I will be carrying a check worth ~ 20,000 $ to pay my fees at CMU.
Will the huge amount cause any problem at customs? I will have to declare the check at customs right? Is there any precaution I need to take or any pointer?
If you are carrying above $10,000 you must declare it in the customs form.
Refer to the following Q&A from TSA.
Q. Will I be delayed during screening if I am carrying large amounts of cash?
A. TSA does not restrict passengers from carrying cash through our security checkpoints. However, when TSA discovers a passenger carrying a sum of cash that appears to be in excess of $10,000 and the passenger is traveling to a location outside of the United States, TSA may notify U.S. Customs and Border Protection (CBP) to ensure compliance with international currency-reporting requirements. Also, TSA may notify law enforcement officers if cash is discovered during the security screening process that appears to be related to criminal activity based on factors such as the quantity, packaging, circumstances of discovery, or the method by which it is carried.
Here is another answer from CBP.
Q. Does a foreign visitor have to carry a certain amount of money to enter the U.S.?
Yes. Travelers visiting the U.S. from a foreign country must be able to prove to a CBP Officer that they have sufficient funds (i.e. credit cards, cash, travelers checks, money orders etc.) to cover their travel, lodging, entertainment, meals, etc. in order to be admitted into the U.S.
CBP Officers are aware that there may be circumstances in which a traveler may have limited funds. In those cases they will determine the admissibility of the traveler based on the information provided to support the reason the traveler has insufficient funds.
If you have invited someone to visit you with the understanding that you will be hosting them at your house and providing meals, etc., it is advised that you confirm your invitation in writing so that they have something to show the CBP Officer. The letter should include your full name and address. This will not guarantee their admission into the U.S., but it will help the CBP Officer fully assess their situation.
Go to New Student Pre-Departure Orientation Page to to get more tips.