The question one naturally asks when it comes to lists like this is the criteria used by the author to organize such lists, well, I...
The question one naturally asks when it comes to lists like this is the criteria used by the author to organize such lists, well, In my own opinion, for an exam to be considered difficult, the following factors has to be put into consideration as well.
- The age of students sitting for(or allowed to) sit for that particular exam. Simply because what might be considered difficult to high school pupils might really be elementary to Phd students.
- The difficulty of the problems. This, I believe, is the most important factor which one can argue to be an indispensable criteria, for some exams requires a exorbitant amount of preparations while others do not.
All protocols observed, here are the top 3 most difficult exams.
3. IIT-JEE and Gaokao.
IIT-JEE and Gaokao are both held in India and China respectively, they are considered to be the most difficult entrance examination for pre-colloge students in the world. Excellence in these exams demands ridiculous amount of preparation, time is usually short and requires superhuman ability to read, understand and solve the problems in a matter of seconds. It is the most prestigious entrance examinations in the world, the pressure is so high that students attempt suicide out of frustration, especially Chinese students.
2. Putnam
The William Lowell Putnam Mathematical Competition is a highly challenging, proof-oriented mathematics competition for undergraduate students in North America.
Top scoring students on the Putnam exam are named Putnam Fellows.
The examination is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually zero or one point out of 120 possible, and there have been only four perfect scores as of 2010. In 2003, of the 3,615 students taking the exam, 1024 (28%) scored 10 or more points, and 42 points was sufficient to make the top percentile.
The competitors describe it as "like hitting your head on a brick".
The problems could usually be solved with just basic knowledge if elementary Mathematics but requires extensive creative thinking.
1. IMO.
Yeah, the International Mathematical Olympiad is the most difficult of all other science Olympiads.
The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required.
The exam is open for High school students under the age of 20 and not registered into any tertiary institution.
This is no ordinary High School competition, handling IMO level problems requires a ridiculous amount of preparation and extensive knowledge of theorems that are not even covered in the Undergraduate Mathematics curriculum, their Algebra, Number Theory and Geometry is impenetrable to the average undergraduate student specializing in Mathematics. And problems on Combinatorics requires extensive creative thinking.
- The age of students sitting for(or allowed to) sit for that particular exam. Simply because what might be considered difficult to high school pupils might really be elementary to Phd students.
- The difficulty of the problems. This, I believe, is the most important factor which one can argue to be an indispensable criteria, for some exams requires a exorbitant amount of preparations while others do not.
All protocols observed, here are the top 3 most difficult exams.
3. IIT-JEE and Gaokao.
IIT-JEE and Gaokao are both held in India and China respectively, they are considered to be the most difficult entrance examination for pre-colloge students in the world. Excellence in these exams demands ridiculous amount of preparation, time is usually short and requires superhuman ability to read, understand and solve the problems in a matter of seconds. It is the most prestigious entrance examinations in the world, the pressure is so high that students attempt suicide out of frustration, especially Chinese students.
2. Putnam
The William Lowell Putnam Mathematical Competition is a highly challenging, proof-oriented mathematics competition for undergraduate students in North America.
Top scoring students on the Putnam exam are named Putnam Fellows.
The examination is considered to be very difficult: it is typically attempted by students specializing in mathematics, but the median score is usually zero or one point out of 120 possible, and there have been only four perfect scores as of 2010. In 2003, of the 3,615 students taking the exam, 1024 (28%) scored 10 or more points, and 42 points was sufficient to make the top percentile.
The competitors describe it as "like hitting your head on a brick".
The problems could usually be solved with just basic knowledge if elementary Mathematics but requires extensive creative thinking.
1. IMO.
Yeah, the International Mathematical Olympiad is the most difficult of all other science Olympiads.
The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required.
The exam is open for High school students under the age of 20 and not registered into any tertiary institution.
This is no ordinary High School competition, handling IMO level problems requires a ridiculous amount of preparation and extensive knowledge of theorems that are not even covered in the Undergraduate Mathematics curriculum, their Algebra, Number Theory and Geometry is impenetrable to the average undergraduate student specializing in Mathematics. And problems on Combinatorics requires extensive creative thinking.
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