CO1: Understand the concepts in Averages of arithmetical function.
CO2: Apply to the distribution of lattice points visible trona the origin, The average order of
μ and
, The partial sums of dirichlet product & Applications to μ
and
.
CO3: Discuss Some elementary theorems on the distribution of prime numbers.
CO4: Classify chebyshev's functions-ψ (x) and θ(x and also a Relation connecting θ and
π.
CO5: Analyze Shapiro's Tauberian theorem.
CO6: Intrepret the partial sums of the mobius function-Selberg Asymptotic formula.
CO7: Analyze Finite Abelian groups and their character.
CO8: Evaluate the orthogonality relations for characters Dirichlet characters-Sums.
involving Dirichlet characters the non vanishing of L(1,χ) for real non principal χ.
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Identify the algebraic structures, groups, cyclic groups, permutation groups, normal subgroups, rings, fields.
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Apply Cayley’s theorem and Lagrange’s theorem.
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CO 1: Understand basic concepts of vector spaces and Linear Transformation with a matrix approach.
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CO 2: Remember the Eigen values and Eigen vectors of a given matrix and Evaluate Rank of a matrix.
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CO 3: Analyse the process of diagonalization.
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CO 4: Understand the properties of inner product spaces and Apply Gramschmdth’s process to orthgonalize sets.
CO1: Expalin basic concepts of vector spaces with a matrix approach.
CO2: Calculate the eigen values and eigen vectors of a given matrix.
CO3: Expalin the process of diagonaliztion of a matrix.
CO4: Evaluate Orthogonal basis set using Gram-schmidt process for a vector space.
CO 1: Interpret the successive differentiation, Partial derivatives, total derivatives of the given function of two variables.
CO2: Apply the concepts to find maximum and minimum values of a function and to expand functions as power series.
CO3: Examine the concepts of curvature and its derivatives.
CO4: Evaluate the length of plane curves and volume of surface of revolution.
Course Objectives:
1. Exposing the students to learn some basic algebraic structures like groups and rings.
2. Training the students to construct the proofs of theorems in a systematic way.
Course Outcomes:
CO 1: Classify sets into mathematical structures such as groups, subgroups and understand their elementary properties.
CO 2: Understand properties of special classes of groups such as cyclic and permutation groups.
CO 3: Learn to construct the proofs of Lagrange‘s theorem, Cayley’s theorem and know their application.
CO 4: Define homomorphism and study their properties.