Ganita Kaumudi
Ganita Kaumudi is a treatise on mathematics written by Indian mathematician Narayana Pandita in 1356. It was an arithmetical treatise alongside the other algebraic treatise called "Bijganita Vatamsa" by Narayana Pandit. It was written as a commentary on the "Līlāvatī" by Bhāskara II. Contents. Gaṇita Kaumudī contains about 475 verses of "sūtra" (rules), and 395 verses of "udāharaṇa" (examples). It is divided into 14 sections (chapters) known as "vyavahāra"s: 1. Prakīrṇaka-vyavahāra. Weights and measures, length, area, volume, etc. It describes addition, subtraction, multiplication, division, square, square root, cube and cube root. The problems of linear and quadratic  equations described here are more complex than in earlier works. 63 rules and 82 examples 2. Miśraka-vyavahāra. Mathematics pertaining to daily life: “mixture of materials, interest on a principal, payment in instalments, mixing gold objects with different purities and other problems pertaining to linear indeterminate equations for many unknowns” 42 rules and 49 examples 3. Śreḍhī-vyavahāra. Arithmetic and geometric progressions, sequences and series. The generalization here was crucial for finding the infinite series for sine and cosine. 28 rules and 19 examples. 4. Kṣetra-vyavahāra. Geometry. 149 rules and 94 examples. Includes special material on cyclic quadratilerals, such  as the “third diagonal”. 5. Khāta-vyavahāra. Excavations. 7 rules and 9 examples. 6. Citi-vyavahāra. Stacks. 2 rules and 2 examples. 7. Rāśi-vyavahāra. Mounds of grain. 2 rules and 3 examples. 8. Chāyā-vyavahāra. Shadow problems. 7 rules and 6 examples. 9. Kuṭṭaka. Linear integer equations. 69 rules and 36 examples. 10. Vargaprakṛti. Quadratic. 17 rules and 10 examples. Includes a variant of the Chakravala method. Ganita Kaumudi contains many results from continued fractions. In the text Narayana Pandita used the knowledge of simple recurring continued fraction in the solutions of indeterminate equations of the type formula_1. 11 . Bhāgādāna. Factorization. Contains Fermat's factorization method. 11 rules and 7 examples. 12. Rūpādyaṃśāvatāra. Contains rules for writing a fraction as a sum of unit fractions. 22 rules and 14 examples. Unit fractions were known in Indian mathematics in the Vedic period: the Śulba Sūtras give an approximation of equivalent to formula_2. Systematic rules for expressing a fraction as the sum of unit fractions had previously been given in the "Gaṇita-sāra-saṅgraha" of Mahāvīra (). Nārāyaṇa's "Gaṇita-kaumudi" gave a few more rules: the section "bhāgajāti" in the twelfth chapter named "aṃśāvatāra-vyavahāra" contains eight rules. The first few  are: 13. Aṅka-pāśa. Combinatorics. 97 rules and 45 examples. Generating permutations (including of a multiset), combinations, partitions of a number, binomial coefficients, generalized Fibonacci numbers. Narayana Pandita noted the equivalence of the figurate numbers and the formulae for the number of combinations of different things taken so many at a time. The book contains a rule to determine the number of permutations of "n" objects and a classical algorithm for finding the next permutation in lexicographic ordering though computational methods have advanced well beyond that ancient algorithm. Donald Knuth describes many algorithms dedicated to efficient permutation generation and discuss  their history in his book "The Art of Computer Programming". 14. Bhadragaṇita. Magic squares. 60 rules and 17 examples.