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# Tag Archives: Learning

## Memory Methods

Image via Wikipedia

Memory, in human reference, is the ability to store retain and recall informations when needed. Without hammering the mind in the definitions, let we look into the ten methods of boosting our memory:

## 1. Simple Repitition Method

The classical method, very popular as in committing poems to memory by reading them over and over.

## 2. Full Concentration Method

Concentrate on the topic content while learning. Do not allow your mind to wander. Focus on names and numbers. Try deliberately to remember. Your approach should not be casual. Review soon after you learn, lest memory should fade away.

## 3. Visual Encoding Method

Translate information into visual formats like pictures, charts, diagrams, tables and graph.

## 4. Logical Organisation

Matter that is logically organised is retained better than the disjointed floating bits of information. Infuse meaning into what ever you learn. No “Nonsense Syllables”.

## 5. Mnemonics Method

Few good people try this method to learn some complicated series. There is no harm in using memory crutches like it, after grasping the spirit of the lesson. VIBGYOR is the most famous mnemonic that helps up to list the seven rainbow colors in their appropriate order. Once, I had remembered the name of the planets in the order of their distances from the sum by the acrostics “My very enlightened mother just served us noodles-in plates”, as it tells me the names of nine planets ( off course now they are eight, but I learned it earlier than the removal of pluto), in the order: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto.

## 6. Mock Teaching Method

If you find a particular portion of a chapter difficult to digest, imagine that you are teaching to a student sitting before you. Explain virtually the content of the lessen. The idea will get hammered into your mind.

## 7. Rhyming Method

Scholars say that verses are better than prose. Change any definition into verse and try to rhym them. Remember, I discuss just verses, and not poetry.

## 8. Chunking Method

Very popular method. You can divide a big list into a number of bits or chunks. For example, to remember a mobile number of ten digits, people usually split it to three or more chunks.

## 9. Pegging

This involves the principal of association. First make a list of ten or twenty convenient pegs or key words that you can easily recall in the right sequence. For example, in alphabetical order, ant, butterfly, cat, dog, elephant, fox, and so on (Living beings are arranged). Cartoons also help in pegging.

## 10. Blogging

This is the best method for that student, who want to learn very complicated topics. When you blog about any topic, you use all the nine methods listed above in your post. I got blogging, superior method to other nine.

## Free Online Calculus Text Books

Once I listed books on Algebra and Related Mathematics in this article, Since then I was recieving emails for few more related articles. Here I’ve tried to list almost all freely available Calculus texts. Here we go:

1. Elementary Calculus : An approach using infinitesimals by H. J. Keisler
2. Multivariable Calculus by Jim Herod and George Cain
3. Calculus by Gilbert Strang for MIT OPEN COURSE WARE
4. Calculus Bible by G S Gill [I found this link broken.]
5. Another Calculus Bible by Neveln
6. Lecture Notes for Applied Calculus [pdf] by Karl Heinz Dovermann
7. A Summary of Calculus [pdf] by Karl Heinz Dovermann
8. First Year Calculus Notes by Paul Garrett
9. The Calculus of Functions of Several Variables by Professor Dan Sloughter
10. Difference Equations to Differential Equations : An Introduction to Calculus by Professor Dan Sloughter
11. Visual Calculus by Lawrence S. Husch
12. A Problem Text in Advanced Calculus by John Erdman
13. Understanding Calculus by Faraz Hussain
14. Advanced Calculus [pdf] by Lynn Loomio and Schlomo Sternberg
15. The Calculus Wikibook [pdf] on Wiki Media
16. Stewart ‘s Calculus by James Stewert.
17. Vector Calculus
18. The Calculus for Engineers by John Perry
19. Calculus Unlimited by J E Marsden & A Weinstein
20. Advanced Calculus by E B Wilson
21. Differential and Integral Calculus by Daniel A Murray
22. Elements of the Differential and Integral Calculus[pdf] by W A Granville & P F Smith
23. Calculus by Raja Almukkahal, Victor Cifarelli, Chun Tuk Fan & L Jarvis

## Essential Steps of Problem Solving in Mathematical Sciences

### Learning how to solve problems in mathematics is simply to know what to look for.

Math problems often require established procedures and one must know What & When to apply them. To identify procedures, you have to be familiar with the different problem situations, and be able to collect the appropriate information, identify a strategy or strategies and use the strategy/strategies appropriately. But exercise is must for problem solving. It needs practice!! The more you practice, the better you get. The great mathematical wizard G Polya wrote a book titled How to Solve It in 1957. Many of the ideas that worked then, do still continue to work for us. Given below are the four essential steps of problem solving based on the central ideas of Polya.

## The Fear, and the Use, of Mathematics and Physics

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The two areas of human enquiry that inspire the greatest terror in the hearts of students are undoubtedly mathematics and physics. You may find history or chemistry or economics difficult, but your reaction to these subjects, and more others is almost certainly not fear. On the other hand, when you encounter an equation, your first reaction is to escape to more amiable company. If you compare subjects to people, you will realize that your reaction to maths or physics is very similar to your reaction to a stern, quiet person who is famous for his wisdom but who makes you very uncomfortable indeed. When he speaks you listen dutifully, because you’ve been told his words contain a lot of meaning, but you understand almost nothing, and you end up feeling foolish and exposed; and what is worse, this person does not need to shout to make you feel this way — he just has to look at you. When you see an equation or a mathematical expression you react in the same way. Let us try to under stand that what mathematics is and why it is so difficult.

## Derivative of x squared is 2x or x ? Where is the fallacy?

As we know that the derivative of $x^2$ , with respect to $x$ , is $2x$.

i.e., $\dfrac{d}{dx} x^2 = 2x$

However, suppose we write $x^2$ as the sum of $x$ ‘s written up $x$ times..

i.e.,

$x^2 = \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}}$

Now let

$f(x) = \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}}$

then,

$f'(x) = \dfrac{d}{dx} \left( \displaystyle {\underbrace {x+x+x+ \ldots +x}_{x \ times}} \right)$

$f'(x)=\displaystyle {\underbrace {\dfrac{d}{dx} x + \dfrac{d}{dx} x + \ldots + \dfrac{d}{dx} x}_{x \ times}}$
$f'(x)=\displaystyle {\underbrace {1 + 1 + \ldots + 1 }_{x \ times}}$
$f'(x) = x$

This argument appears to show that the derivative of $x^2$ , with respect to $x$, is actually x, not 2x..

Where is the error?