Most of the introductory courses in mathematics are primarily concerned with
computational aspects of the discipline. Typically, students learn in these courses how to
solve equations, compute derivatives and integrals, multiply matrices and find determinants
in order to answer practical questions about the real world. In this context, the main goal is
to use the mathematical methods to compute answers and we are far more concerned with
how the methods could be applied than in understanding why they are true. However, there
is another aspect of mathematics that is more fundamental, which is also more theoretical
than computational. Its primary goal is to understand mathematical structures, to prove
mathematical statements, and even to invent or discover new mathematical theorems and
theories. The mathematical techniques, procedures and methods that are used in the introductory
courses are founded on this theoretical side of mathematics which allows to prove
that the mathematical concepts and theories used in practice are true. In this course you
will learn the methods of thought that mathematicians use to prove theorems, explore mathematical
truth and create new mathematical theories. This will prepare you for advanced
mathematics and computer science courses, for you will be better able to understand proofs,
write your own proofs and think critically and inquisitively about mathematics.
computational aspects of the discipline. Typically, students learn in these courses how to
solve equations, compute derivatives and integrals, multiply matrices and find determinants
in order to answer practical questions about the real world. In this context, the main goal is
to use the mathematical methods to compute answers and we are far more concerned with
how the methods could be applied than in understanding why they are true. However, there
is another aspect of mathematics that is more fundamental, which is also more theoretical
than computational. Its primary goal is to understand mathematical structures, to prove
mathematical statements, and even to invent or discover new mathematical theorems and
theories. The mathematical techniques, procedures and methods that are used in the introductory
courses are founded on this theoretical side of mathematics which allows to prove
that the mathematical concepts and theories used in practice are true. In this course you
will learn the methods of thought that mathematicians use to prove theorems, explore mathematical
truth and create new mathematical theories. This will prepare you for advanced
mathematics and computer science courses, for you will be better able to understand proofs,
write your own proofs and think critically and inquisitively about mathematics.
- Teacher: Madjid Allili