Mathematics: Structure and Applications

Calculus, trigonometry, algebra, and geometry

Number theory, algebra, geometry, and analysis (correct)

Logic, differential equations, probability, and set theory

Arithmetic, calculus, statistics, and topology

Discovery of properties of abstract objects and the use of pure reason to prove them (correct)

Application of statistical methods to validate mathematical theories

Experimentation with natural phenomena to derive mathematical laws

Trial and error to find solutions for real-world problems

Reliance on empirical evidence and observations

Random guesses followed by trial and error

Repetitive calculations to verify mathematical theorems

A succession of applications of deductive rules to already established results (correct)

<p>Mathematics is essential in the natural sciences but its fundamental truths are independent from any scientific experimentation</p> Signup and view all the answers

<p>Statistics and game theory</p> Signup and view all the answers