TB Algebra & Trigonometry

SYLLABUS- ALGEBRA & TRIGONOMETRY,
Algebra
Unit-1: Sequence and its convergence (basic idea), Convergence of infinite series, Comparison test, ratio test, root test, Raabe’s test, Logarithmic ratio test, Cauchy’s condensation test, DeMorgan and Bertrand test and higher logarithmic ratio test. Alternating series, Leibnitz test, Absolute and conditional convergence, Congruence modulo m relation, Equivalence relations and partitions.
Unit-2: Definition of a group with examples and simple properties, Permutation groups, Subgroups, Centre and normalizer, Cyclic groups, Coset decomposition, Lagrange’s theorem and its consequences.
Unit-3: Homomorphism and Isomorphism. Cayley’s theorem, Normal subgroups, Quotient group, Fundamental theorem of homomorphism, Conjugacy irelation, Class equation, Direct product.
Unit-4: Introduction to rings, subrings, integral domains and fields, Characteristic of a ring, Homomorphism of rings, Ideals, Quotient rings.
Trigonometry
Unit-5: Complex functions and separation into real and imaginary parts, Exponential, Direct and inverse trigonometric and hyperbolic functions, Logarithmic functions, Gregory’s series, Summation of series.