Presentation on theme: "Common mistakes about mathematics and use of mathematics in everyday life By : Dr. Nitin Oke."— Presentation transcript:
Common mistakes about mathematics and use of mathematics in everyday life By : Dr. Nitin Oke
Our own feelings - - - ! As a student or teacher of mathematics many a times we feel that why to teach problems like – – A tank is filled in 3 hr by a tab and empties in 5 hours then if both tabs are open in how much time tank will be filled? – Instead of calculating this time close the other tab why to keep it open?
Our own feelings - - - ! As a student or teacher of mathematics many a times, we feel that; why to teach problems like – – A work is done in ten days by one worker if five workers are doing the same job the work will be done in how many days? – How many of us really think that after increasing number of workers the work will be done with same speed?
Our own feelings - - - ! As a student or teacher of mathematics many a times, we feel that; why to teach problems like – – A table and a four chairs cost 2000 Rs and two tables and four chairs will cost 3000 then cost of a table is ? – Just imagine such conversation at a shop when you wish to buy a table and chair. You will decide to go to other shop immidiatly.
Our own feelings - - - ! As a student or teacher of mathematics many a times, we feel that; why to teach problems like – – Sum of my age and my father’s age is 60 years and my fathers age is double that of my age then my age is ? – Just imagine such conversation when you asked age of your student and he answers like this.
Our own feelings - - - ! As a student or teacher of mathematics many a times, we feel that; why to teach problems like – – The last digit of is ? – At this moment we start thinking is it really going to make any difference to my life?
Status of Mathematics is Even if we call mathematics as mother of all sciences it itself is NOT science. Well the reason is it never tries to revel the laws behind the facts in nature on the other hand it provides the language to do so, it provides methods to do so in short mathematics can live without science but science can not.
What Mathematics is? Well it is not just study of numbers. Neither it is study of figures. Mathematics; for science is –m–method of proof : Logic, a statement to prove, an implication to prove, note the difference between statement and its converse –l–language of expression : F = m.a, a = (v – u)/t or F = d(P)/dt or a = dv/dt
In short Mathematics is not science itself, so we can not expect to have direct applications of mathematics. This is something like you can not expect; to travel with a can of a 20 liter of petrol, but you can travel by a car using this petrol. So now mathematics turns out a process to train human brain –t–to think –t–to relate –t–to predict.
Some technical mistakes during our teaching or learning During very early school days the process of subtraction is carried by considering “ carry” and then we use to return with thanks this is not scientific.
Concept of rules of division These are not hypothesis these are results so need to have proof. You only need place values for this for example A number is divisible by 3 if sum of all digits is divisible by 3 let the number be abc ( actually it can be ( a 1 a 2 a 3 a 4 ----a n ) so abc = 100a + 10b +c = 99a +9b + a + b + c 3 divides 99a and 9b under any case hence if 3 divides a + b + c then will divide abc and hence the result.
Concept of rules of division These are not hypothesis these are results so need to have proof. You only need place values for this for example A number is divisible by 11 if sum of all digits at even place and sum of all digits at odd place differ by a number divisible by 11 let the number be abcd ( actually it can be ( a 1 a 2 a 3 a 4 ----a n ) so abcd = 1000a + 100b + 10c + d = 1001a - a + 99b+ b + 11c – c + d Remaining part you can get on your own
Euclidian geometry most easy to understand most difficult to explain Concept of point – segment – any figure seen ( ?) as set of points. A for apple why not elephant (?) Future – Nature - ______ Charges of travel a = b ------ 1 = 2
Rational – irrational and real number 2.34555535353467282543846252673748589 5963374364464647484888888888888888888 8888888888888888888888888888888888888 8888888888888888888888866455555555555 5555555555555555555555555555555555555 5555512345678901234567890123456789012 3456789012345678901234567890123456789 0123456789012345678901234567890123456 7890123456789012345678901234567890122
You can be confirm that number is rational if it is expressed in form of –f–fraction of two integers ( with nonzero denominator) –T–Terminating or recurring decimal expansion If the number is not in form of fraction and decimal expansion is there and there and there then because of finite life span we are not in position to tell whether number is rational or not Be careful about difference in surd and or e
Difference between countable and uncountable infinity Concept of infinity is very difficult ( not possible) to explain. Is it not really difficult to explain that you remove half the objects and remaining number is same as before. Please note that
Trigonometry We define trigonometric ratio with the help of triangle but when it comes to sin (0 o ) or cos(0 o ) (can’t even think of cos(180 o ))then it is meaningless by right angle triangle. You need other approach, for the same, as polar co ordinate system and Cartesian system.
We define trigonometric ratio with the help of polar co ordinate system and Cartesian system cos(polar ) = sin(polar ) =