Kazi Nazrul University Syllabus

I will take admission in B.Sc Mathematics Course at Kazi Nazrul University. Before taking admission I want to see syllabus. So will you provide syllabus of B.Sc Mathematics Course of Kazi Nazrul University?

As you want syllabus of B.Sc Mathematics Course of Kazi Nazrul University, so here I am providing following syllabus:

Kazi Nazrul University B.Sc Mathematics Syllabus

MBHCT 11
Unit I: Classical Algebra (30 Marks)
Inequalities: Arithmetic mean, geometric mean and harmonic mean; Schwarz
inequality and Weierstrass’s inequality. Simple continued fraction and its
convergence, representation of real numbers.
Complex numbers: De Moivre’s theorem, roots of unity, exponential function,
Logarithmic function, Trigonometric function, hyperbolic function and inverse
circular function.
Polynomial: polynomial equation, Fundamental theorem of algebra (statement only),
multiple roots, statement of Rolle’s theorem only and its application, equation with
real coefficients, complex roots, Descarte’s rule of sign, location of roots, Sturm’s
theorem, relation between roots and coefficients, transformation of equation,
Reciprocal equations, special roots of unity, solution of cubic equations- Cardan’s
method, solution of biquadratic equation – Ferrari’s method.
Well ordering principle for ℕ, division algorithm, Principle of mathematical induction
and its simple applications, Prime and composite numbers, Fundamental theorem of
arithmetic, greatest common divisor, relatively prime numbers, Euclid’s algorithm,
least common multiple.

Unit 2: Abstract Algebra I (20 Marks)
Surjective, injective and bijective mapping, composition of two mappings, inverse
mapping, extension and restriction of mappings, equivalence relation.
Group: Definition, examples, subgroups, necessary and sufficient condition for a
nonempty set to be a subgroup, generator of a group and a subgroup, order of a group
and order of an element, Abelian group.
Permutation group, cycles, length of a cycle, transposition, even and odd permutation,
alternating group, examples of S3 and K4 (Klein 4-group).
Cyclic subgroups of a group, cyclic groups and their properties, groups of prime order,
coset, Lagrange’s theorem.
Ring, Characteristic of a Ring, subring, integral domain, elementary properties, field,
skew field, subfields, characteristic of a field or integral domain, finite integral
domain, elementary properties.

MBHCT 12
Unit I: Real Analysis I (30 Marks)
A brief discussion on the real number system: Field structure of R, order relation,
Archimedean properties, order completeness properties of R. Arithmetic continuum,
geometric continuum, neighbourhood of a point, neighbourhood system, interior
points, open sets, limit points, derived sets, closed sets, closure.
Sequence, limit of a sequence, bounded sequence, convergence, divergence,
Oscillatory sequence, (only definitions and simple examples). Sandwich Theorem,
Bounded functions, monotone functions. Limit of a function at a point. Sequential
criterion on limit, Continuity of a function at a point and on an interval. Sequential
criterion on continuity, Properties of continuous functions over a closed and bounded
interval. Uniform continuity.
Derivative of a function. Successive differentiation, Leibnitz’s theorem, Rolle’s
theorem, mean value theorems. Intermediate value property, Darboux theorem.
Taylor’s theorem, and Maclaurin’s theorem with Lagrange’s and Cauchy’s forms of
remainders. Taylor’s series. Expansion of elementary functions such as
Envelope, asymptote, curvature. Curve tracing: Astroid, cycloid, cardioids, folium of
Descartes. Maxima, minima, concavity, convexity, singularity. Indeterminate forms.
L’Hospital’s theorem. Real valued Functions of several variables (two and three
variables). Continuity and differentiability. Partial derivatives. Commutativity of the
orders of partial derivatives. Schwarz’s theorem, Young’s theorem, Euler’s theorem.

Unit 2: Integral Calculus (20 Marks)
Definite Integral – Definition of Definite Integral as the Limit of a Sum; Fundamental
Theorem of Integral Calculus (statement only). General Properties of Definite
Integral; Integration of Indefinite and Definite Integral by Successive Reduction.
Multiple Integral – Definition of Double Integral and Triple Integral as the Limit of a
Sum; Evaluation of Double Integral and Triple Integral; Fubini’s Theorem (statement
and applications).
Applications of Integral Calculus – Quadrature and Rectification; Intrinsic Equations
of Plane Curves; Evaluation of Lengths of Space Curves, Areas of Surfaces and
Volumes of Solids of Revolution. Evaluation of Centre of Gravity of some Standard
Symmetric Uniform Bodies: Rod; Rectangular Area, Rectangular Parallelepiped,
Circular Arc, Circular Ring and Disc, Solid and Hollow Spheres, Right Circular
Cylinder and Right Circular Cone.

MBHCT 21
Unit 1: Linear Algebra (30 Marks)
Matrices of real and complex numbers: Algebra of matrices, symmetric and skewsymmetric
matrices, Hermitian and skew-Hermitian matrices, orthogonal matrices.
Determinants: Definition, Basic properties of determinants, Minors and cofactors.
Laplaces method. Vandermonde’s determinant. Symmetric and skew symmetric
determinants. (No proof of theorems).
Adjoint of a square matrix. Invertible matrix, Non-singular matrix. Inverse of an
orthogonal Matrix.
Elementary operations on matrices. Echelon matrix. Rank of a matrix. Determination
of rank of a matrix (relevant results are to be state only). Normal forms. Elementary
matrices. Statements and application of results on elementary matrices. Congruence of
matrices (relevant results are to be state only), normal form under congruence,
signature and index of a real symmetric matrix
Vector space: Definitions and examples, Subspace, Union and intersection of
subspaces. Linear sum of two subspaces. Linear combination, independence and
dependence. Linear span. Generators of vector space. Dimension of a vector space.
Finite dimensional vector space. Examples of infinite dimensional vector spaces.
Replacement Theorem, Extension theorem. Extraction of basis. Complement of a
subspace.
Row space and column space of a matrix. Row rank and column rank of a matrix.
Equality of row rank, column rank and rank of a matrix.
Linear homogeneous system of equations : Solution space. Necessary and sufficient
condition for consistency of a linear non-homogeneous system of equations. Solution
of system of equations (Matrix method). Linear Transformation on Vector Spaces:
Definition of Linear Transformation, Null space, range space of an Linear
Transformation, one-one, onto, invertible, linear transformation, Rank and Nullity,
Rank-Nullity Theorem and related problems.

Unit 2: Abstract Algebra II (20 Marks)
Normal subgroups of groups and their properties, homomorphism between the two
groups, isomorphism, kernel of a homomorphism, first isomorphism theorem,
isomorphism of cyclic groups. Ideal of a Ring (definition, examples and simple
properties).
Partial order relation, Poset, maximal and minimal elements, infimum and supremum
of subsets, Lattices, definition of lattice in terms of meet and join, equivalence of two
definitions.
Boolean algebra, Huntington postulates, examples, principle of duality, atom, Boolean
function, conjunctive normal form, disjunctive normal form, switching circuits.

Attached Files Available for Download

Kazi Nazrul University B.Sc Mathematics Syllabus.pdf (699.2 KB, 47 views)