BSC Maths Syllabus Lucknow University

hii sir, I wants to get the BSc Mathematics syllabus of the Lucknow university will you please provide me the syllabus of the BSc Mathematics syllabus of the Lucknow university ?

[Shaleen]

University Of Lucknow or Lucknow University is a government owned Indian research university based in Lucknow. LU's old campus is located at Badshah Nagar, University Road area of the city with a new campus at Jankipuram.


the syllabus of the BSc Mathematics of the Lucknow university is as follow :


Paper I:

Topology I

Unit I
Countable and uncountable sets, Infinite sets and the axiom of choice, Cardinal numbers and its arithmetic, Schroeder-Bernstein theorem, Cantor’s Theorem and Cantor’s continuum hypothesis, Zorn’s Lemma, Well ordering principle.

Unit II
Definition and examples of topological spaces, Closed sets, Closure, Dense subsets,
Neighbourhoods, Interior, exterior and boundary, Accumulation points and derived sets, Bases and subbases, Subspaces and relative topology.

Unit III
Alternative methods of defining a topology in terms of Kuratoivski closure operator,
interior operator and neighbourhood systems, Continuous functions and
homeomorphism,First & Second countable spaces, Lindeloff theorem and separable
spaces and their relationships.

Unit IV
Separation axioms T0, T1, T2, Nets and filters, Topology and convergence of nets.
Hausdorffness and nets, Filters and their convergence, Ultra filters, Canonical way of
converting nets to filters and vice-versa.

Paper II: Advanced Algebra

Unit I
Group Theory- Series of groups, Schreier Theorem, Jordan Holder Theorem, Solvable
groups, Nilpotent groups, Insolvability of Snfor n>5

Unit II
Field Theory- Field extensions, algebraic extensions, finite extensions, Splitting fields, algebraically closed fields, Normal extensions, Separable extension, Primitive element theorem,






rest of the syllabus you may get from the below attachment that is free to Download


contact details
University Of Lucknow
Address: University Road, Hasanganj, Lucknow, Uttar Pradesh 226007
Phone: 0522 274 0086

Can you provide me the syllabus/course structure of Semester I of B.Sc. (Bachelor of Science) in Mathematics Program offered by University of Lucknow?

[Neelu Bhasin]

The syllabus/course structure of Semester I of B.Sc. (Bachelor of Science) in Mathematics Program offered by University of Lucknow is as follows:


B.A./B.Sc. I
Mathematics

Paper I (Differential Calculus)

Unit 1
Definition of a sequence, Theorems on limits of sequences, Bounded and Monotonic sequences, Cauchy's convergence criterion, Cauchy sequence, limit superior and limit inferior of a sequence, subsequence, Series of non-negative terms, convergence and divergence, Comparison tests, Cauchy's integral test, Ratio tests, Root test, Raabe's logarithmic, de Morgan and Bertrand's tests, Alternating series, Leibnitz's theorem, Absolute and conditional convergence.


Unit II
Limit, Continuity and differentiability of function of single variable, Cauchy’s definition,
Heine’s definition, equivalence of definition of Cauchy and Heine, Uniform continuity, Borel’s theorem, boundedness theorem, Bolzano’s theorem, Intermediate value theorem, Extreme value theorem, Darboux's intermediate value theorem for derivatives, Chain rule, Indeterminate forms.


Unit III
Successive differentiation, Leibnitz theorem, Maclaurin’s and Taylor’s series, , Rolle’s theorem, Lagrange and Cauchy Mean value theorems, Mean value theorems of higher order, Taylor's theorem with various forms of remainders, Partial differentiation, Euler’s theorem on
homogeneous function.


Unit IV
Tangent and Normals, Asymptotes, Curvature, Envelops and evolutes, Tests for concavity and convexity, Points of inflexion, Multiple points, Tracing of curves in Cartesian and Polar forms.


Paper II (Integral Calculus)


Unit I
Definite integrals as limit of the sum, Riemann integral, Integrability of continuous and
monotonic functions, Fundamental theorem of integral calculus, Mean value theorems of integral calculus, Differentiation under the sign of Integration.


Unit II
Improper integrals, their classification and convergence, Comparison test, µ-test, Abel's test,
Dirichlet's test, quotient test, Beta and Gamma functions, properties and convergence


Unit III
Rectification, Volumes and Surfaces of Solid of revolution, Pappus theorem, Multiple integrals, change of order of double integration, Dirichlet’s theorem, Liouville’s theorem for multiple integrals


Unit IV
Vector Differentiation, Gradient, Divergence and Curl, Normal on a surface, Directional
Derivative, Vector Integration, Theorems of Gauss, Green, Stokes and related problems