Mathematics for machine learning
Let's see some early contributions to Calculus:
- Surya Siddhanta (scholars say c. 400-500 CE, tradition considers it before 1st century BCE):
- Introduced versine functions (utkramajya)
- Contained methods for calculating instantaneous planetary motion
- Used techniques for infinitesimal differences
- Developed procedures resembling differential calculus for astronomical calculations
- Advanced interpolation methods
- Sophisticated trigonometric systems
- Aryabhata (476-550 CE):
- Developed methods for solving differential equations
- Used sine and versine functions
- Applied infinite series expansions
- Methods for finding instantaneous velocities
- Systematic solutions for linear equations
- Advanced astronomical calculations
- Brahmagupta (598-668 CE):
- Advanced interpolation methods in Brahmasphuta Siddhanta
- Numerical methods resembling integration
- Solutions for quadratic equations
- Introduced positive/negative numbers
- Methods for calculating with zero
- Pioneering work on algebra and arithmetic
- Sripati (1019-1066 CE):
- Wrote Siddhantasekhara
- Advanced astronomical calculations
- Developed algebraic methods
- Important work on arithmetic operations
- Bhaskara II (Bhaskaracharya) (1114-1185 CE):
- Rolles' theorem (several centuries before Rolle)
- Mean value theorem concepts
- Advanced calculus-like methods in Siddhanta Siromani
- Created the chakravala method for solving equations
- Developed sophisticated astronomical calculations
- Important work on derivatives resembling Leibniz's later work
- Conceived of differential coefficient
- Advanced understanding of infinity
- Madhava (1350-1425 CE) of Kerala School:
- Infinite series expansions for trigonometric functions
- Power series expansions (predating Taylor series)
- Rigorous integration and differentiation methods
- High-precision π calculations using infinite series
- Techniques for working with infinitesimals
- Nilakantha Somayaji (1444-1544 CE):
- Key figure in Kerala School
- Advanced infinite series methods
- Expanded on Madhava's work
8.Parameshvara (1360-1455 CE):
- Major Kerala School mathematician
- Developed mean value theorem applications
- Advanced methods for infinite series
- Improved astronomical calculations
- Drig-ganita system
- Teacher of Nilakantha Somayaji
- Jyesthadeva (1500-1575 CE):
- Wrote Yuktibhasa (first calculus text in local language)
- Documented Kerala School methods
- Detailed proofs of calculus-like methods
- Systematized earlier works
- Key figure in preserving knowledge
- Putumana Somayaji (1660-1740 CE):
- Kerala School mathematician
- Advanced infinite series work
- Developed methods for integration
- Extended Madhava's techniques
- Sankara Varman (1800s CE):
- Wrote Sadratnamala
- Built on Kerala School's work
- Advanced calculus-like methods
- Preserved and systematized earlier knowledge