Camp 2014
The NTU team for the IMC 2014 is:
Team leader - Dr Fedor Duzhin
Mr Johan Christnata, MAS year 3, pure mathematics track.
Ms Huang Ying, MAEC, year 2.
Ms Yang Donglei, MAS year 3, business analytics track.
Please don't relax - prepare for the competition and make NTU proud!
Week 1 (12-16 May) homework
Please choose 10 problems from the following
solve and submit to Fedor (fduzhin@gmail.com).
Please also read about the following topics (you've got to use google to find the materials):
Jordan canonical form, Cauchy Binet Formula, Schur’s determinant.
Symmetric Matrices, Hermitian matrices, properties of positive-definite matrices.
Classification of second degree curves and surfaces (analytic geometry).
Basic Abstract Algebra (only for first-year students), such as the definition of groups, rings, ideal, unique factorization domain, principal ideal domain, etc.
Group theory counting theorems, like orbit counting and Lagrange’s Index Theorem.
Uniform convergence of series and integrals and using it to differentiate and integrate with respect to a parameter.
Week 2 (19-23 May): tutorials
Tutorial 1 (Fedor): handout.
Tutorial 2 (Swee Hong): handout
Tutorial 3 (Poh Wencin): handout
Tutorial 4 (Henk Hollman): handout
Tutorial 5 - there is no class, but there is a handout for you to go through on your own.
Week 3 (26-30 May): selection tests
There will be four very hard five-hour tests and winners will be selected to represent NTU in the IMC 2014. We don't know how many students our budget allows us to send to the IMC. The main tie-breaker is your attitude: hard-working passionate students who really want to go to the IMC and convince us that they are highly motivated will have advantage over their lazy peers.
Strictly speaking, you don't have to be physically present in class. You can even write the exam staying in your home country - we trust that you don't cheat and, at the same time, we hope that the even is not so important to be worth cheating. However, we think that it is psychologically more comfortable to be physically present in class for tutorials and for exams. It's just easier for you.
After:
There will be more homework and more reading. Don't relax and solve an integral every day before you go to bed.
To see the results for the whole camp, click on the rightmost sheet called "Total". For details on grading in particular days, click on those days.
Click HERE for general comments on gradings
After the selection tests are over:
Assignment 1: solve problems of the selection test that you couldn't solve in class. Use the hints provided. We published all the problems with hints here.
Assignment 2: read some books. I have uploaded "Putnam and Beyond", "Problem Solving through Problems", and "The Math Problems Notebook" on the website. There are some useful tricks and a lot of exercises there.
Assignment 3: Try to solve and actually SUBMIT the József Wildt International Mathematical Competition 2014. we don't know if they have any prizes, but it's a competition, so it'll give you some good experience.