Algebraic Fundamentals in Artificial Intelligence for the Purpose of Undergraduate Education and Training

College algebra syllabus setting is of utmost importance for the higher education developments and students education and training, especially for the newly opened bachelor majors. In this research, we investigated the traditional syllabus of college algebra in a nationwide manner, and discussed the algebraic fundamentals in artificial intelligence. Three case studies were proposed to address the fundamentals of abstract logic thinking, data observation and knowledge inference, and data-driven thinking. Eventually, a suggested syllabus for "Advanced Algebra and its Applications in AI" was introduced subsequently for the new major of "artificial intelligence".