수(數)= number, several, count
수학(number+study)= mathematics
수학자(mathematics+person)= mathematician
숫자(number+character)= a number
소수(small+number)= decimal, fraction
지수(finger+number)= index number
배수(multiple times+number)= multiple
산수(calculate+number)= arithmetic
대수(replace+number)= algebra
수열(number+to arrange in order)= progression
Additionally you can also use it as a prefix attached to a (round) number.
(Exemples will clarify)
수백 달러= hundreds of dollars
수천 명= thousands of people
수만 년= tens of thousands of years
수백만 원= millions of wons
Can also be uses as a prefix before 년, 월, 일,시간,세기, 개...to mean several (sth.)
수년= several years
수세기= several centuries
수없이= unnumerably
수많은= a lot of, lots of, many
그곳에는 수많은 사람들이 있었다.
There were a lot of people there.
나는 아직 할 일이 수없이 많다.
I still have a million of things to do.