MATHEMATICAL OLYMPIAD

History of mathematical Olympiad:

            A mathematical Olympiad problem solving competition open to all ‘athletes’ the aim of the competition is to test innate problem solving skills. It is created in 1977 by Dr.George lenchner, an internationally knows mathematics educator, mathematics O

The main international mathematical Olympiad is the international mathematical Olympiad (IMO), a competition held annually since 1959.

Objectives of Mathematical Olympiad:

1.       To stimulate Enthusiasm and love and interest for mathematics.

2.       To introduce important mathematical concepts.

3.       To teach major strategies for problem solving.

4.       To develop mathematical flexibility in solving problem.

5.       To strengthen mathematical instruction

6.       To foster mathematical creativity and ingenuity.

7.       To provide for the satisfaction, Joy and Thrill of meeting challenges.

Organization of the mathematics Olympiad programme in India:

The mathematical Olympiad programme in India leading in participation in the IMO is currently being organized by the “Homi Bhabha” center for science education (HBCSE) on behalf of the national board of higher mathematics (NBHM) and founded by the department of Atomic Energy (DAE).

The correct office bearers in charge of the programmes are:

-          National Co-ordinate-Delhi

-          HBCSE Director – Mumbai

-          Member Secretary, NBHM – Mumbai

-          Scientists’ In-charge-Bangalore.

Procedure for Participation:

There is a three-step procedure in order to represent India of IMO.

1. Regional Mathematical Olympiad (RMO):

      In India, CBSE & Navodaya Vidyalaya samiti are designated and also 21 different regions in country are designated. All school students’ classes XI & XII are eligible to appear in RMO Exam held b/w September and the December.

2. Indian National Mathematical Olympiad (INMO):

       INMO is held on 1^st Sunday of Feb. each year at center of each region. INMO is open only to those selected through RMO from their respective regions or through RMO conducted by CBSE or NVS.

3. International Mathematical Olympiad Training Camp (IMOTC)

       The awardees of INMO are invited to a month – long training camp held in May, June. Each year at HBCSE Mumbai. Training facility from all over the country imparts problem solving skills along necessary theoretical background to the awardees.

Syllabus for Mathematical Olympiads:

There is no prescribed syllabus for mathematical Olympiads. The topics are taken from pre-college mathematics. The areas covered are Arithmetic of Integers, Geometry, Quadratic equations and expressions, Trigonometry, co-ordinate Geometry etc., the major areas from which problems are chosen are number theory, Geometry, Algebra & combinatory etc. The difficulty level increases from RMO to INMO to IMO.

Importance of Mathematics Olympiad

1. It Provide opportunity for gifted children.
2. It develops competitive spirit.
3. It identifies gifted children.
4. Encourage and award gifted children.
5. Expose children to regional, national and international levels.
6. To help children to know their capabilities.
7. To nurture their talents.
8. To enhance their critical and problem-solving skills.

Example problems for Mathematical Olympiad:

1.       Let a, b, c be +Ve real numbers, such that abc=1 prove that (a-1+1/b) (b-1+1/c) (c-1+1/a) < 1

2.       Deter mine all functions f; R-R such that

f (x-f(y)) = f(f(y))+x+(y)+f(x)-1 for all real numbers xy

3.   Find all primes pand q such that, p2+7pq+q2 is square of an integer.

4.   Find all real values of (a) for which the equation x4-2ax²+x+a²-a=0 has all its roots real.

5.   Let ABC be a         in which AB = BC and            

                      CAB= 90⁰ suppose M and N are points on the










 hypothec

On use BC such that   BM+CN=MN, Prove that  MAN=45⁰

 6.     Special Programmes in Teaching Mathematics

      1. Defects in the present day Teaching Mathematics in schools and their possible Remedies.

            It should be frankly admitted that the present-day teaching of Mathematics is far from being satisfactory.

Everybody has a complaint against the teaching of mathematics. It is dull, boring, difficult and useless from the point of view of the learner. “It is too remote from life to the student”. The teachers complain of excessive work load and lack of facilities in the form of aids and equipment.

Defects and possible Remedies:

1. Teacher’s Qualification:

It is a common defect in our educational set-up that most of the subject teachers are not adequately qualified in the subject concerned, without proper qualification and proper training. They fail to do justice to the subject. An adequate, high qualification of the teacher develops self-confidence in him and serves as a source of inspiration to his students. The teacher must be nature in his subject. He must possess real knowledge of and insight on to the processes of mathematics and their effective teaching.

2. Teachers Borden:

Teacher cannot adopt and prepare for, effective methods, as he has no spare time. His burden does not allow him time to remove individual difficulties. It should be lightened to enable him to show his originality and initiative.

3. Teachers Salary:

Mathematics or other teacher economic position is not good. He remains worried, and a worried teacher cannot give his best to the learners. He is a frustrated, discontented and half-hearted worker. In these hard days, he must be suitably paid.

3.      Teacher’s Attitude:

4.        Teacher does not have genuine love for his mathematics subjects and profession. He lacks faith in the utility of the mathematics subject, and therefore, cannot create interest among the students. A teacher’s love for his Job and subject should also be ascertained before giving him his duty.

5. Lack of purpose:

        The students do not recognize the purposes behind the study of the topics of mathematics. The particular and general aims of every topic should be emphasized effectively. If the work lacks purpose, it is the teacher’s duty to make it purposeful. The purpose should be attractive to stimulate the students to work hard. This misconception should be up rooted from the minds of the parents and pupils that most of the mathematics taught in the schools is not purposeful.

6. Lack of Equipment:

There is a serious lack of mathematical apparatus in the schools. Without equipment, the subject becomes abstracts. The establishment of a mathematical laboratory will remove this defect.

7. Method of Teaching:

       The powers of thinking, understanding and retention are not thus developed in the students. If the pupils do not show any interest in the subject (maths) if can be created not by blind memorizing, but by shifting the methods. The authorities run after showy results which are obtainable only through cramming. They have no appreciation for good mathematical teaching. The remedy necessitates a fundamental change in value and methods.

8. Large classes:

It is a general defect. No individual attention cannot be paid. It becomes difficult for the teacher to establish close contacts with the students. Teacher cannot easily Judge the capacities of the individuals. This defect can be removed only by limiting the number of students in each class up to a maximum of Thirty-five.

9. Text – Books:

The traditional style of the syllabus also affects text-books adversely. The illustrations and problems give in the text-books are divorced from actual life. The mathematics text-book material is made available in a readymade form which goes against thinking, discovery and originality. Text books should give possibilities of correlation, application in practical life, use of aids, activities, projects etc., concerning every topic in mathematics. The arrangement of the subject matter should both and laboratories.

10. Libraries and Laboratories.

11. Examinations.

12. Syllabus

13. Mathematical Language.

14. Rigor in study etc.

      Even after removing the above mentioned defects completely there will be a scope for improvement.