUR introduces partially ordered sets. The use of relations to order some or all elements of sets.
LESSON FIVE considers partially ordered sets in which every pair of elements has both a least upper bound and a greatest lower bound.
LESSON SIX touches on basic concepts of groups, rings and fields; algebraic systems whose structure imitates that of inters
LESSON SEVEN introduces the operations and the rules for working with the set{0, 1}.
LESSON EIGHT explores the interchanging of Boolean sums and products and the interchanging of 0s and 1s.
LESSON NINE introduces the basic building blocks of logic.
LESSON TEN explores the proposition that is always true.
LESSON ELEVEN introduces graphs; a collection of points and lines between the points.
LESSON TWELVE explores how adjacency matrices are used in graph theory.
EXAMINATION will bring together the work you have been doing to an end.


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