Maths 168A 27 - Lecture notes 7 PDF

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The lecturer was Ian Wagstaff...

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Maths168A. 27February 2018 Essential that you get the workbook for the class. You are given certain exercises that you need to do in the workbook, these will be checked off, not marked and if you just give it a go you will receive the 10% of the overall marks for this course. Introduction to the history of numbers. This will not be tested on!! Do you think numbers are natural? Do they occur in nature? It is believed that numbers are actually hardwired into our existence. The first historical numbers are the counting numbers, more correctly called the ‘natural’ numbers. When you beginning counting, you usually start at 1, and this was demonstrated by a timeline, looking at 1BC---|----1AD, there is no year ‘0’ To be able to see points and lines, they need to be 2D, and this leads to the ability to measure these. Looked at Roman counting system There are perfect numbers. The first being 6, 1+2+3=6, also 1x2x3=6. There is a formula for perfect numbers….. Prime numbers: 2,3,5,7,11,13,17,19…. Whole numbers 0,1,2,3,4, Integers 0 +-1, +-2, +-3, +-4, (they include both positive and negatives) INTEG-integrity=good,honest,wholeness. Fractions FRAC-ture, which is is broken into parts. 7/11, -10/3, 8 = 8/1, 3.245 =3 142/1000 (decimal fraction). Fractions include all numbers. These numbers are all rational numbers. Irrational numbers…… Most common number sequence 1,2,3,4,5,6, The Fibonacci sequence…..1,1,2,3,5,8,13,21,34,55,89,144. This sequence is everywhere in nature. NOTES FOR TODAY: RULES OF SIGNS: Never say two minus make a plus. Because when doing -3-5, which is -3 take away 5 = -8 FRACTIONS Equivalent fractions: ½=2/4=3/6=4/8=5/10…… In general, if a, b, n, are natural numbers, then na/nb = a/b Simplifying (‘cancelling down’) eg. 48/112, so both numbers are even, so you know they can be divided by 2, but lets cancel by 4…..4 into 48 = 12 and 4 into 112 = 28 = 12/28, then do it again dividing by 4 =3/7 a simplified fraction. Addition and subtraction: 3 /8 + 5/12 = we need to find the lowest number that go into both 8 and 12 3(3) + 5(2)/24 = 19/24 Multiplication: 4/9 x 27/32 = 108/288, you multiply the top numbers and then multiply the bottom numbers, then you simplify….eventually you get ⅜ Division: 8 divided by 2 = 8 x ½ =4 15/28 divide 30/35 = the same as 15/28 x 35/30 =⅝ after you simplify. Decimal Fractions: Please look at notes also in this folder.

NB: Lecture has been recorded on Panopto....