# RTMNU Revised MSc Mathematics Syllabus 2021

# RTMNU Revised MSc Mathematics Syllabus 2021

**RTMNU Revised MSc Mathematics Syllabus 2021| Nagpur University M.Sc Mathematics Syllabus | RTMNU Second Year M.Sc Mathematics Syllabus **

**RTMNU Revised MSc Mathematics Syllabus 2021 Nagpur University New Syllabus 2021** is available for Downloading. The latest **RTMNU Revised Msc Mathematics Syllabus 2021** is published by Nagpur University. The students looking for this syllabus can Download the PDF Syllabus from given respective Links. We keep adding More details about this Syllabus on this page. We given below the Details updated new syllabus. Students of RTMNU are requested to go though the detail syllabus. You can also download the PDF of syllabus from given link. For More updates keep visiting us.

**RTM Nagpur University Revised MSc Mathematics Syllabus 2021** -RTM Nagpur University M.Sc Mathematics Third and Fourth Semester New Revised Syllabus is given below for Downloading. The students can Download the respective Syllabus from following given details. Just go through the given links & read the given syllabus carefully. Nagpur University Second Year New Semester Online Detail syllabus given below.

**RTMNU Revised MSc Mathematics Syllabus 2021**

**M. Sc. MATHEMATICS**

**Foundation Course**

**Foundation Course / Core (Subject Centric):** Student can choose either Foundation course paper or Core (Subject Centric) paper. Once the choice between Foundation Course / Core (Subject Centric) is made by the candidate, it can not be changed in Semester IV.

**Foundation Course:**

1. Candidate can opt for any one foundation course paper as shown below in the semester III and IV (Semester V & VI in case of M. Sc. (Tech) Applied Geology). However, Student shall opt for this paper from any subject other than his / her main subject for postgraduation (Ex. A candidate pursuing M. Sc. Mathematics can opt for foundation

course papers mentioned in other M. Sc. Subjects except papers mentioned under M. Sc. Mathematics). If the candidate decides to opt for foundation course papers then he/she shall not be eligible to opt for Core (Subject Centric) papers in their respective subjects.

2. Once the candidate chooses foundation course paper of any one subject, then he / she can not change the subject in semester IV. Ex. If a M. Sc. Biochemistry candidate has chosen foundation course paper from M. Sc. Mathematics, then he has to pursue the foundation course paper of M. Sc. Mathematics in Semester IV also.

**RTMNU Revised MSc Mathematics Syllabus 2021**

**Semester-III**

**PAPER XV : FOUNDATION (For Students other than Mathematics )**

**Paper – XV (Code: 3T5)**

**MATHEMATICS-I**

**Elementary Mathematics**

**Unit 1:**

Differentiation: Derivative of a constant function, derivative of trigonometric functions, derivative of inverse trigonometric functions, derivative of = , hyperbolic function, derivation of parametrically defined functions, logarithmic differentiation.

**Unit 2:**

Integration: Methods of integration, integration by substitution, three important forms of integrals, six important integrals, integration by parts, definite integrals, reduction formulae.

#### Unit 3:

Matrices & Determinant: Transpose of matrix, orthogonal matrices, unitary matrices, Hermitian and Skew-Hermitian matrices, idempotent matrix, Involutory matrix, minors and factors, properties of determinants, determinants-general treatment, symmetric & Skew-symmetric determinant.

#### Unit 4:

Complex Number: Definition, conjugate, modulus and argument, Algebra of complex number (Addition, Subtraction, Multiplication and Division), power and square root of complex number, properties of complex number, Argand diagram, solution of quadratic equation in complex number system.

#### Text Books:

1. Differential Calculus by Shanti Narayan (Unit 1 & Unit 2)

2. An Introduction to Matrices by S.C. Gupta (Unit 3 & Unit 4)

**RTMNU Revised MSc Mathematics Syllabus 2021**

**M. Sc. Mathematics**

**Semester-IV**

**PAPER XX : FOUNDATION (For Students other than Mathematics )**

**Paper – XX (Code: 4T5)**

**MATHEMATICS-II**

**Elementary Discrete Mathematics**

#### Unit 1:

Mathematical Logic: Introduction, Proposition, compound Proposition, Proposition and truth tables, logical equivalence, algebra of Proposition, conditional Proposition, converse, contra positive & inverse, bi conditional statement, negation of compound statements, tautologies & contradictions, normal forms, logic in proof.

#### Unit 2:

Lattice: Lattice as partially orderd sets, their properties, lattices as algebraic ystem, sub lattices, and some speial lattices eg. Complete, complemented and distributive lattices.

**Unit 3:**

Boolean algebra and Logic Circuits: Boolean algebra, basic operations, Boolean functions, De-Morgan’s theorem, logic gate, sum of products and product of sum forms, normal form, expression of Boolean function as a canonical form, simplification of Boolean expression by algebraic method, Boolean expression form logic & switching network.

**Unit 4:**

Graph Theory: Basic terminology, simple graph, multigraph, degree of a vertex, types of a graph, sub graphs of isomorphic graphs, matrix representation of graphs, Euler’s theorem on the existence of Eulerian path & circuits, directed graph, weighted graphs, strong connectivity, chromatic number.

**Text Book:**

Discrete Mathematical structures with applications to computer science by J.P.

Tremblay and R. Manohar, McGraw-Hill book company,1997.