Investigating the Development of Arithmetic and Algebra in Vedic India: Tribute to Swami Dayananda Saraswati
Historical development of algebra occurred in three stages; rhetorical or prose algebra, syncopated or abbreviated algebra and symbolic algebra - known as "school algebra". The analysis of this paper suggests that the first civilization to develop symbolic algebra was the Vedic Indians. The philosophical and religious ideas influenced the development of the decimal system and arithmetic and that led to algebra. Symbolic algebra appears to be deep rooted in Vedic philosophy. The Vedic mathematic were of a high level at an early period. The Hindus applied algebra freely creating formulas that simplified calculations. In geometry and trigonometry they developed formulas useful to understand the physical world satisfying the needs of religion (apara and para vidya). Geometrical focus, logic and proof type are features of Greek mathematics "boldness of conception, abstraction, symbolism" are evident in Indian mathematics. From history, a number of implications can be drawn. Real life, imaginative and creative problems that encourage risk should be the focus in student learning; allowing students freely move between symbols, numbers and magnitudes rather than taking a static unchanging view. Concrete, pictorial and symbolic modes are present in ancient learning. Real life practical, philosophical and religious needs in concert motivated progress to symbolic algebra. The historical analysis supports the use of rich context based problems that stimulate and motivate students to raise levels higher to transfer knowledge. The road from arithmetic to algebra was clearly in line with current emphasis in mathematics education but at an early stage in human history.
Mathematics, Game Theory and Algebra Compendium
Mathematical Sciences not elsewhere classified
Algebra and Number Theory