tag:blogger.com,1999:blog-49851903209940402092018-03-05T19:24:07.801-08:00Science and MathematicsOur Motto is Practice ..!Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comBlogger27125tag:blogger.com,1999:blog-4985190320994040209.post-32341677328510782852015-11-06T00:52:00.001-08:002015-11-08T09:36:28.589-08:00How to use mathematics while playing snooker (For beginners)Maths is used in almost every sports. But to say that snooker is a very mathematical game, would be an understatement. For beginners, if you guys can come to grip with a few rudimentary mathematical principles, you can curtail hard work of many years down to merely a few months.<br /><br /><b>Cue-Ball Maths</b><br /><br />For a moment consider your 3-dimensional cue-ball to be a 2-dimensional sphere. While making a shot assure that the radius of this sphere is the point from where your start marshaling your every shot. If you want to make a '<b>stun</b>' shot you will be required to strike the cue-ball just below the radius of the sphere. If you want to hit a '<b>screw</b>' shot you should hit the sphere near the lower circumference of the sphere. Finally for a '<b>follow</b>' shot you should aim at the upper circumference of the sphere. For beginners, you guys can use a dotted cue-ball manufactured specifically for this purpose.<br /><br /><b>Bank Shots Maths</b><br /><br />Have you ever seen a professional snooker player aim his forward before making a bank shot. Any guesses why he does this? Well this is where mathematics plays its role. When you are learning bank shots try to study the angles at work very closely. You can use a piece of thread to give you a rough idea and enable you to perfect the shot. 2-rail bank shots are easily to construct so you can start with them. Later on, you can move to 3-rail bank shots.<br /><br /><b>How Should I Approach A Shot When I A Being Snookered</b><br /><br />The rule for these shots is opposite to bank shot. Contrary to bank shots, 3-rail snookered shots are actually easier to get out of as compared to 2-rail snookered shots. Mathematics applies here as well. Since 3-rail shots actually end up giving you a smaller angle to work with (after hitting the second rail), you can easily construct them. So when ever you are trying to make a snookered shot, try to find a 3-railed shot to improve your chances.<br /><br /><b>Probability</b><br /><br />Remember this mathematical principle i.e probability. No matter what kind of shot you are playing, you should always keep probability in your mind. If you are playing a safe shot, consider whether it is probable that your opponent will make it.<br /><br /><b>Addition</b><br /><br />You should have the requisite mathematical acumen to understand what will be the added up result of your current break. Such proactive addition will save you from the hassle of trying to make a hard shot. If you can win a frame by making only smaller numbers (say brown and blue), you should not try for larger numbers then.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-8080412983996098612014-06-14T07:08:00.000-07:002014-06-14T07:08:37.688-07:00Top 5 places to do your mathematical questions<div class="MsoNormal">We all have our own ways of studying mathematics. Some of us are distracted while we are surrounded by people, while to others it makes no difference. Some of us do mathematics while listening to music, while others simply cannot concentrate if music is on. Generally the following five places are suitable for doing mathematics in different scenarios.</div><div class="MsoNormal"><br /></div><div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]-->1.<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span><b>Library</b></div><div class="MsoNormal" style="margin-left: .25in;">Your college or university library can be a suitable place for doing your math-questions, especially for those individuals who prefer a silent environment to concentrate.</div><div class="MsoNormal" style="margin-left: .25in;"><u>Scenario </u>Library can be utilized for doing mathematics immediately after your class to revise what you are taught in the class. This is the best timing to revise what you were taught in the class since most part of the lecture is still fresh in your mind.</div><div class="MsoNormal" style="margin-left: .25in;"><br /></div><div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]-->2.<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span><b>Parks</b></div><div class="MsoNormal" style="margin-left: .25in;">Parks can be a good place to do math problems especially if you want to refresh your mind with the oxygen-rich environment of the park.</div><div class="MsoNormal" style="margin-left: .25in;"><u>Scenario </u>It is scientifically proven that studying at a novel place increases your retaining power, therefore if you are faced with some novel mathematical problems, you can always complete them in a park. While revising later on, your mind will co-relate such problems with the park you visited and you can recall such problems (or formulas) easily.</div><div class="MsoNormal" style="margin-left: .25in;"><br /></div><div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]-->3.<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span><b>Friend’s House</b></div><div class="MsoNormal" style="margin-left: .25in;">You can do mathematics at a friend’s house on a weekend and revise the entire week’s problems.</div><div class="MsoNormal" style="margin-left: .25in;"><u>Scenario </u>Friend’s home is most suitable for such math problems that require combined-study. You can ask your friend the problems that you were facing during the week and in turn he/she can ask you.</div><div class="MsoNormal" style="margin-left: .25in;"><br /></div><div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]-->4.<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span><b>Hostel</b></div><div class="MsoNormal" style="margin-left: .25in;">You can do mathematics at a hostel most preferably near the examinations. This will enable you to avoid the distractions that you were facing while studying at home.</div><div class="MsoNormal" style="margin-left: .25in;"><u>Scenario </u>Here it is worth noting that the practice of going to hostel for preparation should actually enable you to avoid distractions. If you are still distracted in some way, you preparation may not be effective.</div><div class="MsoNormal" style="margin-left: .25in;"><br /></div><div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;"><!--[if !supportLists]-->5.<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span><b>Relative’s House</b></div><div class="MsoNormal" style="margin-left: .25in;">It can help you to revise the most boring topics of mathematics. It might seem to be an inoperative way but you will realize that it is a helpful way of doing mathematics. While visiting a relative you can reduce the boredom of a topic by blending it with the excitement of meeting your relatives (eg. your grandma). And if your grandma can help you with maths, this can have even a more positive impact (since it will also bring the novelty-clause into play).</div><div class="MsoNormal" style="margin-left: .25in;"><u>Scenario </u>The topics that you consider easy are many-a-times neglected because you feel bored while revising them. In such cases, you interest can be developed if you take such topics to a relative’s house and revise them casually (rather than not revising them at all). <b>Remember: Our motto is revision.<o:p></o:p></b></div><div class="MsoNormal" style="margin-left: .25in;"><b><br /></b></div><div class="MsoNormal" style="margin-left: .25in;">Notes:</div><div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo2; text-indent: -.25in;"><!--[if !supportLists]-->a)<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span>This list is not exhaustive.</div><br /><div class="MsoListParagraphCxSpLast" style="mso-list: l1 level1 lfo2; text-indent: -.25in;"><!--[if !supportLists]-->b)<span style="font-size: 7pt;"> </span><!--[endif]--><span dir="LTR"></span>There is no priority in selecting a place. Moreover, if you can do mathematics more effectively at your own house. Stay there! Our strategy should be to pass, not to jump from place to place.</div>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-3105672019505078622014-06-04T06:41:00.001-07:002014-06-04T06:41:34.487-07:00Reasons for the increase in the use of Mathematical BenchmarkingMathematical Bench-marking is becoming prevalent because of the increment in the adoption of International Accounting Standards by almost every country. Company's records are becoming more mathematically comparable and thus bench-marked by many others.<br /><br /><br />Another reason behind bench-marking is the increase in the use of International Auditing Standards. The entity's records are becoming much more transparent and thus more reliable.<br /><br /><br />Another reason behind the increase in mathematical bench-marking is the increase in the number of global organisations. These organisations undertake high amount of research work which is mostly bench-marked by number of niche firms which cannot undertake high research costs themselves.<br /><br /><br />Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-35379627340453014402013-08-25T00:25:00.003-07:002013-08-25T00:25:32.804-07:00Why do we sometimes fail to answer the most easy mathematical questions in exam scenarios?Its part of our psychology that while we are preparing for your exams we tend to focus on the complex portion more. And even if the easy portion has a significant weightage in the marks-distribution gird, we leave it to the end.<br />I am not saying that its a bad strategy, but the dilemma here is that, sometimes when we leave the easier portion for the end, we end up getting an incomplete understanding of it. This leads the eventual marks-loss.<br />Here is what we should do:<br /><i><b><br /></b></i><br /><ol><li><i><b>Never place low importance on the easier portion. Not matter how easy a topic is, try to go through it atleast once. </b></i></li><li><i><b>Lack of appropriate oversight is another cause of score-loss. While covering the easier portion, keep your mind open. Try to understand it thoroughly (since you might not have enough time to revise this particular portion).</b></i></li><li><i><b>When your teacher is teaching you a portion of your exams which you feel is easy. Attend those classes. From my personal experience I am telling you that such an overlooked portion will take its revenge if you do not understand it appropriately.</b></i></li><li><i><b>Leave sufficient time (in the end) for the easy-to-cover questions. One day may not be enough. Place atleast four to five days for such portion. Try to attempt such questions, instead of just reading through your notes.</b></i></li></ol><br /><br /><br />Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-81438739100496221152013-07-02T13:48:00.002-07:002013-07-02T13:48:32.776-07:00What if Mathematics is not my field of expertise?Many of us do not pursue mathematics as our field of expertise. For example, a doctor or a chartered accountant is not fully acquaint with the jargon of mathematicians. But still we require a general understanding of mathematics to be competitive.<br /><br />For example, if you are pursuing a chartered accountancy job and your recruiter asks you a simple mathematics question, he expects to answer it. Despite the fact that maths is not your A-one line of expertise, still you have to have some sort of general understanding of the subject. This will help you not only in your interviews but also in your general life as well.<br /><br />Now the question arises, what should i do if maths in not my field of expertise? How can i manage to get a grip of the subject without investing my hours into it? Well here are a few tips that can be handy:<br /><br />1. First of all keep in mind that no one expects you to be fully acquaint with every niche detail of mathematics (since it is requires entire different set of skills as compared to your field), so you should not worry about the details that much.<br /><br />2. Try to practice simple mathematical problems. Keep your self in practice. If you are a mom, you might already have had much practice while helping your kids with their mathematics home-tasks. But if you are not, try to spare some time helping out your younger brother or sister with their problems. This will unconsciously keep you in practice as well.<br /><br />3. Make a two to three pager short notes of mathematical formulas. They will definitely serve as 'food for thought'. Revise them in your leisure time. Do not consider this activity as time-wasting because revision will always keep you in-touch with these easy-to-forget formulas.<br /><br />4. Practice will give you an alert-mindedness approach while appearing in an interview which does not require a top-notch mathematical experience. Your interview never expects you to be a-one on every aspect on maths but at least you should know the basics of maths. <i><b>So practice as few questions daily at least for seven days before your interview.</b></i>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-56654466305781152442013-04-18T14:10:00.001-07:002013-04-18T14:10:39.828-07:00Understanding Debit and Credit in Mathematical MannerA new accounting student easily gets confused when should an asset be credited and when should a liability be credited. Moreover, students are often faced with a question as to when a debit means 'increase' and when does it mean 'decrease'.<br /><br />If we memorize the following table we will find it very much easy to understand when does a debited item be increased and when should it be decreased?<br /><br /><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"> <tbody><tr style="height: 32.5pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"> <td style="border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Assets<o:p></o:p></div></td> <td style="border-left: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Debit<o:p></o:p></div></td> <td style="border-left: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Plus<o:p></o:p></div></td> </tr><tr style="height: 34.0pt; mso-yfti-irow: 1;"> <td style="border-top: none; border: solid black 1.0pt; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Credit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Minus<o:p></o:p></div></td> </tr><tr style="height: 32.5pt; mso-yfti-irow: 2;"> <td style="border-top: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Liabilities<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Debit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Minus<o:p></o:p></div></td> </tr><tr style="height: 32.5pt; mso-yfti-irow: 3;"> <td style="border-top: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Credit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Plus<o:p></o:p></div></td> </tr><tr style="height: 34.0pt; mso-yfti-irow: 4;"> <td style="border-top: none; border: solid black 1.0pt; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Income<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Debit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Minus<o:p></o:p></div></td> </tr><tr style="height: 32.5pt; mso-yfti-irow: 5;"> <td style="border-top: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Credit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Plus<o:p></o:p></div></td> </tr><tr style="height: 32.5pt; mso-yfti-irow: 6;"> <td style="border-top: none; border: solid black 1.0pt; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Expenses<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Debit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 32.5pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Plus<o:p></o:p></div></td> </tr><tr style="height: 34.0pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes;"> <td style="border-top: none; border: solid black 1.0pt; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Credit<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 34.0pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 80.1pt;" valign="top" width="107"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;">Minus<o:p></o:p></div></td> </tr></tbody></table>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-60412774402091194202013-04-17T16:10:00.002-07:002013-04-17T16:10:40.610-07:00The Tree Diagram Way of Learning MathematicsWe all know that many mathematical formulas are derivatives of other mathematical formulas. By substitution and equating two expressions mathematicians have achieved numerous mathematical formulas. This creates a situation of difficulty for a young maths student. This is particularly the case with trigonometry. In trigonometry, the primary trigonometric functions are sine and cosine. And all the rest is just derivation.<br /><br />Now if we can draw a tree diagram of trigonometric formulas on a wide page. We will assign the primary branches of the tree diagram to sine and cosine. Then we will derive the ratio identities (reciprocal functions) in the secondary branches. And the most complex formulas will be placed in the tertiary branches.<br /><br />This will enable a student to understand the roots of every mathematical formula. This will make it easy to remember.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-48003001166370576392012-07-20T10:49:00.002-07:002012-09-23T03:50:48.851-07:00Doing Mathematics in the MorningThrough out our student-life we are faced with this dilemma in the last weeks before your examinations that whether we should prepare early in the morning or would late night work be a better option?<br /><br />Here are a few points that should help you make a wiser decision.<br /><br />1. Never go against your routine. If, in your routine days, you study in daylight (perhaps after your morning classes), then it will not be a better idea to go against your routine and work at night. Changes in routine may disrupt your daily working. Avoid it.<br /><br />2. Mathematics requires concentration. When you start your maths practice you may be able to concentrate for 3-4 hours. But after that your concentration starts to falter. So if you choose to study in the morning you can always work for a couple of hours in the morning, take some time off and then do another mathematical session for a couple of hours in early afternoon. Working at night does not give you this advantage.<br /><br />3. Doing mathematics in the morning does not mean sleeping over your books. To make this a healthy activity make sure that you have had a good night sleep. And be active once you are out of your bed. This will ensure that you gain the best of your morning-type study or else you will still be the same as night owls.<br /><br />4. Always remember to have a good breakfast before you sit to do your mathematical exercises. Breakfast will give you that additional boast of energy your dearly require to concentrate efficiently on your studies.<br /><br />5. If you are doing mathematics in two sessions, try to tackle the most difficult questions in the morning session when your mind is fresh. Leave the relatively easier problems for the afternoon session.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-31369607899971237222012-04-28T12:04:00.000-07:002012-05-01T04:21:43.194-07:00Choosing The Right Mathematics Book To Start Your LearningChoosing the appropriate mathematical book to begin your learning is very important. In other words, there should be a binary relationship between your mind and your mathematical material to enable you to achieve the desired objectives. Here are a few basic tips to help you choose the appropriate mathematical study books.<br /><br /><br /><ul><li>Always chose those maths books that encourage a progressive nature of learning. In other words, there should exist an arithmetic progression of difficulty through out the book. If an author of a mathematical book feeds you with the most difficult questions right at the start of the topic and never touches the simpler ones, don't go for such a book. This book may be intended for experts and not for beginners. Choose the books that are directed towards the beginners. Ask the shop keeper. He can guide you.</li><li><br /></li><li>Choose the mathematical book that has an answers book available as well. You can always refer to those available answers in the event of any difficulty. Even the most brilliant students require some assistance in the beginning and the confidence of having the mathematical solution available at hand can definitely be helpful.</li><li><br /></li><li>The next point that is very important while choosing the best mathematical book for learning is that you should exercise it completely and don't switch to other authors or editions before you are completely acquaint with the book you have already chosen. Students can get more than one source of reference if they consult different mathematical books simultaneously but such an approach can hurt an in-depth study if the students tend to choose-out the easier parts from each of the books.</li></ul>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-14852811953265383612012-04-25T18:34:00.000-07:002012-09-23T03:54:54.928-07:00A Tale About Geometric ProgressionGeometric progression is a mathematical concept wherein a series of numbers are arranged in a multiplicative order. Each next number of a geometric progression is attained by multiplying the previous number by a common number. This common number remains the same through out the geometric progression.<br /><br />But there was a time when geometric progression was not well-known to the common men. In those days there used to be a filthy rich King. The King used to bless his slaves with a lot of money when ever there was an event that made him happy. He was a man of his word.<br /><br />One day he had a mathematical query and he announced that he will give anything to anyone who answers to his maths problem. His announcement was much enticing to all, since everyone knew he is a man of his word.<br /><br />In those days, there was a young boy who lived in one of the villages governed by the King. He made his way to the King's Court and asked the King that if he is able to answer the King's query will the King give him one penny on the same day and keep on doubling it afterwards.<br /><br />The King was quite astonished to hear this. For he thought that one penny is a very humble amount and even if it was doubled it would mean two pennies tomorrow and four pennies the day after that. The King with all his wealth failed to understand a very simple mathematical concept that if you keep progressing an amount...very soon it will be quite unmanageable. The King quickly agreed to the young boy's request.<br /><br />The boy solved the query and took the one penny home. He knew his maths will very soon make him very rich. He came back tomorrow and took two instead of one and went away. He came back again...took four and went away. He kept on coming back for double the amount he got previously. After a few months the King had to regret what he had agreed upon. The amount became unmanageable even for the wealthy King. The boy's mathematical trick had worked wonders.<br /><br />The principle of Geometric Progression is a tricky one. For the young students this mathematical concept can be easily remembered by keeping this King's story in mind.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-21141514401285996212012-04-16T18:41:00.000-07:002012-10-03T18:42:15.476-07:00Top Books on Algebra<br />Even though this list of top books on algebra is constraint by the requirements of students. A student of 5th standard may have a different ideal book than a professional trainee preparing for a more competitive examination. Keeping these restrictions aside - the following list of the top books on algebra can provide a variety of questions which can be helpful to have a better grasp on the subject of algebra.<br /><br />1.<br /><br />Practical Algebra: A Self-Teaching Guide<br /><br />One among the best self-teaching guides written by Peter H. Selby. Is you have lost your touch with algebra for a couple of years. Its time to go through this book. Based the positive reviews that i have traced over the internet..This book is a must for a beginner in the field of algebra.<br /><br /><br />2.<br /><br />Maran Illustrated Effortless Algebra<br /><br />This book is a production of maranGraphics Development Group. This book adopts a progressive approach towards the understanding of algebra and covers the requirements of many students. The book starts with simple concepts and gains momentum towards more detailed complex mathematical problems.<br /><br />3.<br /><br />Elementary Algebra<br /><br />harles P. "Pat" McKeague has a M.S degree in mathematics. He is a member of MAA and has written over a dozen books. This book offers the readers with basic algebraic concepts and explains the relevance of what you are learning.<br /><br /><br />4.<br /><br />Algebra and Geometry<br /><br />This book is written by Alan F. Beardon. This tries to explain the various linkages between numerous mathematical aspects. The understanding enhances gradually. To top it off, there are many exercises provided in this book, which can help out the students.<br /><br /><br />Despite the above mentioned books on algebra, it is very important to get some advice from your teachers before you start studying one. Because it never helpful if you keep on tackling the harder books before going through the easier ones. The smarter approach should be to develop an overall understanding of algebra. Remember through out your life, your understanding of algebra will always remain at the pre-algebra stage. Such is the diversity of this discipline of mathematics.<br /><div><br /></div>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-69036192331755767262012-04-10T14:23:00.000-07:002012-09-23T04:00:30.559-07:00How To Build An Interest in MathematicsMathematics is a demon for most of our young students and no matter how interesting it may seem to the experts, to newbies its generally a subject they tend to avoid.<br />The most important reason that causes the disinterest in mathematics is that students never consider it as a hobby. Their academic deadlines about their mathematical examinations often put stress on them and while studying mathematics they are generally inclined to unwillingly engulf this subject rather than developing an understanding of the various mathematical concepts. This situation requires three basic procedures from a teacher's point of view:<br /><br /><ol><li>the teacher should recognize the signals of the student's disinterest in mathematics and try to reconcile the situation informally, </li><li>he/she should give the student some margin of comfort. Relaxation in a test will generate confidence within the student, and,</li><li>try to give the students some mathematical tasks that are not apparently academic oriented. For example 2 + 3 = 5 is on way of teaching ( academic oriented way) mathematics, whereas 2 apples + 3 apples = 5 apples ( less formal way) of teaching mathematics. The second approach is a bit more non-formal and thus more effective.</li></ol><br />One more factor that often hampers even the most professionally trained mathematics teachers to perform well, is the distinction between the "attitude towards mathematics" and "aptitude for mathematics".<br />Teachers often perceive a student's lower grades in mathematics as his lack of "aptitude for mathematics". They never consider that aptitude always comes after attitude. In other words, if the teachers try to build a student's "attitude towards mathematics", the aptitude will surely rise with it. But if they mark a student solely on the basis of his apparent grades in mathematics and consider that he will never get better, the scenario is only gonna get worse.<br />The requirement under such cases is that the teacher should encourage the students to develop a more serious attitude towards mathematics. If a student seriously practices mathematics for 3 to 4 hours daily, his/her aptitude for mathematics will surely increase.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-88687347034102708942012-03-15T09:52:00.002-07:002012-03-15T15:15:07.054-07:00How To Tackle Mathematics By its Horns?<span style="font-family: inherit;">There was a time in my childhood when I used to hate mathematics. I hated mathematics more that Hitler hated Jews (never intending to be racist in any manner). I was so biased against maths that I used to deliberately forget maths books at home daily. I thought maths was unworthy of my concentration, so I never concentrated on it. But maths always took its revenge. Maths syllabus and course used to hide unnoticed all semester long. But at the very end of the semester it used to appear like a demon.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">I had all sorts of mathematical problems. When it came to tables I always used my fingers to compute the results but my lack of belief always handed me a wrong answer. Even when I knew the right answer I was never encouraged to speak out in the classroom. I would just let the teacher tell the answer and then I would whisper to my friend saying "I knew the answer".</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">When I aimed at learning algebra I couldn't dissect it from the other parts of maths such as algorithm and trigonometry. When I used to give time to trigonometry, I also found algebraic calculations intermingling with trigonometry. I was like when I intended to diagnose one branch of mathematics the other parts always pinched me. I required me to device a good strategy to cure my illness relating to maths.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">First of all I tried to understand what was it that was annoying me about maths in general. And I soon understood that my core concern was getting to understand various disciplines of mathematics (like calculus, arithmetic, algebra, geometry, trigonometry etc) together. This caused many difficulties and frustration. Normally I would start with a trigonometry question and when that question posed a concept of algebra I would try to consult algebraic expressions and leave that trigonometry question on its fate.This caused a wastage of time, and after a while I would lose my concentration and leave studying mathematics.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Then I changed my style. I started with the simplest questions of algebra. The reason behind starting with algebra was that algebra is basic branch of mathematics. It has many implications on other disciplines like trigonometry and calculus. So I narrow down 15 to 20 basic algebraic questions and tried to solve them on daily basis. I made it my routine. No matter even if I had to miss the other homework, doing 15 - 20 basic algebraic questions became a part of my routine. After a few weeks the very first thing I noticed was that I was not falling asleep in the maths class any more.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">The next step for me was the revision session. I never knew the importance of the phrase " Practice makes a woman perfect " until I actually practised and re-practised these algebraic questions. It was the revision sessions that I started to understand the logic behind various algebraic expressions. Before now I always used to memorize the various formulas. But now that I new the logic behind it, I was quite comfortable with trying more complex mathematical questions. I could see my confidence developing.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">But the best help on mathematics came from my friends, colleagues and tutors. When I started learning maths, quite often I was faced with many problems that frustrated me a lot. I could understand the point even after looking at the solution. And here is where my initiative oriented personality played its part. I was always asking from help. Many of my mathematical problems were straightened out by my friends. When I used to describe my problems to others I used to gain their take on it and this also helped me to express what I thought about those mathematical situations.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">When I kept on moving forward I learned yet another beautiful trick to solve various equations. Previously I thought of mathematics as a passive activity. But now as I was gaining exposure I understood that there are many ways to phrase an equation. I rephrased many equations and develope</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Now my transition to the other disciplines of mathematics was an easy one. Next I started trigonometry. I did the same thing here as well. I started with the basic and the most easy questions and attempted them twice (sometimes trice as well).</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">I never used an particular book for learning mathematics. I used various notes and other explanatory material written by many authors. Had I remained content with only one book, I would have found it hard to have a complete grasp of the subject. Different authors have different view points and when you consult various books it widens your mind. So I consulted various books on mathematics.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Gradually I developed another fruitful habit. Previously I was very curious on whether or not I am doing the question rightly. So I used to check the answer when I was mid-way through the solution. This was not a productive thing to do because it reduced my mental creativity, and when ever I was faced with a new type of question, I was unable to solve it. But now I changed this habit. I used to solve the question completely before referring to the answer. Even if I was unable to answer the question rightly, still I used to wait until I was finished. I noticed that almost every time I was just a couple of steps in the wrong direction. And while repeating the question I used to get it right. This helped in developing my confidence as well.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">But the most beneficial activity that helped me the most while learning mathematics was consulting my friends, colleagues and tutors. Previously when I was faced with a problem it made be gravely frustration. I couldn't understand the point even when I used to consult the solution. And here is where my initiative oriented personality played its part. When I used to ask a mathematical query from a colleague, this helped me understand his/her point of view as well. It also enabled me to address my mathematical problems in a better way. Now I could answer others in a more concrete and mathematical way. Plus my increasing grasp on the subject enable me to include various suggestions and postulates in my sentences.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">An even more beautiful advantage that I gained with the passage of time was the ability to solve various equations in different ways. Now I could rephrase my equations and apply different formulas to derive the same solution. I learned a very key fact that almost all the mathematical problems that involve variables can be solved by using graphs. This simple fact was very effective to understand different relationships and enabled me to exploit different paths on theoretical mathematics. Previously I thought that maths is a boring activity where only numbers are involved. But now I understood that maths was not at all a passive activity. Solving variables by graphs can be a very interesting and thought provoking activity. Such graphs could be used in every you-name-it disciplines of our daily business routines. If the appropriate data is graphically represents on a piece of paper, we can develop budgets, build productive forecasts and undertake surveys.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">But I did all this slowly and gradually. I never intended to read a complete book in one go. I started chapter-wise. Sometimes even topic-wise or page-wise. The most important fact that I always kept in my mind was that I never intended to jump forward and leave a point behind. I never step ahead until my previous queries were properly addressed.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">I will leave you all with a couple of mathematical tricks that might help someone (hopefully):</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Trick 1:</span><br /><span style="font-family: inherit;">When I was young, I couldn't make up when to use sin, cos and tan while solving right-angled triangles. I used to mix it all up. Then a friend of mine taught me this following trick.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">He taught me this sentence: "Some people have curly brown hair. They prove beauty."</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">I did know what it meant and how it will eventually help me. But it was a great idea. Now let me teach you how it was helpful.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">He used the beginning alphabet of each of the nine words used in the above sentence ( namely S, P, H, C, B, H, T, P, B) and produced the formulas of sin, cos and tan. Now all I had to do was to remember the sentence 'Some people have curly brown hair. They prove beauty', and the formulas became much much each to recall.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Sin = Perp./Hyp (Some People Have)</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Cos = Base/Hyp (Curly Brown Hair)</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Tan = Perp./Base (They Prove Beauty)</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Use can obviously see that the bold alphabets are the initial alphabets of the sentence that I used. If you are teacher or a mother you can teach this simple trick to your students or children to memorise this basic trigonometry formulas.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Trick 2:</span><br /><span style="font-family: inherit;">This trick is a bit of a smartness check trick. As a new teacher you will always be wanting to get some knowledge about the students of the class so that you can pinpoint which student requires more efforts and which student can be an asset of the future.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">It is a simple trick but it checks the alertness of many individuals. The beauty of this trick is that you can also use it during flirting. It is a harmless little trick but it can attract an audience that is interest in the subject of mathematics. As a new teacher, you must try this trick on the very first day of the new session. No matter whether the class is of sixth graders or of a sufficient acquaint individuals. This can be an impression building trick.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Here is how it goes:</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Imagine someone using simple mathematics to make you feel as if he/she is playing some kind of a magic with you. Just ask someone to imagine a number. Set the range from 1-100 so that you can easily do mental calculations. Lets assume that the person imagined 25 as his/her secret number. Now he/she is the only one that knows what the real number is. As far as you are concerned just let it be x. Then ask him/her to add and then subtract a few easy mathematical numbers into x.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Lets suppose you ask him to add 15 into his secret number and then subtract 10 from it. You will get as follows:</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">x + 15 - 10</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">= x + 5</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Now you can find out any calculations you want him to add or subtract.... The only digit you don't know is x.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Keep making his mind work over. Keep asking him to add and subtract numbers randomly. For example ask him to add 20 further and then add 5 more and then finally subtract 17.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">You will have the following resultant figure.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">x + 5 + 20 + 5 - 17</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">x + 13</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">After making him do these sort of calculations for about 4 to 5 times, you should never forget that the resultant figure is x + 13. The other person knows that the answer is 38 (25 + 13). But you only know that the answer is x + 13. Now here is the trick. Ask that person to subtract the original number he thought at the beginning (which for him would be 25 and for you would be x). When he subtracts that number now he and you have the same amount of information (i.e 13).</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">At this point almost all the average students will unconsciously subtract 25 (or for you x) from the resultant solution.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">When its done. Just ask them "Is you answer 13".</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">You will get some bizarre and questioning faces you have never seen before. You will get the exact attention you were dreaming off on the very first day at your new place.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Now at this point (as I give a full-stop to my pen) I will just want you to remember only one word when ever you think of mathematics. PRACTICE.</span>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-30018941096898772222012-03-11T13:21:00.003-07:002012-09-23T03:55:51.870-07:00How Do I Memorize Mathematical Formulas?<span style="font-family: inherit;">Mathematical Formulas are like linking pins that serve as the path routes of mathematics. Just like when you supposed to move from one city to another you require a map, so in case of mathematics when you work yourself from one step of a question to another, you require the help of mathematical formulas. These formulas are like the governing bodies of the subject of mathematics and are responsible for the web structure of mathematics.</span><br /><b><span style="font-family: inherit;">Such is the beauty of mathematical formulas, that if you can understand them and memorize them, your memory can replace scores of helping books and bulky mathematical solutions.</span></b><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">The following are a few basic techniques that can be used to memorize the governing bodies of mathematics, called the 'mathematical formulas'. There is no doubt in my mind that if you can following these steps, your grasp on the subject of maths will be enhanced.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;"><span style="font-size: large;">1.</span> Formulas should be written by hand instead of just going through them orally. Vast majority of the students just unconsciously overlook the easier formulas while solving a problem. They never give a reference to these formulas in the solutions and just consider that these easy formulas are nothing more than mere 'understood by all' trivial facts. But here lies a major problem. When a student keeps overlooking such formulas, he is unable to repeat them and thus with the inclusion of more and more complex formulas, he starts to forget the basic ones. This a major flaw in the learning curve of majority of the students. If we can just bear the extra efforts of a few seconds and make a reference to these formulas, by writing them besides our solutions, we can indeed benefit from it in the long run.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;"><span style="font-size: large;">2.</span> Student should design a time-table wherein they can include a formula revision session. Such a session can either be at the start of a fresh lecture or at the end of it. The perfect scenario will be to include these sessions both at the beginning of their mathematical practice and at the end of it as well. If you have just overlooked a previously learned maths formula, a revision session will ensure that you can memorize it again and again.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;"><span style="font-size: large;">3.</span> In mathematics, there are scores and scores of formulas for every discipline. For example algebra has many formulas and so does trigonometry. But for every discipline of mathematics there is a set of primary formulas and the rest of the complex formulas and sub-formulas are more or less derivatives of these basic formulas.</span><br /><span style="font-family: inherit;">And the basic mistake that most of the students make while preparing formulas is that they emphasize on every single formula separately. This puts a major stress on their memory, since there as many formulas in a particular discipline of mathematics. Assume the case of Trigonometry. If you try to learn every primary and tertiary (derived from primary) formula separately it will be a time consuming and attention diverting exercise.</span><br /><span style="font-family: inherit;">But there is a more effective technique to memorize these various formulas.</span><br /><span style="font-family: inherit;">Just try to learn the primary formulas and try to work out the tertiary formulas by using the primary (basic) formulas.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">The below example will help you understand the importance of just memorizing the basic formulas and just working out the more complex formulas by using these basic formulas.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Here is a formula .............. (a + b)^2 + (a - b) ^2 = 2 (a^2 + b^2)</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Now if you can memorize the two basic algebraic formulas of (a + b)^2 and (a - b)^ 2 you can easily work out the above mentioned formula, without wasting the extra energy of learning the third one as well.</span><br /><span style="font-family: inherit;">This requires practice - But remember our motto is practice. Nothing in maths can be achieved without PRACTICE.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;"><span style="font-size: large;">4.</span> Always pay attention to the mathematical symbols while learning a formula. Never overlook and make a mistake by using + instead of - or the other way round. If you get confused by the symbols used in two different formulas try to revise these formulas together and pay attention to the different symbols used in each of them. For example the difference between (a + b)^2 and (a - b)^2 is that in the first formula there is a +2ab and in the second formula there is -2ab.</span><br /><span style="font-family: inherit;">Always be attentive to such differences to avoid errors.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;"><span style="font-size: large;">5.</span> If you have any confusion regarding any two formulas, always practice them together. This will enable your mind to develop an understanding regarding their use.</span><br /><span style="font-family: inherit;">For example if you have a confusion regarding the formulas of the circumference, diameter and area of a circle, try to revise them together.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Circumference = 2∏r</span><br /><span style="font-family: inherit;">Area = ∏r^2</span><br /><span style="font-family: inherit;">Diameter = 2r</span>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-62762328483408033702012-02-29T11:54:00.000-08:002012-04-02T05:32:14.267-07:00How to Simplify the Roots and any NumberSolving the roots of any number can be a tough exercise especially when the number is a huge one. Here is a simple technique employed to solve the roots of any number easily.<br /><br />For cube roots of 1000, the following simple procedure should be followed:<br /><br />Factorize 1000 in the following manner.<br /><br /><br /><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr style="height: 29.25pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 29.25pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">2<o:p></o:p></div></td> <td style="border-bottom: solid windowtext 1.0pt; border: none; height: 29.25pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">1000<o:p></o:p></div></td> </tr><tr style="height: 27.65pt; mso-yfti-irow: 1;"> <td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 27.65pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">2<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border: none; height: 27.65pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">500<o:p></o:p></div></td> </tr><tr style="height: 29.25pt; mso-yfti-irow: 2;"> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 29.25pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">2<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border: none; height: 29.25pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">250<o:p></o:p></div></td> </tr><tr style="height: 27.65pt; mso-yfti-irow: 3;"> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 27.65pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">5<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border: none; height: 27.65pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">125<o:p></o:p></div></td> </tr><tr style="height: 29.25pt; mso-yfti-irow: 4;"> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 29.25pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">5<o:p></o:p></div></td> <td style="border-bottom: solid black 1.0pt; border: none; height: 29.25pt; mso-border-bottom-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-left-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">25<o:p></o:p></div></td> </tr><tr style="height: 29.25pt; mso-yfti-irow: 5;"> <td style="border-right: solid black 1.0pt; border: none; height: 29.25pt; mso-border-right-alt: solid black .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border: none; height: 29.25pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">5<o:p></o:p></div></td> </tr><tr style="height: 27.65pt; mso-yfti-irow: 6;"> <td style="border: none; height: 27.65pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border: none; height: 27.65pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> </tr><tr style="height: 30.9pt; mso-yfti-irow: 7; mso-yfti-lastrow: yes;"> <td style="border: none; height: 30.9pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> <td style="border: none; height: 30.9pt; padding: 0in 5.4pt 0in 5.4pt; width: 44.35pt;" valign="top" width="59"><div class="MsoNormal" style="margin-bottom: 0.0001pt;"><br /></div></td> </tr></tbody></table><br />You should ensure that each time you factorize 1000 with the lowest multiple of resultant in each step. For example if 500 is divisible by both 5 and 2, you should go for 2 which is the lowest multiple of 500.<br /><br />The second steps involves the listing of all the multiples of 1000 in ascending order in the following way:<br /><br />2,2,2,5,5,5<br /><br />Now rewrite the above numbers in their cubical forms as unders:<br /><br />2^3, 5^3<br /><br />Now simply cancel out the cubes and the product of the resultant would be the cubic under root of 1000 ie 5x2=10.<br /><br />Here it is worth nothing that while canceling out the cubes make sure that you only cancel out the cubes and let the remaining numbers as it is.<br />Another point worth remembering is that when you are calculating fourth roots of a number make sure that you following the similar procedure as summarized below.<br /><br />Firstly simplify the number by its lowest multiples.<br />Then arrange the multiples in their ascending order.<br />Then write them in their fourth root forms.<br />Then cancel out their fourth roots.<br />Then multiply the multiples after removing their fourth roots.<br />The result will give you the fourth roots of that number.<br /><br />You can practice this exercise to find out the roots of any number.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-38633742264571911472012-02-15T18:50:00.000-08:002012-03-15T19:30:42.229-07:00Choosing An Appropriate Mathematical Statistic For a Data<span style="font-family: inherit;">Mathematical Statistics are the instruments that aids it's users to make decisions by using mathematical data. A bar diagram is a simple example of a mathematical statistic that makes use of two sets of mathematical data (each on one axis), to generate interpret-able information for its audience.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Most of the mathematical statistics can have a similar visual format but however it is a very essential key to select an appropriate statistic to produce a true result. It is important to note that there is a fine distinction between a mathematical statistic that gives a true (free from overstated-ness or understated-ness) figure and a mathematical statistic that gives a desirable figure.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">To drive the point home, lets consider a simple mathematical data of the profits of 6 products as 2,50,50,45,55,100.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">Now a desirable mathematical statistic will consider the average of profits as 2+50+50+45+55+100/6.</span><br /><span style="font-family: inherit;">The result will be 50.333.</span><br /><span style="font-family: inherit;">But a true and a more appropriate mathematical statistic will eliminate the 2 extreme figures in the data i.e 2 and 100.</span><br /><span style="font-family: inherit;">Now the trimmed mathematical average of the profits will be 50+50+45+55/4 = 50. Thus avoiding an overstatement of 0.3333 of the profits.</span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">The appropriateness of a mathematical statistic is not limited only to it being unbiased. But it also considers other factors such as:</span><br /><span style="font-family: inherit;"><br /></span><br /><u><span style="font-family: inherit;">Size of the data</span></u><br /><u><span style="font-family: inherit;"><br /></span></u><br /><span style="font-family: inherit;">For a large sized data, bar diagrams can be appropriate mathematical statistics ensuring that the entire data is enclosed into the length of the paper.</span><br /><span style="font-family: inherit;"><br /></span><br /><u><span style="font-family: inherit;">Data containing a few abnormally deviated figures</span></u><br /><u><span style="font-family: inherit;"><br /></span></u><br /><span style="font-family: inherit;">For a mathematical data that contains a few skewed figures a scattered diagram can be an appropriate mathematical statistic.</span><br /><span style="font-family: inherit;"><br /></span><br /><u><span style="font-family: inherit;">Data Showing Relationships / Not Showing Relationships</span></u><br /><u><span style="font-family: inherit;"><br /></span></u><br /><span style="font-family: inherit;">For a mathematical data the represents a relationship, for example, a data of the birth-rates of the last 5 decades, such a mathematical statistic should be used that can be graphically plotted. </span><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">For the below table a bar mathematical statistic will be more appropriate.</span><br /><span style="font-family: inherit;"><br /></span><br /><br /><table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;"><tbody><tr style="height: 30.75pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;"> <td style="border: solid black 1.0pt; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">Decade<o:p></o:p></span></div></td> <td style="border-left: none; border: solid black 1.0pt; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-themecolor: text1; mso-border-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">Birth Rate (as compared to Death Rate)<o:p></o:p></span></div></td> </tr><tr style="height: 29.05pt; mso-yfti-irow: 1;"> <td style="border-top: none; border: solid black 1.0pt; height: 29.05pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">50s<o:p></o:p></span></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 29.05pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">1.1/3<o:p></o:p></span></div></td> </tr><tr style="height: 30.75pt; mso-yfti-irow: 2;"> <td style="border-top: none; border: solid black 1.0pt; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">60s<o:p></o:p></span></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">1.56/3<o:p></o:p></span></div></td> </tr><tr style="height: 29.05pt; mso-yfti-irow: 3;"> <td style="border-top: none; border: solid black 1.0pt; height: 29.05pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">70s<o:p></o:p></span></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 29.05pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">1.83/2.5<o:p></o:p></span></div></td> </tr><tr style="height: 30.75pt; mso-yfti-irow: 4;"> <td style="border-top: none; border: solid black 1.0pt; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">80s<o:p></o:p></span></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">2.1/2.5<o:p></o:p></span></div></td> </tr><tr style="height: 30.75pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes;"> <td style="border-top: none; border: solid black 1.0pt; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">90s<o:p></o:p></span></div></td> <td style="border-bottom: solid black 1.0pt; border-left: none; border-right: solid black 1.0pt; border-top: none; height: 30.75pt; mso-border-alt: solid black .5pt; mso-border-bottom-themecolor: text1; mso-border-left-alt: solid black .5pt; mso-border-left-themecolor: text1; mso-border-right-themecolor: text1; mso-border-themecolor: text1; mso-border-top-alt: solid black .5pt; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 82.7pt;" valign="top" width="110"> <div class="MsoNormal" style="margin-bottom: 0.0001pt;"><span style="font-family: inherit;">3.2/2<o:p></o:p></span></div></td> </tr></tbody></table><br /><span style="font-family: inherit;"><br /></span><br /><span style="font-family: inherit;">But for a mathematical data that is not related to any other but it self a pie chart can be a more appropriate mathematical statistic.</span><br /><span style="font-family: inherit;"><br /></span><br /><u><span style="font-family: inherit;">The Use of More Than One Mathematical Statistic</span></u><br /><u><span style="font-family: inherit;"><br /></span></u><br /><span style="font-family: inherit;">Different mathematical statistics can be used to withdraw different interpretations from one data. So while using mathematical statistics to make important decisions, the use of more than one mathematical statistic is advisable.</span>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-64903854409361459722012-02-12T19:37:00.002-08:002012-07-07T10:17:20.815-07:00Mathematical Ways of ThinkingMathematics is a branch of science that can have a significant influence on a person's behavior. Biology can merely explain how our brains are functioning, but maths can go ahead and influence such functioning.<br /><div>When you are given the option of a new job whereby you are supposed to be paid 5000 $ per month with 1 day off in a week but your existing job is paying you 4500 $ with 2 days off in a week (without considering the other perks attached), you just don't go for the new job without considering your per day pay in both the cases. And since your existing job is paying you more per day pay (204 ) as compared to your new one (192 ), you don't consider moving. This explains the mathematical way of thinking is somewhat the consideration of opportunity cost for any outcome.</div><div>Mathematical way of think is never a natural attribute, but it is learned one. Over your life time you keep learning and you keep employing various mathematical ways of going about any thing.</div><div>Consider yourself entering a shoe shop. You notice the price tags on various shoes. Your unconscious mind keeps making notes of the various prices. You roam around for a while and after that you leave the shop with a deep tagging of prices on your mind. Later on, you recall one of the price tags quoting 9.99$.</div><div>Your unconscious mind considers the price to be 9. You know that the price was 9.99 and not 9, but somehow the not-so-mathematical corner of your mind keeps missing the extra 0.99. But only if can realize that the price was set to make you think that it is actually costing you 9 and not 10, is when you can mathematically rationalize the real cost.</div><div>Next time when you enter the same shop your mind will round off the price to help you make a mathematical decision. Now you will consider paying 10 for 9 or 100 for 99. This will help you consider the other choices as well.</div>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-40343859441626421472012-02-02T11:29:00.002-08:002012-03-29T11:53:01.820-07:00How to Make a More Profitable Decision Using MathematicsThere are numerous mathematical ideas and concepts that we unconsciously use in our daily lives to make our business decisions more effective and profitable. But it is worth an effort if you can consciously recognize these mathematical concepts and make them a part of our decision-making.<br /><br /><b><u>Break - Even Point</u></b><br /><b><u><br /></u></b><br />Break - Even Point Analysis is a very significant way of interpreting our business decisions and optimum levels of outcomes. Mathematical curves can be used to determine the break - even point in terms of quantity as well as in terms of value. Such analysis can help us make better decisions.<br /><br /><b><u>Opportunity Cost</u></b><br /><b><u><br /></u></b><br />Mathematics can help us compare the cost of two products and thus enable us to make better decisions.<br /><br /><b><u>Probability</u></b><br /><b><u><br /></u></b><br />In mathematics, this is the most important field of study. Probability is a scientific term which adds rationality to our brainstorming sessions. Mathematical probability can enable us to forecast the future conditions using concrete sets of available mathematical data.<br /><br /><b><u>Percentages and Ratios</u></b><br /><b><u><br /></u></b><br />Mathematical ratios can enable us to make predictions and thus ensure that our malfunctioning departments are closely supervised.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-1181089931788549102011-11-08T05:31:00.000-08:002016-03-12T21:54:13.276-08:00Best Mathematical Gadgets Used in Movies<b>Jack Sparrow's Compass</b><br /><br />Jack Sparrow's compass was useless as far as navigation is concerned. But it was still a good mathematical gadget. The compass always pointed towards the most desired object. In this way, the compass was still quite operative in a sense that it could still be used as a tool to measure distances. And compasses, when used as dividers, are useful in measuring distances, in particular on maps.<br /><br /><b>Doc Brown's Time Travelling Car</b><br /><br />Doc Brown's stainless steel time-travelling car operated on plutonium and was quite a work of friction. Yet there was a careful mathematical computation behind every time travel. This precise computation enabled the movie characters to avoid disasters. Moreover, we learned that some gadgets can be more productive that others if we feed the appropriate sports statistics into it.<br /><br /><b>Will Smith's EXR (Movie Focus)</b><br /><br />Though this was not a physical gadget but it was still a gadget in software form. Such mathematical gadgets are mostly developed using probability theory. However, there is one drawback with such a mathematical software. They are based on <b><i>past data</i></b> and may not be effective in case of changing environments.<br /><br /><br /><br /><br /><b><br /></b><b>Some Other Note Worthy Contribution of Mathematics to Movies</b><br /><br /><i>se7en </i>shows how statistical data can help cops narrow down the list of suspects.<br /><br /><br />Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-65615545857070318432011-10-31T07:15:00.000-07:002012-12-26T14:46:06.106-08:00How to Answer Kid's Questions on MathematicsKid's often ask you the most interesting mathematical questions. And it is your peak responsibility to answer these mathematical questions in an appropriate manner to ensure that they keep on learning and never lose their interest in the subject.<br /><br />You have to understand that kids will never have the same IQ level as yours. So when you are answering to their questions make sure that your explanation is simple. Start from the basics.<br /><br />Moreover, take their queries seriously and do not dilute their curiosity by undermining the importance of their childish questions. For them, those questions are the most serious and difficult.<br /><br />Kids can sometime ask you a question that might amaze you. Here are a few questions, that might make your face blank if asked by an eight year old.<br /><br /><b>1. Why are x, y, z always considered as variable whereas a, b, c are always considered as constants?</b><br /><br />Imagine that you are a maths teacher. And on the very first teaching day, one of your young students asks you a mathematical question which has no apparent explanation. To maintain your authority you have to reply to such a question or else the students will not take you seriously for the rest of the semester. The explanation may not be convincing but you have to add some sort of logic to it. Here is how you should reply the young mathematician.<br /><br /><i>You can simply tell your student that since x, y and z are the initials of the x-axis, y-axis and z-axis, and since the x-, y- and z-axis may have numerous variable values, so we consider x, y and z as variables. Since a, b and c do not represent axis, so they are considered constants.</i><br /><br />By giving such a reply you will add some sort of logic to an apparently illogical question.<br /><br /><b>2. What do you get when you divide 1 by zero?</b><br /><br />As a teacher, if you want the young minds of your students to accept your answer to such a mathematical question, you will have to relate your explanation to something tangible. Here is how you should reply to this question.<br /><i><br /></i><i>Remember that the numerator will always be equal to the number of cakes.</i><br /><i><br /></i><i>i.e Numerator = Cakes</i><br /><i><br /></i><i>And remember that the denominator will always be equal to the number of friends.</i><br /><i><br /></i><i>i.e Denominator = Number of Friends</i><br /><i><br /></i><i>So if two friends have four cakes (4/2), how many cakes will each of them get?</i><br /><i><br /></i><i>4/2 = 2 (each of the friends will have one cake each).</i><br /><i><br /></i><i>Similarly if the two friends had no cakes (0/2), how many cakes would each of them have had?</i><br /><i><br /></i><i>0/2 = 0 (each of them would have had nothing).</i><br /><i><br /></i><i>Now if there are two cakes but no one to take them (2/0), how many cakes will each of them get?</i><br /><i><br /></i><i>In this case no one knows who will get the cakes? So we will never know who will take how many cakes?</i><br /><i>So we will conclude that our answer is unachievable.</i><br /><br /><br />Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-82755688438645489982011-10-14T16:57:00.000-07:002012-10-14T16:58:01.139-07:00Counting Something UncountableIn our early school days we are taught the difference between countable and uncountable things. Mathematics is a field of only countable things. Uncountable things (which cannot be assigned any numbered value) has apparently no place in mathematics.<br />Such uncountable things are the unconscious expenses that can be avoided if we create an understanding as to their impact on our budgets. Mathematical planning and awareness can help us eliminate such uncountable expenses (or in other words), mathematical planning and awareness can help us convert such uncountable things into countable things.<br />Some of the uncountable expenses are incurred on a courteous note (e.g a tip at a restaurant), while other such expenses are incurred on sheer unconscious grounds. If you use a car for transportation purposes just to avoid a trivial discomfort to walk a couple of blocks, you are incurring an unconscious uncounted expenses.<br />It requires an element of awareness to assign a mathematical value to such uncounted expenses in order to avoid such unconsiously uncounted expenses. The following key tips can be helpful in this regards:<br /><br />i) Try to save up the petty cash. Trivial uncountable sums can enable you to buy something crafty in the future.<br /><br />ii) While making your purchases try to keep the concept of cost-benefit analysis in your mind. Buying a nail cutter is one type of spending while buying a nail cutter cum bottle opener is just another level of mathematical decision. This will save you the uncountable expenditure to buy a separate bottle opener.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-61241364538039476852011-04-03T19:19:00.001-07:002012-04-04T17:22:26.028-07:00How to Teach Small Kids Simple Mathematical CalculationsI am sure many of us would have been taught in our childhood days to count the sheep as we sleep. Even though that was taught to make us sleep faster, it served a very important role in teaching us how to do mathematical additions.<br />The key to understand is that children will be inclined to do such mathematical exercises that don't require much efforts. And since in the bed they had nothing else to do, the counting sheep exercise was a much effective one.<br />So the first thing that we agree upon is that the mathematical exercises must be easy to ensure that the kids don't loss their interest.<br />Maths is an intangible concept. And one of the key attributes of mathematics is counting. When we count some physical thing, we are adding a tangible attribute to mathematics. This physical counting can build an additional understanding of mathematics. When you are teaching mathematics to your children, make sure that you make them use their hands while counting. When they use their hands, their visual senses will make it easy for them to understand what is 2 +2 ? This is the most easiest way to make children understand simple addition calculations. Children don't know what 2 is? But they do know what 2 apples means? It means one apple and one more apple.<br />Another good way of developing a kid's understanding about mathematics is through the use of numbered building blocks. The visual printing of numbers on mind can help a kid differentiate between two mathematical numbers.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-54511188514998380252011-03-25T02:39:00.000-07:002012-03-26T19:39:59.949-07:00How to Represent an Algebraic Equation on a GraphGraphical representation of an algebraic equation (lets say 2x + 2y = 2) can be established by considering the intercepts of both the variables involved in the mathematical equation.<br /><br />An intercept is such a co-ordinate of a variable for which the corresponding co-ordinate of the other variable is zero. In other words, an intercept of a variable crosses through it's axis (x-intercept crosses through the x-axis and y-intercept crosses through the y-axis).<br /><br />For the above hypothetical mathematical equation the x-intercept will be (1,0)<br /><br />2x + 2(0) = 2<br />x = 1<br /><br />and the y-intercept will be (0,1)<br /><br />2(0) + 2y = 2<br />y = 1<br /><br />Such technique can be used to find the solution set of two straight lines.<br />Consider the two straight lines be:<br />2x + 2y = 2<br />3x - 3y = 6<br /><br />Now for our 2nd mathematical equation (3x - 3y = 6) the x and y intercepts will be (2,0) and (0,-2) respectively.<br /><br />By drawing the above two mathematical equations on a graph, you can find the solution set of the two equations. That will be the point where the two equations intercept each other.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-14660337083336721852010-09-27T05:19:00.000-07:002012-10-20T02:56:46.403-07:00A Mathematical Evaluation of Prize BondsPrize Bonds are injected by banks into the cash-stream of general public to gather-up finance. It's a monetary control measure exercised world-wide. General public give-up their money in hope to be lucky and get rich over-night. Ofcourse, with the added advantage to recover their cash-amount at their will. But thats not what generally happens. People generally keep their bonds with them for many years in hope of success someday.<br /><br />The evaluation of Prize Bonds being fake or not! is an entirely different story. But since these bonds are operating for long while, lets just consider them to be 100 percent genuine. Ofcourse, the Government can fake a winner. But since there are prize bonds of numerous denominations that are announced on monthly or even bi-monthly basis and since there are many winners of the prize bond of the same denomination - it will require a lot of faking from the Government.<br /><br />They have thus devised, which i would call, a more mathematical way of dealing with the human psychology. We all are highly motivated with something which we consider is achievable, even if it is a prize bond (in which the probability is highly stacked against us). Same is the case with prize bonds. If the Government can somehow keep us interested in buying the prize bonds and retaining them for a longer period of time - they will consider it a 'job well-done'.<br /><br />To achieve this, prize bonds are alloted a long (usually 6 or 7) digit number. Now here is the trick. Actually it is not a trick, rather a flaw of our minds. When we compare our prize bond number with the winner's prize bond number, we fail to realize the real difference between the two numbers.<br /><br />For example, if the winner's number is 654321 and our number is 754321. We think of it as a difference of one number. We think that we are just short by one number and if we had a 7 instead of a 6 at the beginning of our prize bond, we would have won.<br /><br />But that is not the case. The real difference is actually a big big one. There is a difference of 100,000 (754321 - 654321) between the two bond numbers.<br /><br />In reality the two bonds were worlds apart from each other. We were never ever near the winner. But this never changes our decision regarding the future holding of prize bonds and we generally maintain our holdings in prize bonds for a much longer period.<br /><br />If we can done simple mathematics and learn probability in our school life, we can surely make much more prudent decisions.Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.comtag:blogger.com,1999:blog-4985190320994040209.post-49399947010956611672010-01-19T12:02:00.000-08:002013-10-29T13:06:50.426-07:00Mathematics vs PhilosophyIt might be interesting for you to know that certain reasoning and deductive inferences of maths have in reality been extracted from the field of philosophy. Infact the entire section of 'Theorems' have been derived from philosophy.<div><br /></div><div>A simple example would be as follows:</div><div><br /></div><div><i>Prime Numbers are divisible only by 1 or by themselves. (In philosophy this would be Premise 1).</i></div><div><i>And 7 is divisible only by 1 and 7. (In philosophy this would be Premise 2).</i></div><div><i>Hence 7 is a prime number. (In philosophy we call it 'Conclusion'.)</i></div><div><br /></div><div>Various other formulas involving Union (U) and Intersect are also derivations of Philosophy.</div><div><br /></div><div><br /></div><div>Various early philosophers have also contributed in the filed of trigonometry as well (most famous is Pythagoras).</div><div><br /></div><div><br /></div>Shahkar khanhttp://www.blogger.com/profile/10003925069340959132noreply@blogger.com