Dr. Alexei Krouglov was born in St. Petersburg, Russia. He graduated from the math department of St. Petersburg State University (Russia) with a master's degree. Afterwards he received a Ph.D. degree in mathematical economics from St. Petersburg State University. He was working as Associate Professor of Mathematics at Academy of Public Administration in St. Petersburg. Later he immigrated to Toronto, Canada. In Canada he has been working in the IT field. He also continued his research in the field of Mathematical Economics and published a book "Mathematical dynamics of economic markets." The current book is a continuation of the aforesaid book.