Introduction to Complex number
About the Course
Complex numbers form the final step in the construction of the number system in Mathematics. They are a basic tool in calculus and have a variety of applications to a number of different contexts. As a matter of fact complex numbers are covered inside Mathematics curricula of some but not all secondary schools. They used to be a standard topic in many University Courses in Mathematics, typically offered to first year undergraduates. As a consequence of the various reforms of University curricula that took place in Italy over the years, it turns out very often that this classical topic is no longer covered, simply because it does not fit in the schedule. As a consequence, the phenomenon that many instructors in scientific and technological subjects are experiencing nowadays is that many of their students at the end of their first year at University never came in touch with complex numbers. On the other hand, courses placed in the second year or later do assume acquaintance with complex numbers. The treatment of complex numbers cannot take place in these courses either, for the same reason: instructors need to cover their specific topics and often need to rush. The primary scope of this MOOC is to try to cope with a difficulty that a student might face, because of the situation described above.Science
Training hours6
LevelBeginner
Course ModeSelf Paced
Italiano
Duration4 weeks
TypeOnline
Course StatusSelf Pacement
Course Agenda
Enrollments Start
Course Opens
Course Closes
Learning outcomes
At the end of the course the students will acquire knowledge about the representations of complex numbers and the methods of operation with them; they will also be able to complete easily some standard exercises.Background and Requirements
It is taken for granted that the student is familiar with some standard concepts of secondary school mathematics. In particular: real numbers and their representation on a straight line, polynomials and algebraic fractions, trigonometry, the Cartesian plane.Textbooks
Many university manuals deal with complex numbers, but we mention two of them for the sake of brevity, the first very new and the second very old, but known to generations of students:
- M. Bramanti, C.D. Pagani, S. Salsa - Analisi Matematica 1 con elementi di geometria e algebra lineare - Zanichelli, Bologna 2014 (Capitolo 1, Sezione 8);
- G. Zwirner - Istituzioni di Matematiche - Cedam, Padova 1975.
We will also mention one of the many texts used in upper secondary education that deal with the subject:
- L. Sasso - La matematica a colori - Petrini, De Agostini Scuola - Novara 2015 (volume 4).
