My Best Mathematical and Logic Puzzles

 Best Collection of Math Puzzle

 

Discription

A mind blowing Math puzzle and riddle collection which bother anyone to think twice or thrice for the solutions.

The present volume contains a rich selection of 70 of the best of these brain teasers, in some cases including references to new developments related to the puzzle. Now enthusiasts can challenge their solving skills and rattle their egos with such stimulating mind-benders as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, The Fork in the Road, Bronx vs. Brooklyn, Touching Cigarettes, and 64 other problems involving logic and basic math.

Another best thing is Solutions are included.

About the Author

"A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?" — Martin Gardner

Martin Gardner was a renowned author who published over 70 books on subjects from science and math to poetry and religion. He also had a lifelong passion for magic tricks and puzzles. Well known for his mathematical games column in Scientific American and his "Trick of the Month" inPhysics Teacher magazine, Gardner attracted a loyal following with his intelligence, wit, and imagination.

Personal review

 whenever I encountered such puzzles and riddles, I often thinks that who the minded has discovered that and who has created such puzzles. Now when I've faced this book I've found Martin Gardner is one of that minded person.

As a Martin Gardner's book one can never feel that he or she has buy only piece of binded papers.

The book is proven to be a better guide to enhance thinking power, being reasoning and to build "never give up" quality.
One must give a shot to this book.

A good resource for learners, creative ones, and students and for those who always try to think beyond the level.

Get a copy

   My best mathematical and logic puzzles

How to study Mathematics as major

How to study Mathematics as major

 

Description

Every year, thousands of students declare mathematics as their major. Many are extremely intelligent and hardworking.
Most of the math major tries hard to solvenew concepts and catch the real mean of the topic.

However, even the best will encounter challenges, because upper-level mathematics involves not only independent study and learning from lectures, but also a fundamental shift from calculation to proof.

This shift is demanding but it need not be mysterious -- research has revealed many insights into the mathematical thinking required, and this book translates these into practical advice for a student audience.

This book sectioned into two parts such as:
Part 1- discusses the nature of upper-level mathematics, and explains how students can adapt and extend their existing skills in order to develop good understanding.

Part 2- covers study skills as these relate to mathematics, and suggests practical approaches to learning effectively while enjoying undergraduate life. 

As the first mathematics-specific study guide, this friendly, practical text is essential reading for any mathematics major. 

Review

"Students can benefit from just 'picking it up' for a short time - now and then - and reading just about any section. The sections are relatively short - sometimes just two or three pages, but are very informative. One could easily recommend [ How to Study as a Mathematics Major] to undergraduates." --Mathematical Association of America.

About the Author

Lara Alcock is Senior Lecturer in the Mathematics Education Centre at Loughborough University, UK. An accomplished undergraduate and graduate mathematician at Warwick, her doctorate was in mathematics education before holding various academic posts including Assistant Professor of Mathematics Education and Mathematics at Rutgers University, New Jersey.
Her research focuses on the challenges students encounter as they make the transition from calculation-based to proof-based mathematics.
She was awarded the 2012 MAA Seldon Prize for Research in Undergraduate Mathematics Education. She has been awarded National Teaching Fellows of 2015 by The Higher Education Academy. 

Publisher

•Oxford University Press

Personal Review

The book is having a great exposure over learning experience and gives an easy to understand explainations of topics belongs to higher level of math.
In higher studies most of the math major find it to be boring subject (even sometimes I was having same feeling) to reduce such kind of experiences Lara Alcock has given a very creative effort for making those topics more interesting by relate them to practical life.

Apart from all above reviews the best part of this book is that it is appreciated by Mathematical Association of America.

Reviews by owners of a copy

Get a Copy 

How to study Mathematics as major

Mathematical Mindsets: Unleashing Students' Potential

Mathematical Mindsets

Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching

Mathematical Mindsets

A Very creatively crafted math Book which shows a clear roadmap to get success in math concepts with practical examples and strategies. This Book gives proper explaination towards the problems and proven to be very helpful for parents, teachers and for students too and even for those who believes that they are not so good at math.
Jo Boaler : Stanford researcher, expert in math learning, has researched about why most of the learners find problems and difficulties in math learning and gives a proper and a brief solution in the form of this book.

Boaler has used Carol Dwek's concept of "mindset" into math teaching and parenting strategies. She suggested steps that must be taken in schools to make math more interesting to grasp.

Mathematical Mindset Teaches that how to convert mistakes and squeezing experiences into valuable learning experience. Briefly given rich math activities shows how to be reasoning in Mathematics instead of rote learning method. This book is also gives positive math mindset which also works as a boost to learner.

Mathematical Mindset provides a proven way to get success in math learning.

• Review

"positive and absorbing"
 (Teach Secondary, February 2016) 

"..full of useful and creative maths excercises."  (In Tuition, October 2016)

•  From the Back Cover

PRAISE FOR MATHEMATICAL MINDSETS

"Mistakes, struggles, creativity, beauty, flexibility, equity Jo Boaler uses these words to describe a vision of mathematics where every student thrives and becomes a mathematical thinker. By following Boaler′s roadmap, perhaps we can once and for all lay to rest decades of archaic and destructive notions about what it takes to be good at math."
Cathy Seeley, Past President, National Council of Teachers of Mathematics and author of Faster Isn′t Smarter and Smarter Than We Think

• Review by customers on Amazon :-

• About the Author :

DR. JO BOALER is a professor of mathematics education at Stanford University. The author of seven books and numerous research articles, she serves as an advisor to several Silicon Valley companies and is a White House presenter on girls and STEM (Science, Technology, Engineering, and Math). She is a regular contributor 6to news and radio in the United States and England and recently formed youcubed.org to give teachers and parents the resources and ideas they need to inspire and excite students about mathematics.

  • My opinion 

For those who want math to be more creative and interesting subject,

and also those who think they are not good at math they must have to try this and feel a great exposure over various practical math learnings.

• Get a Copy 

Mathematical Mindsets

How to Find remainder of any Polynomial in 2 easy steps ?

      For a long time I wanted to write about remainder theorem, as most of my students used to ask me frequently about this and I thought probably you also want to read about this topic. So, here it is...

Remainder theorem

     As I've have discussed about Polynomial in my earlier post and also about Long Division method to solve any fractions of polynomials, Now this time is to explain the most favourable method to find remainders of fractions.

     With the help of long division method remainder and quotient can be evaluated but this turn to be lengthy method, while we are only tend to find, whether any fractions are divisible or not.

      

     So, when someone is looking to find whether the Polynomial is perfectly divisible by another polynomial or not i.e. remainder theorem comes in existence to find remainders direct without any hassle and struggle with only in two steps.

    

 • So here is step by step method of remainder theorem:-

      Let any quadratic, cubic or any Polynomial P(x) is divided by another polynomial say g (x) then remainder can be evaluated by following method of two easy steps

Say P(x) = x³ + 3x² - 5x +6 

  &    g(x) = x + 1

• STEP 1:  by g(x) = 0,

               x+1= 0

               x = -1

• STEP 2:  P (-1) = (-1)³ + 3 (-1)² - 5(-1) + 6

                   = -1     + 3 ×1    + 5   + 6

                   = -1  + 3 + 11

        P (-1)  = 13

hence, If P(x) = x³ + 3x² - 5x +6 when divided by g(x) = x + 1 left with remainder 13.

the same remainder can be obtained from long Division method and can verify this.

let's have an another example:

P(x) = x³ + 3x² + 3x + 1

& g(x) = 5+2x

• STEP 1:   5+2x = 0  

               2x = -5

              x =  -5/2

 now, 

• STEP 2:  

   P(-5/2) = (-5/2)³ + 3(-5/2)² + 3(-5/2) + 1

             = -125/8  + 75/4  - 15/2 + 1

             = -27/8

     hence, I hope you've got to know about remainder theorem and it's most utility in the field of algebra.

 I personally consider this method is a shortcut to verify whether any Solution of  Long Division is correct or not by observing remainders.
now over to you, what you have found about this tutorial special and what else you want to add here do let me know by commenting.

How to construct Trigonometry table in 5 minutes without memorising ?

      Most of the students or learner who are studying trigonometry usually get confused at beginning with bunch of formula, angle values and Identities.

     But if Once, They are all learnt properly then Trigonometry becomes one of the most favourite topic of math for them.

 some of the initial Queries do most of us have while studying Trigonometry i.e.

Trigonometry Table

  •   Why Trigonometry ?  •   What are the basics of Trigonometry?  •   What are the values of Angles of various T-ratios ?

    so, For the answer of all these questions click this post:

     

  •     Trigonometry functions & Basic concepts with formula

now as I've titled this post, I'm going to reveal the best method which I recommend to construct Trigonometry table within or less than​ 5 minutes.

 •   How to construct Trigonometry table within or less than 5 minutes without memorising :

       There are 6 T-ratios and we all are well known with , and

yes, of course...!!! 

       This T-ratios posses some numerical values at different angles like 0°, 30°, 45°, 60°, 90° etc. but this doesn't mean that they don't have other values, Na !!

  Each T-ratios have numerical values for every angle from 0° to infinity but the most and commonly used angles are 0°, 30°, 45°, 60°, 90° and also 180° too and we can construct a table for such values.

so, let's start,

 •  we'll start with Sin∅ 

                  0°       30°       45°        60°    90°

sin∅         0        1/2       1/√2      √3/2     1

these values of Sin∅ at different angles we have to keep these in mind now all other values can be derived from these, how ?

look at below,

 •  for Cos∅, values will be reversed means Sin 90° = Cos 0° so,

Cos∅      1         √3/2       1/√2       1/2      0

 •  Sec∅ = 1/ Cos∅, hence Cos∅ values will reciprocate for Sec∅ :

Sec ∅     1        2/√3         √2         2        1/0 =∞

 •  Cosec∅ = 1/ Sin∅, hence Sin∅ values will reciprocate for Cosec∅ :

Cosec∅   1/0=∞     2         √2        2/√3       1

 •  Now for Tan∅ = Sin∅/Cos∅ 

Tan∅      0         1/√3       1          √3              ∞

•  And for Cot∅, values of tan∅ will get reversed  i.e.  (tan 0° = Cot 90°)

Cot∅       ∞         √3           1        1/√3          0

so, This is how we can construct the whole table within or less than 5 minutes.

look at the whole table below,

                  0°       30°       45°        60°    90°

sin∅         0        1/2       1/√2      √3/2     1

Cos∅        1       √3/2       1/√2       1/2      0

Sec ∅       1        2/√3         √2         2       ∞ 
Cosec∅   ∞         2             √2        2/√3    1

Tan∅      0         1/√3       1          √3        ∞

Cot∅       ∞         √3           1        1/√3      0

   For, finding further values there may apply certain rules which I'll discuss in my next tutorials.

Till then if you are having anything you think that should be shared here, please do let me know via comment or email. It would be pleasure for me.

Euclid's Division Algorithm:Algebra form

Euclid's Division Algorithm

is also have it's utility in algebra in same formation.

whenever, one intended to perform long Division of algebraic terms then that procedure also follow Euclid Division Algorithm, or I can give you an idea to clear the concept so have a look at this,

when we divide 23 by 5
then this divided as
23/5 = 4 ³/5

here quotient is 4 and remainder is 3.
But to justify this division we tend to multiply quotient to Divisor and result is added to remainder hence
5×4+ 3 =23

this is what can be expressed in generalisation as

B×q+ r = A

What Euclid has given.

On the other aspect of algebra this can be applied similarly likewise.

But the representation is quiet different as each term is considered as polynomial in algebra and represented by P(x) that's why
p(x) is considered as Dividend
q(x) as quotient
r(x) as remainder
and
g(x) as Divisor

so the algorithm will be

p(x) = q(x) × g(x) + r(x)

this is for justification of long Division of algebraic terms.
Alternatively this formula is useful to evaluate any of the polynomial be it quotient​, be it remainder or Divisor​ if all the other three polynomials are given.
Suppose, we've to evaluate q(x), then

q(x) =  [ p(x) - r(x) ]/ g(x).
Now, over to you let me know by comment if I'm missing something.

Basic Concept of Addition and Multiplication

As I usually try to explain some of the topics of mathematics in which I used to try to take some basic concepts too,

similarly today I aren't taking any of the topic but at the same time in this tutorial I'm going to explain a very deep concept i.e.

Belongs to Addition and Multiplication which I encountered today while I was teaching in my class & I found to be shareable with you all.

Basic Concept : Addition and multiplication

let me tell you the whole story
A group of curious student has asked me..!!

Question:-  If it is
 2×2 =4 and 2+2=4
and
3+3=6
then likewise why not it is
3×3= 6 instead of 3×3=9.

Ans:-
I explained this problem in such manner which might also helpful for others...

yes..! this is true that if we multiply and add 2 with 2 then answer will remain same i.e. 4.
I also states that this is the only number in Mathematics which have this specific behaviour but for other numbers the situation becomes different.

for addition it is okay i.e.
2+2= 4       &      3+3 = 6

but when we tend to multiply any number
to itself it gives different values,
I explained this happens because when 3 is multiplied with 3 this means 3 is being added 3 times i.e.
3×3 = 3+3+3
which equals to 9.
similarly for any other example
like
 4×4 = 4+4+4+4 = 16.

so the conclusion accordingly is the concept of multiplying arises to comprise or saturate the long addition process for such big additions like
25+25+25+25+25.........(25 time)= 25×25
625                                                 = 625.

Alternative Method of addition :-

3×3    
or we can write
3+3+3
common out 3
3 (1+ 1+ 1)
3× 3
9.


hence 3+3 = 6
but 3× 3 = 9


hence I explained my students, while reading this article I hope you also come across this concept and finds interesting.

so, here I'm ending this post now If you find some suggestions or any topic you want me to explain via my tutorials, then let me know by commenting under the comment section.
till then check out our recent and most readed tutorials over web:-

• Exponents and their rules

• Divisibility test of 3,5,7,9,11,13....

• Fractions Solutions with ease

• BODMAS rule - how and when to apply

How to solve Trignometry Functions

Here Is one of the best topic of MATHEMATICS which allows us to find out

• The heights of Buildings, towers, skyscraper sand trees, and mountain etc.

• the elevation angle of top of any building with the horizon.
• trigonometry allows us to project any thing from a certain distance​ and certain angle to attain maximum distance..
• Best thing for Trigonometry I can say these progress​ what we are seeing around us couldn't be possible without Trigonometry.

Trigonometry functions and their basics

now I'm going to explain the basic concepts of trigonometry

there are six Trigonometry functions exist 

i.e.

sin ,  cosine ( cos ) , tangent ( tan ) , cotangent ( cot ) , sec , Cosec.

these functions are having different values around the axis with angles.

so you can observe from the image all the different values of trigonometry​ functions  varies for sin and cos from 0 to 1 as angle varies from 0° to 90°.
but for other functions it is from 0 or 1 to 1 or undefined values.

for better understanding of trigonometry functions how they behave on Cartesian plane check this image out :-

from the above image it is clearly shown that for 1st quadrant all the functions are possessing positive values as we can see in above table and for 2nd, 3rd and 4th quadrant t.here is (Sin, cosec), (tan, cot), and (cos, sec) are positive respectively and rest are negative in particular quadrants.

i.e. :-
sin90° = 1 but
sin 270° = ౼1
the reason is
sin 270° = sin ( 180° + 90°)
sin 270° = sin(౼ 90°)
sin 270°= ౼1
because up to 180° sin will remain positive after that it becomes negative.

From above table this doesn't mean that Trigonometry functions have only values from 0° to 90° rather these functions have from 0° to up to whichever degree you can assume.

• LET ME TELL YOU THE BEST THING ABOUT TRIGONOMETRY IS THAT THIS TOPIC DEPENDS ONLY UPON RIGHT ANGLE TRIANGLES.

In any right angle triangle there is one base and perpendicular and a hypotenuse i.e.
briefly you can observe in following image:-

from this image we can find any of the Trigonometry ratio or angle with the help of three sides of any right angle triangle.
If we don't know any of the side of triangle then we can find out by Pythagoras Formula i.e.

 H² = B² + P²

let H = 5 and B = 3 then P = ?q

by relationship 

5² = 3² + P² 

25 = 9 + P²

P² = 16

P = 4

Also read:

• Math helpful topics 

• Interrelation of Trigonometry functions:-

sin∅ = 1/ cosec∅

cos ∅ = 1/ sec∅

tan∅ = 1/ cot∅

and vice verse.

tan∅ = sin∅/ cos∅

cot∅ =cos∅ / sin∅

some Trigonometry Identities which are much useful to solve problems are

sin²∅ + cos²∅ = 1

1+ cot²∅ = cosec²∅

tan²∅ + 1 = sec²∅

I hope this tutorial about Trigonometry has been proved very useful for you and now it's over to you, If you want here to add something more which I'm missing do let me know, I'll be pleased to hear from you.

Introduction: Math's Buddies

Introduction: Math's Buddies

Hey there,

This is SM Faizan Ali, (MATH lover).

This is my First written Blog post includes my intro and my interest,
as you can have an Idea from the Name of this blog i.e. this not only about MATHEMATICS but also we're here connected as buddies, to solve and to provide and spread the best knowledge about MATHEMATICS.

I'm here to provide the best solutions of Math problems. If you have any query drop an email or comment.
I'll try my best to provide the solution.

To be frank,
Do remember, I'm too a human being...I can
also be stuck somewhere.But I'll try me best.
Hoping to have best response from your side.
Thank you,
regards ,
SM Faizan Ali