Mathematics in Enabling the Understanding of Todays Social Issues - Essay Example

Mathematical Enquiries Mathematical Enquiries Mathematics is the study of relationships that exist among magnitudes, quantities and properties. The relationship equally exists in logical operations where magnitudes, quantities and properties that are unknown may be inferred. Mathematics came into existence a long while ago and has gone through various steps of growth to get to what it is today. It is through the discipline that various disciplines like engineering, science as well as philosophy have thrived. It was earlier on known for simple calculations, counting, and measurements and studying of various shapes and movements of objects, to what can now be referred to as a complex, broad and abstract discipline. This essay will therefore evaluate various mathematical functions involving numbers, measurements as well as how math has developed overtime to get to what it is today. Just like humanity, mathematics is quite old and is said to have originated in Egypt and Greece as simple to the complex one we have today. In the historical times, mathematics encompassed arithmetic, geometry and algebra, making it get known as a science of quantity; while others referring it to as science of simplicity (Rouseball, 2010). Several developments in the field however got realized in the 19th century where mathematics spread its wings to an extent of being regarded as a science of inferences and relations to the fact that it now consisted of logic that was symbolic (Lavine, 1994). To date, mathematics as a discipline now covers a wide range of areas including numbers, geometry, algebra, calculus, set theory and mathematical logic, as well as statistics and probability that are known to be more applied aspects of the discipline. Mathematics also covers other areas like graph theory, differential geometry, topology, model theory, among many others. When it comes to number bases, we have two types; the binary and hexadecimal systems. As for the case of binary number bases, what is contained here is the ones and zeros and zero through nine for the hexadecimal system. In the base ten system, the ten stands for 1 and 0, and not a single numeral 10. In this case therefore, for one to count one more than nine, the ones column is zeroed out ant the tens column added 1 onto. If the tens column gets too big, both the ones and tens column are zeroed out and add one to the ten times ten (Stapel, 2014). Another thing worth noting is that any number raised to power 0 is 1. For instance, in conversion of base 2 numbers to their corresponding base 10, all you need are digits of the binary number as well as the numbering containing powers of base 2. For Example, 100110101(Digits of the binary number) 876543210(Numbering containing powers of base 2) (1*28)+(0*27)+(0*26)+(1*25)+(1*24)+(0*23)+(1*22)+(0*21)+(1*20) =(1*256)+(0*128)+(0*64)+(1*32)+(1*16)+(0*8)+(1*4)+(0*2)+(1*1) =256+32+16+4+1 =309. Therefore, 1001101012=30910 As in the case of converting the decimal numbers to binary, the method is simple; all you have to do is divide the decimal part by two all through and ensure remainders at each step are kept in mind. For instance, 309/2=154(remainder 1) 154/2=77(remainder 0) 77/2=38(remainder 1) 38/2=19(remainder 0) 19/2=9(remainder 1) 9/2=4(remainder 1) 4/2=2(remainder 0) 2/2=1(remainder 0) ½=0(remainder 1) Therefore, 30910=1001101012 The cummutative law of addition deals with addition of numbers, it says that; 2+3=3+2, as the two equally amount to 5. Consider the illustration below for instance, There is a geometric difference between the two number lines presented, though the resultant solution is the same. It should be noted that subtraction cannot be considered as cummutative. Associative law on the other hand shares the addition property of the cummutative law. Following any order, it is possible for whole numbers to get added at a time and come up with the same result (Victor & Addison, 2008). An example can be cited from the above illustration of the cummutative law, where 2+3 gives us 5, regardless of the addition order taken. Another example can be in the case of 61+58+59+22. Here most of us will tend to pair the numbers that result in tens for our calculation to be easier. For instance, (61+59) + (58+22) = 120+80=200. According to the distributive law of arithmetic, a number multiplied by a group of numbers added together is same as carrying out the multiplication separately. For example, 2*(3+6) = 2*3+2*6 =18. In this case, the number 2 is multiplied all through 3 and 6 to become 2*3 and 2*6. Moving onto prime numbers, they can be defined as those whole numbers that are greater than one and can only be divided through by one or the prime number itself. Numbers such as 2, 3, 5, 7 and so on are prime numbers because they can only be divided through by 1 or the number itself (Martin, 1970). Prime factor on the other hand are prime numbers which when multiplied, give come up with the original number. For example: In the case of 35, it takes the multiplication of two prime numbers to come up with it, and these numbers are; 7 & 5. 7&5 are prime numbers, yet prime factors of 35. We cannot talk of whole numbers and decide to ignore fractions and decimals. Whole numbers are numbers like: 1, 2, 3, 4, 5, 6, and so on. Fractions have a numerator and denominator, while decimals exist in the form of whole numbers, with a separation of the numerator and denominator by a decimal point. They are therefore called decimal fractions and the number of decimal places provide us with a clue of the number of zeros to be in the denominator. For example: 0.256 into a fraction means that the denominator of the resultant fraction will have 3 zeros. Let’s take a look at this: 0.256=. As for 0.8, the denominator of the fraction should have 1 zero, which is;. It also should be a reminder to us that the number of decimal digits=the power of 10. Let us also look at conversion of fractions to decimals. As earlier noted, the number of decimal digits indicate the number of zeros to appear in the denominator of a fraction. However, the number of zeros in the denominator of a fraction do not at all mean that it is the same number of zeros in the decimal. Example, Into a decimal. =0.0515 (Here, the number of zeros in the denominator of the fraction is not the same as those in the decimal) In the case of mixed fractions, the whole number becomes the first part of the decimal, before the decimal point and the common fraction takes the part after the decimal point. For example, Into a decimal=4.15. The decimal 6.0013 into a common fraction= There also are fractions whose denominators are not the power of 10. In converting such fractions to decimals, it is important to first make the denominator a power of 10. For in the case of , the number to find is one which if multiplied by 25 will give us a power 10 denominator. This number is 4, and because anything done to the denominator should equally happen to the numerator, 4 is multiplied by both the denominator and numerator to come up with; which then is 0.24. When looking at various units of measurement such as length, area and volume, the important aspect to remember is that they have different units; which is what places them apart. Length is measures in units, area in square units and volume in cubic units; this is because length is one dimensional, area two dimensional and volume three dimensional. These units could be meters, centimeters, inches or feet. For instance, in measuring the length of a rod or stick, only one area of the stick is needed, so the measurement occurs along the stick in question. In this case therefore, the units for length will be in units (one dimensional). In the case of calculating the area of the floor of a classroom, two dimensions of the floor are needed; the length and width, in order to come up with square units of the measured floor. As for the volume of a squared room, to find out the volume of the room, one will need the length, width and height; and the resultant solution will be in cubic units. For example, calculate the perimeter of a yard, with all of its sides being 24, 38, 42, and 32. In this case, we are seeking to find the length of this yard; which will then be 136’, upon addition because it is one dimensional. In calculating the area of a bedroom floor measuring 36’ length and 53’ width, the area can be found by multiplying the units of length and width, which is equal to 1908 sq. units. As for the volume of a cylindrical school tank, with a base area of 260 sq. units and a height of 16 units, the volume can be calculated by multiplying the base area with the height, to come up with 4160 cubic units. Two lines are said to be perpendicular if they meet at right angles (90degrees). It is also possible for a line to be perpendicular to a plane if it is passing through the plane at an angle of 90 degrees (right angle). See the illustration below, Parallel lines on the other hand are those lines that move in the same direction, they never meet and are always the same distance apart. See the illustration below, An exponent in synonymous to power, which can be illustrated in the manner: xr. This is then referred to as x raised to the power of r or x to power r. A collection of objects or numbers is referred to as set. Sets are represented by the use of set brackets {}. For example, 2,5,6,4 are objects which when put together are referred to as set. {2, 5, 6, 4}, and in this case finite set. If the set goes on and on and is indicated by ellipses, it is called an infinite set (Bagaria, 2008). For example, {2, 5, 6, 4 …} Mathematics is a very important discipline in enabling the understanding of today’s social issues that are often presented in quantity measures. The presence of sets, power, numbers and other forms of arithmetic is a clear indication of how math has experienced growth. It is therefore crucial that one understands these practical concepts so that our social issues are tackled appropriately and decisions are made in a proper manner. Mathematics also gets us empowered as citizens and consumers, making the world a better place. References Bagaria, J. (2008). Set Theory in the Princeton Companion to Mathematics. Princeton: Princeton University Press. Lavine, S. (1994). Understanding the Infinite. Cambridge, M. A: Havard University Press. Martin, G. (1970). Mathematical Circus. New York: Penguin Publishers. Rouseball, W. (2010). History of Mathematics. New York: Dover Publications, Inc. Stapel, E. (2014). Introduction to Binary Numbers. Chicago: Max Press. Victor, J., & Addison, W. (2008). A History of Mathematics: An Introduction (3rd ed.). New York: Princeton University Press. Read More