Showing posts with label I.S.I.. Show all posts
Showing posts with label I.S.I.. Show all posts
Monday, 13 May 2013
Sunday, 12 May 2013
Friday, 10 February 2012
Monday, 2 January 2012
I.S.I. Entrance Model Test @ Cheenta Schedule
All Cheenta Model Test will be held on Saturdays. The tests will start at 10 AM in the morning in our Kolkata center.
External Students may also appear in the tests. For registration call 09804005499, 07381944396 or mail us at helpdesk at cheenta dot com.
| Model Test | Date |
| 1 | 17th December, 2011 |
| 2 | 31st December, 2011 |
| 3 | 14th January, 2012 |
| 4 | 28th January, 2012 |
| 5 | 11th February, 2012 |
| 6 | 25th February, 2012 |
| 7 | 10th March, 2012 |
| 8 | 24th March, 2012 |
| 9 | 7th April, 2012 |
| 10 | 21st April, 2012 |
Tuesday, 13 December 2011
Monday, 5 December 2011
Sunday, 29 May 2011
IIT Mathematics: Why it is important and which book is better?
IIT Mathematics books are important for I.S.I. preparation because they give a comprehensive problem collection on high school mathematics. I.S.I. entrance preparation has two layers.
Layer 1- High School Mathematics - Calculus, Trigonometry, Analytical Geometry, Algebra
Layer 2- Olympiad Mathematics - Plane Geometry, Combinatorics, Number Theory, Inequalities, Polynomials, Functional Equations
For high school mathematics portion, IIT Mathematics books are useful. Ofcourse you will need typical books like Maron for Calculus, Loney for Trigonometry and analytical geometry, Hall and Knight or Bernard Child for Higher Algebra, but to enhance problem solving ability you must have an IIT book as your companion.
There several such books available. Some of the most renowned are:
The bottom line is get M.L. Khanna IIT Math as a problem book. If you can finish it, you may move over to TMH.
Layer 1- High School Mathematics - Calculus, Trigonometry, Analytical Geometry, Algebra
Layer 2- Olympiad Mathematics - Plane Geometry, Combinatorics, Number Theory, Inequalities, Polynomials, Functional Equations
For high school mathematics portion, IIT Mathematics books are useful. Ofcourse you will need typical books like Maron for Calculus, Loney for Trigonometry and analytical geometry, Hall and Knight or Bernard Child for Higher Algebra, but to enhance problem solving ability you must have an IIT book as your companion.
There several such books available. Some of the most renowned are:
- M.L. Khanna,
- Tata Mcgraw Hill (TMH)
- Arihant
- Pearson
- Dinesh
- MTG
The bottom line is get M.L. Khanna IIT Math as a problem book. If you can finish it, you may move over to TMH.
Monday, 16 May 2011
NEXT 30 DAYS for TARGET ISI+OLYMPIAD '12 - a minimalistic strategy
What to study and how much to study is a relative question (depends much on the student). We present here a minimalistic strategy which is good for someone who has a fair idea about high school math (and who is interested to crack I.S.I. or C.M.I. undergraduate math/stat entrance in 2012). The strategy is minimalistic because we suggest the must-do stuff only. The more work the better you are off.
Regular (problems that you must to every day, every season)
Regular (problems that you must to every day, every season)
- I.S.I. 10+2 - subjective 100 problems and objective 300 problems (that is just 13 problems per day)
- Geometry - Challenges and Thrills of pre college math - 10 riders + theorems per day
- Calculus - TMH IIT math - 10 problems per day
- High School centric topic - Trigonometry - TMH IIT math + Loney (Height and Distance harder + Properties of triangle harder) - 10 problems per day
- Olympiad centric topic - Inequalities + Functional Equation + RMO (4 papers), INMO (2 papers) + IMO (2 papers) = 300 problems i.e. about 10 problems per day.
I.S.I. 10+2 Subjectives Solution
P148. Show that there is no real constant c > 0 such that \(\cos\sqrt{x+c}=\cos\sqrt{x}\) for all real numbers \(x\ge 0\).
Solution:
If the given equation holds for some constant c>0 then,
f(x) = \(\cos\sqrt{x}-\cos\sqrt{x+c}=0\) for all \(x\ge 0\)
\(\Rightarrow 2\sin\frac{\sqrt{x+c}+\sqrt{x}}{2}\sin\frac{\sqrt{x+c}-\sqrt{x}}{2}=0\)
Putting x=0, we note
\(\Rightarrow\sin^2\frac{\sqrt{c}}{2}=0\)
As \(c\not=0\)
\(\sqrt{c}=2n\pi\)
\(\Rightarrow c=4n^2\pi^2\)
We put n=1 and x=\(\frac{\pi}{2}\) to note that f(x) is not zero.
Hence no c>0 allows f(x) =0 for all \(x\ge 0\). (proved)
Solution:
If the given equation holds for some constant c>0 then,
f(x) = \(\cos\sqrt{x}-\cos\sqrt{x+c}=0\) for all \(x\ge 0\)
\(\Rightarrow 2\sin\frac{\sqrt{x+c}+\sqrt{x}}{2}\sin\frac{\sqrt{x+c}-\sqrt{x}}{2}=0\)
Putting x=0, we note
\(\Rightarrow\sin^2\frac{\sqrt{c}}{2}=0\)
As \(c\not=0\)
\(\sqrt{c}=2n\pi\)
\(\Rightarrow c=4n^2\pi^2\)
We put n=1 and x=\(\frac{\pi}{2}\) to note that f(x) is not zero.
Hence no c>0 allows f(x) =0 for all \(x\ge 0\). (proved)
The INEQUALITY quest!
Inequalities are important for olympiads and I.S.I., C.M.I. entrances. Sometimes they appear as standalone problems. However mostly they are clubbed with other problems (geometry, calculus etc). The Cheenta Inequality course is a 7-session-super-course to achieve excellence and efficiency in solving inequalities. The course work consists of 600 problems on inequalities with interdisciplinary treatment in certain special areas. For example while discussing triangular inequality or Euler's inequality we bring geometry in action. Similarly we discuss Lagrange's mean value theorem, idea of limit while discussing sequential inequalities, convexity of function and so on.
The 600 problems are sourced from:
Then we move over to Jensen (convexity etc.) Rearrangement, Schur, Murihead and some other not-so-trivial-looking inequalities. Triangular inequality and application of calculus in understanding inequalities is discussed in the final phase.
The Kiran Kedlaya Inequality pack and similar courses available freely online were helpful. We tried to incorporate the best part of all of them. A course on inequality must be holistic as well as efficient. We must not loose our focus from problem-solving techniques. At the same-time the course must bear an elegance of the art-form.
The 600 problems are sourced from:
- 70 problems from Little Mathematical Library
- 125 problems from Arthur Engel
- 100 problems from Excursion in Math and Challenges and Thrills of Precollege Math
- 300 problems from Inequalities: An Approach Through Problems By Venkatchala, International Math Olympiads and other national olympiads.
Then we move over to Jensen (convexity etc.) Rearrangement, Schur, Murihead and some other not-so-trivial-looking inequalities. Triangular inequality and application of calculus in understanding inequalities is discussed in the final phase.
The Kiran Kedlaya Inequality pack and similar courses available freely online were helpful. We tried to incorporate the best part of all of them. A course on inequality must be holistic as well as efficient. We must not loose our focus from problem-solving techniques. At the same-time the course must bear an elegance of the art-form.
Wednesday, 11 May 2011
I.S.I. 10+2 Subjectives Solution (2 problems)
P164. Show that the area of the bounded region enclosed between the curves \(y^3=x^2\) and \(y=2-x^2\), is \(2\frac{2}{15}\).
Solution:
Note that \(y=x^{\frac{2}{3}}\) is an even function (green line).
P165. Find the area of the region in the xy plane, bounded by the graphs of \(y=x^2\), x+y = 2 and \(y=-\sqrt {x}\)
Solution:
The parabola and straight line intersects at (1,1) (we find that by solving the \(y=x^2\) and x+y=2)
Thus the area is found by adding area under parabola (from 0 to 1) and area under straight line (from 1 to 2).
\(\int^1_0 x^2\,dx=\left[\frac{x^3}{3}\right]^1_0=\frac{1}{3}\) (area under parabola)
area under straight line above 'x' axis is the triangle with height 1 unit and base 1 unit (from x=1 to x=2, area under x+y=2)
that area = \(\frac{1}{2}\times 1\times 1=\frac{1}{2}\)
Thus total area above x axis (of the required region) is \(\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)
Now we come to the region below 'x' axis.
x+y = 2 and \(y=-\sqrt{x}\) intersect at (4, -2) (found by solving the two equations). We calculate the area under the curve \(y=-\sqrt{x}\) from x=0 to x=4 and subtract from it the area of the triangle with base from x=2 to x=4 and height =2 (hence the area of the triangle to be subtracted is 2 sq unit).
Area under the square root curve is
\(|\int^4_0 -\sqrt{x}\,dx|=\int^4_0 \sqrt{x}\,dx= \left[\frac {x^{\frac{1}{2}+1}} {\frac{1}{2}+1}\right]^4_0\).
=\(\frac {2}{3}\times 8=\frac {16}{3}\)
Delete 2 square unit from this and add the area computed before (above 'x' axis).
Area = \(\frac {16}{3} - 2 + \frac{5}{6} = \frac{25}{6}\) (ANS)
Solution:
Note that \(y=x^{\frac{2}{3}}\) is an even function (green line).
P165. Find the area of the region in the xy plane, bounded by the graphs of \(y=x^2\), x+y = 2 and \(y=-\sqrt {x}\)
Solution:
The parabola and straight line intersects at (1,1) (we find that by solving the \(y=x^2\) and x+y=2)
Thus the area is found by adding area under parabola (from 0 to 1) and area under straight line (from 1 to 2).
\(\int^1_0 x^2\,dx=\left[\frac{x^3}{3}\right]^1_0=\frac{1}{3}\) (area under parabola)
area under straight line above 'x' axis is the triangle with height 1 unit and base 1 unit (from x=1 to x=2, area under x+y=2)
that area = \(\frac{1}{2}\times 1\times 1=\frac{1}{2}\)
Thus total area above x axis (of the required region) is \(\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\)
Now we come to the region below 'x' axis.
x+y = 2 and \(y=-\sqrt{x}\) intersect at (4, -2) (found by solving the two equations). We calculate the area under the curve \(y=-\sqrt{x}\) from x=0 to x=4 and subtract from it the area of the triangle with base from x=2 to x=4 and height =2 (hence the area of the triangle to be subtracted is 2 sq unit).
Area under the square root curve is
\(|\int^4_0 -\sqrt{x}\,dx|=\int^4_0 \sqrt{x}\,dx= \left[\frac {x^{\frac{1}{2}+1}} {\frac{1}{2}+1}\right]^4_0\).
=\(\frac {2}{3}\times 8=\frac {16}{3}\)
Delete 2 square unit from this and add the area computed before (above 'x' axis).
Area = \(\frac {16}{3} - 2 + \frac{5}{6} = \frac{25}{6}\) (ANS)
Tuesday, 10 May 2011
So you have got a year?!!
That is a good start. And a demanding one. All good starts are demanding by birth-right. They ask you to do more in the subsequent days. This article is mainly targeted at class 12 pass-outs who are targeting I.S.I. 2012 (or those 12th graders who are able to devote some serious time to mathematics).
Target to solve 100 problems a day (no less). You DO NOT HAVE 365 DAYS. Actually it's about 360 days (counting 2012 to be a leap year and assuming I.S.I. entrance to be held in first week of May). So really we are looking at some 36000 problems in the coming year and trust me that is sufficient to get you there.
Wake up at 5 in the morning. Do about 5 hrs of mathematics. In the afternoon devote 2-3 hours. Same in the evening. That is sufficient for 100 problems a day. That is sufficient as far as time management is concerned.
The books you need to solve->
1. TMH IIT Math and M.L. Khanna IIT Math books make about 20000 problems together. They are important because they are comprehensive.
2. I.S.I. 10+2 Test of Mathematics has about 1500 problems (along with Test Papers)
3. Excursion in Mathematics + Challenges and Thrills in Pre college mathematics together have about 2000 problems.
4. Algebra - Hall and Knight (or better Barnard Child), Complex Numbers from A to Z, (2000 problems)
5. Trigonometry - Loney (about 1000 problems)
6. Coordinate Geometry - Loney (about 1000 problems)
7. Calculus - A combined effort of Apostle, Maron, Piscunov, Tarasov (about 4000 problems)
8. Mathematical Circles, Combinatorics by Brualdi, Selected Problems by yaglom, Problem Solving Strategies by Arthur Engel, IMO compendium, Functional Equation by Venkatchala, Inequalities of Little Mathematical Library and Venkatchala, Number Theory by Burton or Zuckermann should account for the rest 4000-5000 problems.
Note that some problems will need superb intellectual effort, some will ask for tidy computation. So the key is to distribute all kinds of problems in a day. Try about 20 challenging problems per day. Rest 80 should be normal (or subnormal) stuff.
All the best and keep working!
Target to solve 100 problems a day (no less). You DO NOT HAVE 365 DAYS. Actually it's about 360 days (counting 2012 to be a leap year and assuming I.S.I. entrance to be held in first week of May). So really we are looking at some 36000 problems in the coming year and trust me that is sufficient to get you there.
Wake up at 5 in the morning. Do about 5 hrs of mathematics. In the afternoon devote 2-3 hours. Same in the evening. That is sufficient for 100 problems a day. That is sufficient as far as time management is concerned.
The books you need to solve->
1. TMH IIT Math and M.L. Khanna IIT Math books make about 20000 problems together. They are important because they are comprehensive.
2. I.S.I. 10+2 Test of Mathematics has about 1500 problems (along with Test Papers)
3. Excursion in Mathematics + Challenges and Thrills in Pre college mathematics together have about 2000 problems.
4. Algebra - Hall and Knight (or better Barnard Child), Complex Numbers from A to Z, (2000 problems)
5. Trigonometry - Loney (about 1000 problems)
6. Coordinate Geometry - Loney (about 1000 problems)
7. Calculus - A combined effort of Apostle, Maron, Piscunov, Tarasov (about 4000 problems)
8. Mathematical Circles, Combinatorics by Brualdi, Selected Problems by yaglom, Problem Solving Strategies by Arthur Engel, IMO compendium, Functional Equation by Venkatchala, Inequalities of Little Mathematical Library and Venkatchala, Number Theory by Burton or Zuckermann should account for the rest 4000-5000 problems.
Note that some problems will need superb intellectual effort, some will ask for tidy computation. So the key is to distribute all kinds of problems in a day. Try about 20 challenging problems per day. Rest 80 should be normal (or subnormal) stuff.
All the best and keep working!
Thursday, 5 May 2011
INDIAN MATH IVY
Indian Statistical Institute (I.S.I.), Chennai Mathematical Institute (C.M.I.) and Institute of Mathematics and Application (I.M.A.) can be regarded as three Indian institutions that provided world class mathematics course at undergraduate level. The B.Stat Course at I.S.I. is also world famous. The courses at C.M.I. and I.M.A. have computer science as second major.
Each of these three institutes conduct entrance test at the month of May. The prospective students are expected to know more rigorous mathematics than the IIT's. Apart from High School math, the entrance test syllabus includes Math Olympiad curriculum- plane geometry, combinatorics, number theory, inequalities, functional equation, polynomials and more.
Indian National Math Olympiad qualified students are not required to take the Entrance test. They will directly appear for the interview. Yes, there is an interview after the entrance test where students are asked math related questions.
The entrance tests are on Mathematics only. There is no age bar and non science students may also sit in the test provided he/she had pure maths in High School. The alumni of these three institutes are working in the most prestigious labs, universities and corporate sectors of the world. India hopes to regenerate it's mathematical fervor through state-of-art institutes like these.
Preparatory guidance for I.S.I., C.M.I. and I.M.A. entrances (and Math Olympiads) are difficult to find. Check out our website for some help.
Each of these three institutes conduct entrance test at the month of May. The prospective students are expected to know more rigorous mathematics than the IIT's. Apart from High School math, the entrance test syllabus includes Math Olympiad curriculum- plane geometry, combinatorics, number theory, inequalities, functional equation, polynomials and more.
Indian National Math Olympiad qualified students are not required to take the Entrance test. They will directly appear for the interview. Yes, there is an interview after the entrance test where students are asked math related questions.
The entrance tests are on Mathematics only. There is no age bar and non science students may also sit in the test provided he/she had pure maths in High School. The alumni of these three institutes are working in the most prestigious labs, universities and corporate sectors of the world. India hopes to regenerate it's mathematical fervor through state-of-art institutes like these.
Preparatory guidance for I.S.I., C.M.I. and I.M.A. entrances (and Math Olympiads) are difficult to find. Check out our website for some help.
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