University of Zimbabwe

Chinhoyi University of Technology

School of Engineering Sciences and Technology

Department of ICT and Electronics

CUIT102 Computer Mathematics Course Outline

LECTURER Donna Musiyandaka (Mrs.)

LECTURE TIMES TBA as per university-wide timetable.

OFFICE No. / CONSULATION HOURS E15 / Fridays 1pm – 4pm

CREDITS & NOTIONAL LEARNING HOURS

Lecture hrs: 36 / Practical hrs: 0 / Tutorial hrs: 12
Individual Study hrs: 54 / Assessment: 18 / Total Notional Hours: 120
Total Credits: 12

COURSE DESCRIPTION

This course is a foundation course for all students studying a computing science related discipline. The use of mathematics in information technology is increasingly becoming complex because of the increased sophistication of user requirements and the desire for better and more efficient systems. Thus this course addresses the fundamentals, providing the basic mathematical building blocks required in information technology, so that a student is able to understand the more senior applications in algorithm design, database design, programming and hardware. Thus the course aims to:

· Give the student fluency in precise mathematical language to deal with discrete structures

· Develop skills in algorithmic problem solving, recursive and combinatorial thinking

· Develop respect for careful definition and skills in mathematical argument

LEARNING OUTCOMES

At the end of the course the student must be able to:

· Apply formal methods of propositional and predicate logic.

· Create a truth table to determine whether a given formula in predicate logic is valid.

· Render a well formed formula in predicate logic in English.

· Construct formal proofs of arguments.

· Explain, with examples, the basic terminology of sets, relations and functions.

· Perform standard operations on sets, relations and functions.

· Apply principles of counting to various scenarios.

· Relate practical examples to the appropriate set, functions and relations, and interpret the associated operations and terminology in context.

· Calculate probabilities of events and expectations for random variables.

· Differentiate between dependent and independent events.

· Illustrate basic terminology of graph theory.

· Demonstrate different traversal methods for graphs and trees.

TOPICS & COVERAGE

1. LOGIC (week 1 & week 2)

- Introduction, Prepositional logic, Logical connectives, Conditional propositions, Truth tables, Logical reasoning, Predicates and Quantifiers

2. PROOF (week 3)

- Direct, Indirect, Contradiction, Counter-example, Proof by mathematical induction

3. SETS (week 4)

- Notation, operations on sets, diagrammatic representation of sets , Algebra of sets, Theory of Counting

4. RELATIONS (week 5)

- Notation, Properties of relations, Closures of relations

5. TEST & TUTORIALS (week 6)

6. FUNCTIONS/MAPPINGS (week 7)

- Notation, Types of functions, Pigeon-hole principle, Inverse of functions

7. GRAPHS AND TREES (weeks 8 & 9)

- General introduction (notation) and definitions, Connectivity of graphs, Digraphs, In-degree, Out-degree, Rooted trees, Binary trees, n-tree and levels, Shortest route (i.e. traveling salesman) problem,

8. COUNTING (week 10)

- Counting in sets, Sequences, Factorials, Binomial theory, counting subsets (ordered subsets, subsets of a given size), Permutations, Combinations

9. DISCRETE PROBABILITY (week 11)

- Random variables and Sample Spaces (probability spaces), Events and probabilities, Tree diagrams, Independent repetition of an experiment, Determining probabilities, Infinite sample spaces

10. TUTORIALS, REVISION AND TESTS (week 12)

ASSESSMENT