tag:blogger.com,1999:blog-9004452969563620551.post4677799046242093571..comments2017-09-25T12:48:32.845+05:30Comments on Paramanand's Math Notes: On Mathematics Education: Algebra vs. Calculustesternoreply@blogger.comBlogger4125tag:blogger.com,1999:blog-9004452969563620551.post-78176368009369306832017-09-25T12:48:32.845+05:302017-09-25T12:48:32.845+05:30@samir,
Thanks for the exact quote from Rudin. My...@samir,<br /><br />Thanks for the exact quote from Rudin. My statement also conveys the similar feeling. And the way he introduces real number and also their construction so formal/uninspiring/boring that one would never read it. I don't know how such cheap textbook became famous globally. Rudin writes with almost no enthusiasm and to me it appears that he really disliked writing books and was in this only for the money. And that book is highly unsuitable for self study.<br /><br />Regards, <br />Paramanand Paramanand Singhhttps://www.blogger.com/profile/03855838138519730072noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-51869685442095512072017-09-23T14:06:10.143+05:302017-09-23T14:06:10.143+05:30In my edition of Rudin's book, the preface say...In my edition of Rudin's book, the preface says "It is pedagogically unsound (though logically correct) to start off with the construction of the real numbers from the rational ones" ... I am not sure if you have a different edition of the book.<br /><br />The point is that he introduces real numbers as an ordered field, develops the theory for some time, then brings in the concept of how one can create the reals from rational numbers using Dedekind's construction. All this is in Chapter 1 before getting to analysis proper. <br /><br />Sorry for commenting on an old post, but i just came across your blog a few days ago and have found it very useful.<br />samirhttps://www.blogger.com/profile/04724519053575833468noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-31413906725000658712013-09-02T09:40:50.860+05:302013-09-02T09:40:50.860+05:30@Pritesh Rajput
I am really happy that you took t...@Pritesh Rajput<br /><br />I am really happy that you took time and effort to provide a serious feedback for this post. In case you have read some of my other posts you will find the best advice that I can give to my readers is to get hold of G. H. Hardy's "A Course of Pure Mathematics". This book is available free of cost online if you search enough. It is written for people of your age. A review of this book is available at http://paramanand.blogspot.com/2005/11/book-review-course-of-pure-mathematics.htmlparamanandhttps://www.blogger.com/profile/03855838138519730072noreply@blogger.comtag:blogger.com,1999:blog-9004452969563620551.post-44603553055675788442013-09-01T22:52:15.098+05:302013-09-01T22:52:15.098+05:30I must say, I didn't find any such intuitive a...I must say, I didn't find any such intuitive analysis of algebra and flaws of mechanical approach as you provided. You were truly correct onto the point of hiding concepts and insisting student to advance at the cost of his grasp of the subject. Teachers far away from the fact shoot in the bush to rush the concept leaving students baffling and complaning about the difficulty of the subject. Students are kept away from the practical application behind the concept. Even sometimes teachers themselves are unclear about the conceptual understanding. It affects a student's life badly. The rigour based study without real analysis turns a student into a function assigned for specific task without any bargain. <br /><br />The examples on the product of HCF & LCM were the actual way of describing the disadvantage of prevailing education. I even doubt some students that grow up doing a lot of maths but are simply unaware of the full form of LCM (lowest common multiple).<br /><br />I'm a 12th grade student. I know the obstacles in interpreting any concept into useful form. At my stage students run over every other topic and get entangled into inescapable trap of confusion. Literally, teachers do not focus on analysing the set theory and importance of relations. It results in unclearness of the concept of functions. And, you must be knowing the need to understand functions at such early point. The incomplete understanding of functions leads to disaster! You could even dare to calculus and precalculus!!!.But, unfortunately majority students suffer the brunt.<br /><br />Calculus is mountain of mathematics, where algebra is prerequisite. The approch of calculus is viable and practical.<br /><br />The traditional methodology, brings calculus as an supernatural study with advance definitions and rigour. The formidable presentation of calculus breaks the morale of student. While, capturing the notion of calculus is far more easier than absorbing the ideas of expansion and factorisation!!!!<br /><br />'Limits' become very barbaric. Wandering every time like spooking nightmare. Majority of students pass out without knowing the need or real application of limits in calculus. We know that limits provide approximation to the discontinuites in the curves of function which are undefined for several of the values in the domain.<br />But, the boring and condemnable description in our textbooks brings about disinterest and disrespesct for the subject. "When x approaches some value in domain then y approaches some in range." Our textbooks define the limits in the kind of way. It reflects nothing on why x approaches some value for y to approach some another value! The need of Limits is avoided and is left to students for the face off.<br /><br />Well, there are several more instances of negligence over the practicability. But, these were the basic flaws of prevailing education at my level.<br /><br />You brought a clear-cut line between calculus and algebraical approach. I hope everyone to seek some inspiration from here. I'm glad to know about your way of educating students in rightful and fruitful manner.<br /><br />I'm presently preparing for JEE 2014. If you could recommend some advice, then it would be bliss.<br /><br /> Pritesh Rajput<br /> (priteshrajput1@gmail.com)pritesh rajputhttps://www.blogger.com/profile/01040390688744095601noreply@blogger.com