The main goal of this series of conferences is to bring together experts and prominent scientists in order to foster the exchange of ideas and techniques, as well as to discuss in formal and informal atmosphere the modern trends in application of mathematics in various fields of engineering, mechanics, wave motion, physics, chemistry, economics, biology, ecology, etc. The scientific program of the 4rd edition of the conference included 67 presentations. Several world renown specialists delivered plenary and keynote lectures. In addition to the regular sessions of invited and submitted talks, two special and one poster session diversified the AMiTaNS’12 program. In order to broaden the scope of the program with talks whose authors were not able to travel, we have organized a telebridge between the conference site and Japan. The presentations were in real time and were attended by theparticipants in interactive mode. In addition, various social activities during the event helped create useful new personal contacts and to initiate possible collaboration on existing and new projects. During the reviewing procedure, fruitful and constructive discussions between the contributors, editors and anonymous referees helped the authors to revise and improve their contributions essentially. The result of this vigorous interaction is the presented here volume of circa 400 pages. The editor hope that publishing these proceedings will serve to promote the application of mathematics in various fields. A wide spectrum of professionals will find something interesting in the rich collection of papers of 4rd AMiTaNS’12.