Curriculum
Title Sequences and Series (09010401)
S.N  Unit  Time (Hrs)  Content of the topics  Learning objects  Teaching Guidelines  Methodology 
1  one  15  Boundedness of the set of real numbers;
least upper bound, greatest lower bound of a set, neighborhoods, interior points, isolated points, limit points, open sets, closed set, interior of a set,closure of a set in real numbers and their properties. BolzanoWeiestrass theorem, Open covers,Compact sets and HeineBorel Theorem. 
Students will be able to
1.Boundedness of the set of real numbers; least upper bound, greatest lower bound of a set, 2.BolzanoWeiestrass theorem. 3.HeineBorel Theorem.

Lecture should be effective so that student can grasp the topics easily.  1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment. 
2  Two  15  Sequence: Real Sequences and their convergence,
Theorem on limits of sequence, Bounded and monotonic sequences, Cauchy’s sequence, Cauchy general principle of convergence,
Subsequences, Subsequential limits.
Infinite series: Convergence and divergence of Infinite Series, Comparison Tests of positive terms Infinite series, Cauchy’s general principle of Convergence of series, Convergence and
divergence of geometric series, Hyper Harmonic series or pseries.
Infinite series: DAlembert’s ratio test,
Raabe’s test, Logarithmic test, de Morgan and Bertrand’stest, Cauchy’s Nth root test, Gauss Test, Cauchy’s integral test, Cauchy’s condensation test. 
Students will be able to
1. Sequence,. Cauchy general principle of convergence, 2. Hyper Harmonic series or pseries. 3. Raabe’s test, Logarithmic test, de Morgan and Bertrand’stest 
Lecture should be effective so that student can grasp the topics easily.  1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment

3  Three  15  Alternating series, Leibnitz’s test, absolute and conditional convergence, Arbitrary series:
abel’s lemma, Abel’s test, Dirichlet’s test, , Dirichlet’s theorem, Riemann’s Rearrangement theorem, Pringsheim’s theorem (statement only), Multiplication of series, Cauchy product of series, (definitions and examples only) Convergence and absolute convergence of infinite products.

To make students familiar with Alternating series, Leibnitz’s test, absolute and conditional convergence, Arbitrary series: Multiplication of series, Cauchy product of series, (definitions and examples only)
Convergence and absolute convergence of infinite products

Lecture should be effective sothat student can grasp the topics easily.

1. Lecture.
2. Seminar. 3. Discussion/Interaction with Students. 4. Assignment. 5. Discussion on Assignment. 6. Evaluation of Assignment 