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Course: Elements of Mathematics I Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Syllabus: Sets: Sets and their representation; Universal Set; Empty Set; Subsets; Power Set Venn Diagrams; Union and Intersection of Sets; Difference of Sets; Complements of Sets. Trigonometry: Measuring angles in radians and degrees and conversion between the two measures. Positive and negative angles. Definitions of trigonometric functions sin, cos, tan, sec, cosec and cot. Signs of trigonometric functions and sketch of their graphs. Expressing sin(x + y), cos(x + y) in terms of sinx, siny, cosx and cosy. Identities related to sinx + siny, cosx + cosy, sinx - siny, cosx - cosy, tan (x y), cot (x y). Identities related to sin2x, cos2x, tan2x, sin3x, cos3x, tan3x. Simple applications of the sine and cosine formulae. Algebra: (a) Definition of rational and irrational numbers; (b) Logarithms: Definition, simple applications, expansions of log(1+x), log(1-x) and ex; (c) Surds: definitions and applications; (d) Quadratic equations solutions; (e) Complex numbers: need for complex numbers, motivation based on the inability to get real solutions for every quadratic equation; Definition of i (v-1), polar representation, simple applications; (f) Binomial theorem: statement and proof, general and middle term in the binomial expansion, simple applications; (g) Permutations and Combinations: Fundamental principle of counting, factorial n, permutations and combinations, simple applications; (h) Sequence and Series: Basic descriptions, arithmetic and geometric progressions (AP and GP), general terms, sum of n terms, mean (AM) and Geometric Mean (GM), relation between AM and GM, sum to n terms of special series such as _i, _i2 and _i3; (i) Basic idea of mathematical induction; Coordinate Geometry: (a) Straight line: slope of a line, angle between two lines, various forms of equation of a straight line, distance of a point from a line; (b) Conic Sections: circles, ellipse, parabola, hyperbola, standard equations and simple properties. Reference Texts: Top of the page Past Exams | |||||||||
Midterm
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[Indian Statistical Institute] |