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BASIC MATHS

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  September 6, 2011  UNIVERSITY OF NAIROBIFACULTY OF SCIENCEFIRST YEAR LECTURE NOTES SMA 101: BASIC MATHEMATICSFirst Edition WRITTEN BY : Dr. Bernard Mutuku Nzimbi REVIEWED BY:School of Mathematics, University of NairobiP.o Box 30197, Nairobi, KENYA.EDITED BY:  Copyright c ⃝ 2011 Benz, Inc. All rights reserved .All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem or transmitted in any form or by any means, electronic, mechanical, photocopy-ing, recording or otherwise, without the prior permission of the publisher. 2  This page is intentionally left blank. i  Contents About the Author viPreface viiGoals of a Basic Mathematics Course ix1 ELEMENTARY SET THEORY 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Rudiments of Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Notation and Terminology . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Fundamental Operations on Sets . . . . . . . . . . . . . . . . . . 51.3 Laws of Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3.1 Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3.2 Elements Argument Method . . . . . . . . . . . . . . . . . . . . . 161.4 Fundamental Counting Principle . . . . . . . . . . . . . . . . . . . . . . . 181.4.1 Counting and Venn Diagrams . . . . . . . . . . . . . . . . . . . . 201.5 Real Number Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.5.1 Some Useful subsets of Real Numbers . . . . . . . . . . . . . . . . 291.5.2 Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301.6 Application of Laws of Set Theory . . . . . . . . . . . . . . . . . . . . . . 341.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361.8 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391.8.1 Arithmetic Operations of Complex Numbers . . . . . . . . . . . . 401.8.2 The Complex Plane or The Argand Diagram or The Gauss Plane 411.8.3 Conjugates, Absolute Values and Arguments of Complex Numbers 41 ii
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