Syllabus
For
B.A./B.Sc. (Hons) in Mathematics
(Semester I & II)
Under NEP (2020)
Department of Mathematics
North Lakhimpur College (Autonomous)
1
Semester wise credit distribution for B.A./B.Sc.
(Hons) in Mathematics under NEP (2020)
Discipline Discipline Multidisciplina Ability Skill Value
Research Project
Specific Core Specific Elective ry/ Enhancem Enhancement Addition
Semester
(DSC)/ Major (DSE)/ Open Interdisciplina ent Courses Courses
Internship
(Core) Elective Course ry Compulso (SEC) (VAC)/
(OEC)/ Minor (MDC) ry Dissertat
Total
Courses ion/
(AECC) Thesis
I Paper code: Paper code: Paper code: Communic Paper code: - VAC –I - 21
MJ-T5-MTH-101 MN-T5-MTH-101 MD-T3-MTH-101 ative SE-P3-MTH-101 (3 Credit
English-I Credit)
CREDIT: 5 CREDIT: 5 CREDIT: 3 (2 Credit) CREDIT: 3
(L-3, T-0, P-0) (L-0, T-0, P-3)
(L-4, T-1, P-0) (L-4-, T-1, P-0)
Foundation In Computer
Algebra-I Algebra-I Lab-I
Mathematics-I
II Paper code: Paper code: Paper code: Language Paper code: - VAC –II - 21
MJ-T5-MTH-201 MN-T5-MTH-201 MD-T3-MTH-201 And SE-P3-MTH-201 (3credit) Credit
Literature
CREDIT: 5 CREDIT: 5 CREDIT: 3 (Mil/Regio CREDIT: 3
(L-4, T-1, P-0) (L-4, T-1, P-0) (L-3, T-0, P-0) nal (L-0, T-0, P-3)
Language)
Real Analysis-I Foundation In (2 Credit) Programming
Real Analysis-I
Mathematics-II With
Mathematical
Software
2
FIRST SEMESTER
Discipline Specific -MAJOR Course
(ALGEBRA-I)
Paper code: MJ-T5-MTH-101
CREDIT: 5 (L-4, T-1, P-0)
Total Marks=70
Objectives:: This course will enable the students to:
CO1: Understand the importance of roots of real and complex polynomials and learn various
methods of obtaining root and employ De Moivre’s theorem in a number of applications to solve
numerical problems.
CO2: Familiarize with divisibility theory & modular arithmetic of integers.
CO3: Recognize the mathematical objects called groups; link the fundamental concepts of
groups and symmetries of geometrical objects; explain the significance of the notions of subgroups,
cyclic groups and their classifications.
Unit – 1 : (Marks-30)
Theory of Equations and Complex Numbers: General properties of polynomials and
equations, Fundamental theorem of algebra, Relations between the roots and the coefficients,
Upper bounds for the real roots; Theorems on imaginary, integral and rational roots;
Newton’s method for integral roots, Descartes’ rule of signs; De-Moivre’s theorem for integer
and rational indices and their applications, The nth roots of unity, Cardan’s solution of the
cubic, Descartes’ solution of the quartic equation.
Unit – 2: (Marks-15)
Basic Number Theory: Division algorithm in ℤ, Divisibility and the Euclidean algorithm,
Fundamental theorem of arithmetic, Modular arithmetic and basic properties of congruences.
Unit – 3: (Marks-25)
Basics of Group Theory: Groups, Basic properties, Symmetries of a square, Dihedral group,
Order of a group, Order of an element, Subgroups, Center of a group, Centralizer of an
element, Cyclic groups and properties, Generators of a cyclic group, Classification of
subgroups of cyclic groups.
Reference Books:
1. Titu Andreescu, D. Andrica, Complex numbers from A to...Z, Birkhäuser.
2. Leonard Eugene Dickson , First Course in the Theory of Equations. John Wiley & Sons,
Inc.
3. Joseph. A. Gallian, Joseph. A, Contemporary Abstract Algebra , Cengage Learning India
Private Limited.
4. Edgar G. Goodaire, Michael M. Parmenter, Discrete Mathematics with Graph Theory,
Pearson Education Pvt. Ltd.
3
SECOND SEMESTER
Discipline Specific -MAJOR Course
( REAL ANALYSIS-I)
Paper code: MJ-T5-MTH-201
CREDIT: 5 (L-4, T-1, P-0)
Total Marks=70
Objectives:: This course will enable the students to:
CO1: Understand many properties of the real line R and learn to define sequence in terms of
functions from N to a subset of R .
CO2: Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to
calculate their limit superior, limit inferior, and the limit of a bounded sequence.
CO3: Apply the ratio, root, alternating series and limit comparison tests for convergence and
absolute convergence of an infinite series of real numbers.
Unit-1: (Marks-25)
Review of Algebraic and Order Properties of R , Equivalent sets in R , Idea of countable sets
and uncountable sets, Uncountability of R , Bounded Sets, Unbounded sets, Suprema and
Infima, The Completeness Property of R , The Archimedean Property, Intervals,
neighborhood of a point in R , Limit points of a set, Isolated points, Derived sets, Open sets,
Closed sets, Bolzano-Weierstrass theorem for sets.
Unit-2: (Marks-25)
Sequences, Bounded sequence, Convergent, Divergent & Oscillatory sequences, Limit of a
sequence. Limit Theorems, Monotone Sequences, Monotone Convergence Theorem,
Sandwich theorem, Subsequences, Bolzano Weierstrass Theorem for Sequences. Cauchy
sequence, Cauchy’s Convergence Criterion for sequence.
Unit-3: (Marks-20)
Infinite series, convergence and divergence of infinite series, Cauchy Criterion for series,
Tests for convergence: Comparison test, Limit Comparison test, Ratio Test, Cauchy’s nth root
test, Alternating series, Leibnitz test, Absolute and Conditional convergence.
Reference Books:
1. R.G. Bartle, D.R. Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia) Pvt. Ltd.
2. S.C. Malik, S. Arora, Mathematical Analysis, New age International (P) Ltd.
4
FIRST SEMESTER
Discipline Specific-MINOR Course
( ALGEBRA-I)
Paper code: MN-T5-MTH-101
CREDIT: 5 (L-4-, T-1, P-0)
Total Marks=70
Objectives:: This course will enable the students to:
CO1: Understand the importance of roots of real and complex polynomials and learn various
methods of obtaining root and employ De Moivre’s theorem in a number of applications to solve
numerical problems.
CO2: Familiarize with divisibility theory & modular arithmetic of integers.
CO3: Recognize the algebraic structures called groups; explain the significance of the
notions of subgroups, cyclic groups and analyse consequences of Lagrange’s theorem.
Unit – 1: (Marks-30)
Theory of Equations and Complex Numbers: General properties of polynomials and
equations, Fundamental theorem of algebra, Relations between the roots and the coefficients,
Upper bounds for the real roots; Theorems on imaginary, integral and rational roots;
Newton’s method for integral roots, Descartes’ rule of signs; De-Moivre’s theorem for integer
and rational indices and their applications, The nth roots of unity, Cardan’s solution of the
cubic, Descartes’ solution of the quartic equation.
Unit – 2 : (Marks-15)
Basic Number Theory: Division algorithm in Z , Divisibility and the Euclidean algorithm,
Fundamental theorem of arithmetic, Modular arithmetic and basic properties of congruences.
Unit – 3: (Marks-25)
Basics of Group Theory: Binary Operations, algebraic structures, Groups, Basic properties,
Order of a group, Order of an element, Subgroups, Cyclic groups, Lagrange’s theorem,
Center of a group, Centralizer of an element.
Reference Books:
1. Titu Andreescu, D. Andrica, Complex numbers from A to...Z, Birkhäuser.
2. Leonard Eugene Dickson, First Course in the Theory of Equations. John Wiley & Sons,
Inc.
3. Joseph. A. Gallian, Joseph. A, Contemporary Abstract Algebra, Cengage Learning India
Private Limited.
5
4. Edgar G. Goodaire, Michael M. Parmenter, Discrete Mathematics with Graph Theory,
Pearson Education Pvt. Ltd.
6
SECOND SEMESTER
Discipline Specific-MINOR Course
( REAL ANALYSIS-I)
Paper code: MN-T5-MTH-201
CREDIT: 5 (L-4, T-1, P-0)
Total Marks=70
Objectives:: This course will enable the students to:
CO1: Understand many properties of the real line R and learn to define sequence in terms of
functions from N to a subset of R .
CO2: Recognize bounded, convergent, divergent, Cauchy and monotonic sequences and to
calculate their limit superior, limit inferior, and the limit of a bounded sequence.
CO3: Apply the ratio, root, alternating series and limit comparison tests for convergence and
absolute convergence of an infinite series of real numbers.
Unit-1: (Marks-25)
Review of Algebraic and Order Properties of R , Equivalent sets in R , Bounded Sets,
Unbounded sets, Suprema and Infima, The Completeness Property of R , The Archimedean
Property, Intervals, neighborhood of a point in R , Limit points of a set, Isolated points,
Derived sets, Open sets, Closed sets, Bolzano-Weierstrass theorem for sets.
Unit-2: (Marks-25)
Sequences, Bounded sequence, Convergent, Divergent & Oscillatory sequences, Limit of a
sequence. Limit Theorems, Monotone Sequences, Monotone Convergence Theorem, Bolzano
Weierstrass Theorem for Sequences. Cauchy sequence, Cauchy’s Convergence Criterion for
sequence.
Unit-3: (Marks-20)
Infinite series, convergence and divergence of infinite series, Cauchy Criterion for series,
Tests for convergence: Comparison test, Limit Comparison test, Ratio Test, Cauchy’s nth root
test, Alternating series, Leibnitz test.
Reference Books:
1. R.G. Bartle, D.R. Sherbert, Introduction to Real Analysis, John Wiley and Sons (Asia) Pvt. Ltd.
2. S.C. Malik, S. Arora, Mathematical Analysis, New age International (P) Ltd.
7
FIRST SEMESTER
Multidisciplinary/Interdisciplinary Course - MDC
(Foundation in Mathematics-I)
Paper code: MD-T3-MTH-101
CREDIT: 3 (L-3, T-0, P-0)
Total Marks=42
OBJECTIVES: This course will enable the students to:
CO1: Learn about set theory and mathematical logic.
CO2: Familiarize with relation, binary operation and function.
CO3: Recognize determinants and matrices with applications.
UNIT-1: Sets and Logic: (Marks-18)
Sets, subsets, types of set, operations on sets, Cartesian product, Statements, truth values and
truth table, negation, conjunction and disjunction, Statements with quantifiers, compound
statements, implications, biconditional proposition, converse, contrapositive and inverse
proposition, propositional equivalence, predicates and quantifier, tautology and contradiction.
UNIT-2: Relations and functions: (Marks-12)
Relation and functions, types of relation and functions, graphs of functions, compositions of
functions and invertible function, Binary operations.
UNIT-3: Determinants and Matrices: (Marks-12)
Determinants and its properties, matrices and their types, algebra of matrices, elementary
transformation, elementary matrices, adjoint & inverse of a matrix, solution of a linear system
of equations.
Reference Books:
1. H.S. Hall, S.R. Knight, Higher Algebra, MacMilan and Co., limited.
2. Swapan Kr. Dey, Discrete Mathematics, S. Chand publications.
8
SECOND SEMESTER
Multidisciplinary/Interdisciplinary Course - MDC
(Foundation in Mathematics-II)
Paper code: MD-T3-MTH-201
CREDIT: 3(L-3, T-0, P-0)
Total Marks=42
OBJECTIVES: This course will enable the students to:
CO1: Learn about rank of matrices and its applications.
CO2: Find numerical solutions of system of linear equations and check the accuracy of the
solutions.
CO3: Obtain numerical solutions of transcendental and polynomial equations.
UNIT-1: Rank of matrices (Marks-14)
Rank of matrix, Echelon form, reduced Echelon form, normal form.
Applications of rank of matrix in solving: system of linear equations, business & Economics
Problems.
UNIT-2: System of linear algebraic equations: (Marks-14)
System of linear algebraic equations: Gaussian elimination, Gauss Jordan method, Gauss
Jacobi method, Gauss-Seidel method and their convergence analysis.
UNIT-3: Transcendental and Polynomial equations: (Marks-14)
Bisection method, Newton’s method, Regula falsi method, Secant method, Rate of
convergence of these methods.
Reference Books:
1. M.K. Jain, S.R.K. Iyengar, R.K. Jain, Numerical methods for scientific and engineering
computations, New Age Intl. Publisher.
2. S.S. Sastry, Introductory methods of numerical analysis, PHI.
9
FIRST SEMESTER
Skill Enhancement Course -SEC
(COMPUTER LAB-I)
Paper code: SE-P3-MTH-101
CREDIT: 3(L-0, T-0, P-3)
Total Marks=42
OBJECTIVES: This course will enable the students to:
CO1: Understand and apply the concepts of open source mathematical software for solving
mathematical problems.
List of practical to be performed using any mathematical software:
(Marks-42)
Basic commands and syntax.
Evaluation of mathematical expressions.
Solution of equations: Algebraic and transcendental equations.
Plotting 2D and 3D graphs.
Matrix operations.
Tracing of conics.
Derivatives and integrals of real functions.
Solution of ODE.
Reference Books:
1. Martha L Abell, James P Braselton, Differential Equations with Mathematica, Elsevier
Academic Press.
2. Rudra Pratap, Getting Started with Matlab: A quick introduction for scientist and engineers,
Oxford University Press.
10
SECOND SEMESTER
Skill Enhancement Course -SEC
(PROGRAMMING WITH MATHEMATICAL SOFTWARE)
Paper code: SE-P3-MTH-201
CREDIT: 3(L-0, T-0, P-3)
Total Marks=42
OBJECTIVES: This course will enable the students to:
CO1: Understand and apply the concepts of open source mathematical software for solving
mathematical problems.
Programming with any mathematical software: (Contact
hour- 90)
Logical symbols and expressions, variables, constants
Conditional statements
Loops: do, while, for
Creating functions
Programming examples: sum of series, solving equations and systems of equation using different
numerical methods, checking for primes, finding perfect numbers, solution of quadratic equations,
finding C.I., calculating EMI etc., finding mean, median, mode, standard deviation, mean
deviation.
Reference Books:
1. Martha L Abell, James P Braselton, Differential Equations with Mathematica, Elsevier
Academic Press.
2. Rudra Pratap, Getting started with Matlab: A quick introduction for scientists and engineers,
Oxford University Press.
11
