### Bsc Third Year Maths Syllabus 2022-23 Session

Today we will discuss the bsc third year maths syllabus for the 2022 and 2023 sessions.

This syllabus provides guidelines to those students, who want to know about the lessons and details of BSc maths.

Basically, bsc 3rd year maths syllabus provides the material that students want to learn in the course.

Students are expected that the given guidelines fulfill the objective.

This syllabus may differ from other university syllabi.

If your university did not release the new syllabus, then this one help to guide the BSc maths course and lessons.

Here’s an excerpt of a detailed bsc maths syllabus 3rd year.

Although this syllabus is for a particular course (bsc 3rd year syllabus maths), We’ve included a section-by-section explanation for your convenience.

Here we have included bsc third year maths syllabus paper 1, paper 2, and paper 3. Apart from this included some additional information in detail.

The best utilization tactics of this bsc 3rd year maths syllabus is to go systematically in every part and understand, what you have to learn.

This will help to prepare for the upcoming examination.

Every university has its own syllabus and it may be possible that so many details could not be matched.

In that case, you should focus on your bsc final year maths syllabus.

### B.sc 3rd Year Mathematics Syllabus

**Bsc 3rd Year Mathematics 1st Paper Syllabus**

Paper-1 Real Analysis

- Unit-1 Axiom study of real numbers, Completeness principle in R, Archimedes principle, Countable and uncountable sets, Neighborhoods, Interior points, Limit points, Open and closed sets, Derivative sets, Dense sets, Perfect sets, Bolzano- Weierstrass theorem
- Unit-2 Sequences of real numbers, Subsequent, bounded and monotonic sequences, Convergent sequences, Cauchy's theorem, Cauchy sequences, Cauchy's general principle of convergence, Uniform convergence of sequences and series of functions, Weierstrass M-test, Abel and Dirichlet test
- Unit-3 Sequential continuity, Limit and intermediate value properties of continuous functions, Uniform continuity, Meaning of sign of derivative, Darboux theorem, Limit and continuity of functions of two variables, Taylor's theorem for functions of two variables, Functions of three variables Maxima and minima of Lagrange's method of undetermined multiples
- Unit-4 Riemann Integrals, Integrability of Continuous and Monotonic Functions, Fundamental Theorem of Integral Calculus, Mean Value Theorem of Integral Calculus, Improper Integrals and their Convergence, Comparison Test, -test, Abel's Test, Dirichlet's Test, Functions of a Parameter Integral as in and it's Differential and Integral
- Unit-5 Metric Space, Neighborhood, Interior Points, Limit Points, Open and Closed Sets, Subspaces, Convergence, and Cauchy Sequence, Completeness, Definition, and Examples of Cantor's Theorem

#### Bsc 3rd Year Math 2nd Paper Syllabus

Paper-2 Complex Analysis

- Unit-1 Functions of Complex Variables, Concept of Limit, Continuity, and Differentiation of Complex Functions, Analytical Functions, Cauchy-Riemann Equations (Cartesian and Polar Forms), Harmonic Functions, Orthogonal Systems, Power Series as an Analytical Function
- Unit-2 Elementary Functions, Mapping by Elementary Functions, Linear and Bilinear Transformation, Fixed Point, Cross-Ratio, Inverse Point and Critical Point, Corresponding Transformation
- Unit-3 Complex Integration, Line Integral, Cauchy's Fundamental Theorem, Cauchy's Integral Formula, Moreira's Theorem, Liouville Theorem, Maximum Modulus Theorem, Taylor and Laurent Series
- Unit-4 Singularities and zeros of an analytic function, Rouche's theorem, Fundamental Theorem of Algebra, Analytical Continuity

- Unit-5 Residue theorem and its applications to the evaluation of definite integrals, Logic Theorem

#### Bsc 3rd Year Maths 3rd Paper Syllabus

**Paper-3 Numerical Analysis and Programming In C **

**Numerical Analysis**

- Unit-1 Shift Operators, Forward and Backward Difference Operators and their Relationships, Differential Theorem of Difference Calculus, Interpolation, Newton-Gregory's Forward and Backward Interpolation Formula
- Unit-2 Divided Difference, Newton's Divided Difference Formula, Lagrange's Interpolation Formula, Central Difference, Formula Based on Central Difference: Gauss, Strolling, Bessel, and Everett Interpolation Formulas, Numerical Differentiation
- Unit-3 Numerical Integration, General Quadrilateral Formula, Trapezoidal and Simpson's Laws, Wedel's Law, Cote's Formula, Numerical Solutions of First Order Differential Equations: Euler's Method, Picard's Method, Runge-Kutta Method) and Milne's method, numerical solution of linear, homogeneous and generating differential equations, function method
- Unit-4 Solution of Transcendental and Polynomial Equations by Repetition, Bifurcation, Regula-Falci and Newton-Raphson Methods, Algebraic Eisen Value Problems: Power Method, Jacobi's Method, Given Method, Householder's Method and Q-R Method, Approximation: Different types of approximation, Least squares polynomial approximation, Polynomial approximation using orthogonal polynomials, Legendre approximation, Approximation with trigonometric functions, Exponential functions, Rational functions, Chebyshev polynomials
- Unit-5 Programming in C, Programmer Model of Computer, Algorithms, Data Types, Arithmetic, and Input/Out Instructions, Decisions, Control Structures, Decision Statements, Logical and Conditional Operators, Loop Case Control Structures, Functions, Recursion, preprocessor, arrays, puppet strings, structs, pointers, file formatting

**[**Optional Paper-4A]: Number Theory and Cryptography Paper (B): Linear Programming Paper (C): Differential Geometry and Tensor Analysis Paper (D): Principles of Computers (Science Paper): Mathematics Paper (F): Mathematical Statistics** ]**

**Paper-4 (A): Number Theory and Cryptography**

- Unit-1 Divisibility: GCD, LCM, Primes, Fundamental Theorem of Arithmetic, Whole Numbers, Floor and Ceiling Functions, Congruence: Properties, Complete and Least Remainder System, Fermat's Theorem, Euler Function, Chinese Remainder Theorem
- Unit-2 Primality Testing and Factorization Algorithms, Pseudo-Primes, Fermat's Pseudo-Primes, Pollard's RO Method for Factorization
- Unit-3 Introduction to Cryptography: Attacks, Services and Mechanisms, Security Services (Attacks, services, and mechanisms), Traditional Encryption - Classical Techniques: Models, Steganography, Classical Encryption Techniques, Modern Techniques: DES, Cryptanalysis, Block Cipher Theory and Design, key distribution problem, random number generation
- Unit-4 Hash function, Public key cryptography, Diffie-Hellman key exchange, Discrete logarithm-based crypto-system, RSA crypto-system, Signature scheme, Digital signature standard (DSA), RSA signature scheme, Knapsack problem
- Unit-5 Elliptic Curve Cryptography: Introduction to Elliptic Curves, Group Structure, Rational Points on Elliptic Curves, Elliptic Curve Cryptography, Applications in Cryptography and Factorization

**Paper-4 (B) Linear Programming**

- Unit-1 Linear Programming Problems, Description and Formulation of Common Linear Programming Problems, Graphical Methods, Slack, and Surplus Variables, Standard and Matrix Forms of Linear Programming Problems, Basic Viable Solutions
- Unit-2 Convex Sets, Fundamental Theorem of Linear Programming, Simplex Method, Artificial Variables, Big-M Method, Two Step Method
- Unit-3 Resolution of degeneration, Modified Simple Method, Sensitivity Analysis
- Unit-4 Problem in Linear Programming, Dual Simplex Method, Initial-Dual Method Integer Programming
- Unit-5 Transportation Problems, Assignment Problems

**Optional Paper-4 (C) Differential Geometry and Tensor Analysis**

**Differential Geometry**

- Unit-1 Local Theory of Curves- Space Curves, Examples, Plane Curves, Tangent and Normal and Binormal, Oscillating Plane, Normal Plane, and Rectifying Plane, Helis, Seurat-Frenet Apparatus, Curves and Contact between Surfaces, Tangent Surfaces, Involve and Evolution of curves, Internal equations, Fundamental existence theorems for space curves, Local theory of surfaces - Parametric patches on surface curves, Revolution surfaces, Helicoids, Metric-first fundamental forms and arc (arc) lengths
- Unit-2 Local Theory of Surfaces, Direction Coefficients, Families of Curves, Intrinsic Properties, Geodesy, Canonical Geodetic Equations, General Properties of Geodesy, Geodesic Curvature, Geodetic Polar, Gauss-Bonnet Theorem, Gaussian Curvature, Normal Curvature, Messner's Theorem, Mean Curvature, Gaussian Curvature, Focal Point, Lines of Curvature, Roderick's Formula, Euler's Theorem
- Unit-3 Fundamental Equations of Surface Theory – Gauss's Equation, Weingarten's Equation, Menardi-Codazzi Equation, Tensor Algebra: Vector Spaces, Dual Spaces, Tensor Product of Vector Spaces, Transformation Formula, Contraction, Special Tensor, Inner Product, associated tensor
- Unit-4 Differential Manifold-Examples, Tangent Vectors, Relations, Covalent Differentiation, Elements of General Riemannian Geometry-Riemannian Metric, Fundamental Theorem of Local Riemannian Geometry, Differential Parameters, Curvature Tensors, Geodesics, Geodesics of Curvature, Geometric Interpretation of Curvature Tensors and Special Riemannian Spaces

**Tensor Analysis**

- Unit-5 Contravariant and covariant vectors and tensors, Mixed tensors, Symmetric and skew-symmetric tensors, Algebra of tensors, Contractions and inner products, Quotient theorem, Reciprocal tensors, Christoffel's symbols, Covariant differentiation, Gradient, divergence and curl notation in tensors
- Paper-4 (D) Principles of Computer Science
- Unit-1 Data Storage - Storage of bits, Main memory, Mass storage, Storage of information, Binary systems, Storage integers, Fractions, Communication errors, Data manipulation - Central processing unit, Stored program concept, Program execution, Other architecture, Arithmetic/ Logic Instruction, Computer - Peripheral Communication
- Unit-2 Operating System and Network - Development of Operating System, Operating System Architecture, Coordinating Machine Activity, Process, Network, Handling competition between network protocols
- Unit-3 Algorithms - Concept of Algorithms, Algorithm Representation, Algorithms, Discovery, Iterative Structures, Recursive Structures, Efficiency, and Correctness, (Implementing Algorithms in C++)
- Unit-4 Programming Languages - Historical Perspectives, Traditional Programming, Concepts, Program Units, Language Implementation, Parallel Computing, Declarative Computing
- Unit-5 Software Engineering - Software Engineering Discipline, Software Life Cycle, Modularity, Development, Tools and Techniques, Documentation, Software Ownership and Liability, Data Structures - Arrays, Lists, Stacks, Queues, Trees, Optimized Data Types, Object-Oriented

**Paper-4 (E) Discrete Mathematics**

- Unit-1 Propositional Logic - Propositional Logic, Basic Logic, Logical Connectors, Truth Table, Essentialism, Paradox, General Forms (Combinative and Disjunctive), Methods and Methods, Validity, Predicate Logic, Universal and Existential Quantification, Method of Proof - Mathematical Induction, Proof by Implication, Inverse, Inverse, Rejection, Negation and Contradiction, Direct Proof using Truth Table, Proof by Counter Example
- Unit-2 Relation - Definition, Types of Relation, Structure of Relations, Domain and Limit of Relation, Graphical Representation of Relation, Properties of Relation, Partial Order Relation, Posets, Hasse Diagrams, and Lattices - Introduction, Ordered Sets (ordered set), Hase Diagram of Partially Ordered Sets, Isomorphic Ordered Sets, Well Ordered Sets, Properties of Lattices and Complementary Lattices, Boolean Algebra – Basic Definitions of Products Sum and product of sums, logic gates, and Karnaugh maps
- Unit-3 Graphs - Simple Graphs, Multi Graphs, Graph Terminology, Representation of Graphs, Bipartite, Regular, Planar, and Connected Graphs, Connected Components in Graphs, Euler Graphs, Hamiltonian Paths and Circuits, Graph Coloring, Chromatic Numbers, Isomorphism and Homomorphism Graphs, Tree - Definition, Root Trees, Properties of Trees, Binary Search Tree, Tree Traversal
- Unit-4 Combinatorics - Basics of Calculation, Permutation, Combination, Inclusion-Exclusion, Recurrence Relation (nth order recurrence relation with constant coefficients, Homogeneous recurrence relation, Inhomogeneous recurrence relation), Generating function (closed form expression), properties of g.f.) gf. Using recursion relation, g.f. Solving the combinatorial problem using
- Unit-5 Finite Automata - Basic Concepts of Automation Theory, Deterministic Finite Automation (DFA), Transition Functions, Transition Table, Non-Deterministic Finite Automata (NDFA), Mealy and Moore Machines, Minimization of Finite Automation

**Paper-4 (F) Mathematical Statistics**

- Unit-1 Three definitions of probability (mathematical, empirical, and axioms), dependent, independent, and mixed events, probability, addition and multiplication theorems of conditional probability, binomial and polynomial theorems of probability, Bay's theorem, mathematical expectation, and its properties, moments generating functions (m.g.f.) and cumulants

**Distributions**

- Unit-1 Discrete distributions – Binomial and Poisson distributions and their properties, Continuous distribution – Distribution function, Probability density function (PDF), Cauchy’s distribution, Rectangular distribution, Exponential distribution, Beta, Gamma normal distribution and their properties

**Correlation and Regression**

- Unit-3 Bivariate Population, Meaning of Correlation and Regression, Coefficient of Correlation, Rank Correlation, Lines of Regression, Properties of Regression, Coefficient, Partial and Multiple Correlation and their Simple Properties, Curves by the Method of Least Squares Key Fitting - Straight Line, Parabola and Exponential Curve Sampling Theory
- Unit-4 Types of Population, Parameters, and Statistics, Null Hypothesis, Level of Significance, Critical Area, Procedure for Testing Hypotheses, Type-1 and Type-2, x2 Distribution and its Properties
- Unit-5 Simple and Random Sampling, Testing for Significance of Large Samples, Distribution of Sampling Mean, Standard Error, Testing Based on T, F & Z Distribution, ANOVA

#### Bsc Final Year Maths Book (Bsc 3rd Year Maths Book 2022-2023)

Bsc 3rd Year Maths Book Name

- Probability and Statistics - Dr.Sharma
- Discrete Mathematics - Education Literature Publications
- Real Analysis - G.Vishweshwara Rao
- Dynamics - Ranbir Kadian, M.L. Jain, Gurvinder Kaur, Dr. Vivek Prakash Tyagi, Suraj Bhan Malik
- Linear Algebra and Vector Calculus - Dr.B.Leela Lakshmi Kumari
- Abstract Algebra - HK Pathak
- Complex Analysis - GN Purohit and SP Goyal
- Linear Bijavali - Dr. Gokhru and Saini

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