Mathematics

Complex Numbers and Quadratic Equations 97 5.1 Introduction 97 5.2 Complex Numbers 97 5.3 Algebra of Complex Numbers 98 5.4 The Modulus and the Conjugate of a Complex Number 102 5.5 Argand Plane and Polar Representation 104 5.6 Quadratic Equations 108

Principle of Mathematical Induction 86 4.1 Introduction 86 4.2 Motivation 87 4.3 The Principle of Mathematical Induction 88

Trigonometric Functions 49 3.1 Introduction 49 3.2 Angles 49 3.3 Trigonometric Functions 55 3.4 Trigonometric Functions of Sum and Difference of Two Angles 63 3.5 Trigonometric Equations 74

Relations and Functions 30 2.1 Introduction 30 2.2 Cartesian Product of Sets 30 2.3 Relations 34 2.4 Functions 36

Sets 1 1.1 Introduction 1 1.2 Sets and their Representations 1 1.3 The Empty Set 5 1.4 Finite and Infinite Sets 6 1.5 Equal Sets 7 1.6 Subsets 9 1.7 Power Set 12 1.8 Universal Set 12 1.9 Venn Diagrams 13 1.10 Operations on Sets 14 1.11 Complement of a Set 18 1.12 Practical Problems on Union and Intersection of Two Sets 21

Probability-1, Permutations and Combinations, Selections with repetition when order is important, Selections without repetition when order is important, Selections without repetition when order is not important,

1729 is the natural number following 1728 and preceding 1730. It is known as the Hardy-Ramanujan number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation: I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." The two different ways are:1729 = 13 + 123 = 93 + 103 The quotation is sometimes expressed using the term "positive cubes", since allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a divisor of 1729):91 = 63 + (−5)3 = 43 + 33 Numbers that are the smallest number that can be expressed as

In 2012, the Indian government declared 22 December to be National Mathematics Day. This was announced by Prime Minister Manmohan Singh on 26 February 2012 at Madras University, during the inaugural ceremony of the celebrations to mark the 125th anniversary of the birth of the Indian mathematical genius Srinivasan Ramanujan (22 Dec 1887- 26 Apr 1920). On this occasion Singh also announced that 2012 would be celebrated as the National Mathematics Year. Since then, India's National Mathematics Day is celebrated every 22 December with numerous educational events held at schools and universities throughout the country. In 2017, the day's significance was enhanced by the opening of the Ramanujan Math Park in Kuppam, in Chittoor, Andhra Pradesh. Srinivasa Ramanujan ( 22 December 1887 – 26 April 1920) was an Indian mathematician who lived during the British Rule in India. Though he had almost no formal training in pure mathematics, he made substantial contri