# B.Sc 3rd Year Maths Syllabus and Subjects 2022-23 (with PDF)

Are you a student of BSc Maths and have completed your 2nd year and searching for the BSc Maths 3rd Year Syllabus? If yes, then don’t worry because you landed at the right place. In this article, I will share the B.Sc 3rd-year maths syllabus and subjects which are completely provided by the University Grant Commission (UGC).

As you all know, a Bachelor of Science in Mathematics is a 3 to 4 years undergraduate course which provides complete in-depth knowledge in the field of mathematics. It is one of the most popular and demanded courses among students. The minimum educational qualification required to do this course is 12th.

B.Sc maths 3rd year has two core papers and two discipline-specific elective papers in the 5th and 6th semesters respectively. However, the papers/subjects may vary in your university.

It is quite possible that the syllabus of BSc maths in your university and the syllabus given below may have some differences because the syllabus of B.Sc maths may vary from university to university.

Let’s move toward the syllabus.

## B.Sc 3rd Year Maths: Overview

### BSc 5th Semester Maths Syllabus

#### Multivariate Calculus

• Functions of Several Variables
• Total Differentiability and Differentiability
• Sufficient Condition for Differentiability
• Directional Derivatives
• Maximal and Normal Property of the Gradient
• Extrema of Functions of Two Variables
• Method of Lagrange Multipliers
• Definition of Vector Field, Divergence and Curl
• Charge of Variables in Double Integrals and Triple Integrals
• Applications of Line Integrals
• Fundamental Theorem for Line Integrals
• Conservative Vector Fields
• Independence of Path
• Green’s Theorem
• Integrals Over Parametrically Defined Surfaces
• Stoke’s Theorem
• The Divergence Theorem

#### Group Theory II

• Automorphism
• Applications of Factor Groups to Automorphism Groups
• Commutator Subgroup and Its Properties
• Properties of External Direct Products
• Fundamental Theorem of Finite Abelian Groups
• Stabilizers and Kernels
• Applications of Group Actions
• Generalized Cayley’s Theorem
• Index Theorem
• Sylow’s Theorems and Consequences
• Cauchy’s Theorem

#### Discipline Specific Elective-1

##### Portfolio Optimization
• Financial Markets
• Investment Objectives
• Measures of Return and Risk
• Types of Risks
• Risk Free Assets
• Portfolio of Assets
• Expected Risk and Return of Portfolio
• Diversification
• Mean-variance Portfolio Optimization
• Portfolios with Short Sales
• Capital Market Theory
• Capital Assets Pricing Model
• Index Tracking Optimization Models
• Portfolio Performance Evaluation Measures
##### Number Theory
• Linear Diophantine Equation
• Chinese Remainder Theorem
• Fermat’s Little Theorem
• Wilson’s Theorem
• Totally Multiplicative Functions
• The Mobius Inversion Formula
• The Greatest Integer Function
• Euler’s Theorem
• Some Properties of Euler’s Phi-Function
• Order of an Integer Modulo n
• The Legendre Symbol and Its Properties
• Public Key Encryption
• RSA Encryption and Decryption
• Fermat’s Last Theorem
##### Analytical Geometry
• Techniques for Sketching Parabola
• Ellipse and Hyperbola
• Reflection Properties of Parabola
• Spheres
• Cylindrical Surfaces

#### Discipline Specific Elective-2

##### Industrial Mathematics
• Medical Imaging and Inverse Problems
• Introduction to Inverse Problems
• X-ray
• X-ray Behavior and Beers Law Lines in the Place
• Back Projection
• CT Scan
• Algorithms of CT Scan Machine
##### Boolean Algebra and Automata Theory
• Examples and Basic Properties of Ordered Sets
• Duality Principle
• Products and Homomorphisms
• Boolean Polynomials
• Quinn-McCluskey Method
• Switching Circuits and Applications of Switching Circuits
• Alphabets, Strings, and Languages
• Finite Automata and Regular Languages
• Deterministic and Non-deterministic Finite Automata
• Context Free Grammar and Pushdown Automata
• Properties of Context-Free Languages
• Turing Machine
• Undecidability
• Turing Machines
##### Probability and Statistics
• Sample Space
• Discrete Distributions
• Continuous Distributions
• Joint Cumulative Distribution Function and Its Properties
• Joint Probability Density Functions
• Marginal and Conditional Distributions
• Independent Random Variables
• Linear Regression for Two Variables
• Chebyshev’s Inequality
• Markov Chains
• Chapman-Kolmogorov Equations

Also Read:- BSc 1st Year Maths Syllabus

Also Read:- BSc 2nd Year Maths Syllabus

### BSc 6th Semester Maths Syllabus

#### Metric Spaces and Complex Analysis

• Metric Spaces
• Sequences in Metric Spaces
• Cauchy Sequences
• Complete Metric Spaces
• Cantor’s Theorem
• Sequential Criterion and Other Characterizations of Continuity
• Uniform Continuity
• Banach Fixed Point Theorem
• Properties of Complex Numbers
• Derivatives
• Cauchy-Riemann Equations
• Sufficient Conditions for Differentiability
• Examples of Analytic Functions
• Logarithmic Function
• Derivatives of Functions
• Contours Integrals and Its Examples
• Cauchy-Goursat Theorem
• Cauchy Integral Formula
• Liouville’s Theorem and The Fundamental Theorem of Algebra
• Taylor Series and Its Examples
• Laurent Series and Its Examples

#### Ring Theory and Linear Algebra II

• Division Algorithm and Consequences
• Principal Ideal Domains
• Factorization of Polynomials
• Eisenstein Criterion
• Divisibility in Integral Domains
• Euclidean Domains
• Eigen Spaces of a Linear Operator
• Diagonalizability
• Cayley-Hamilton Theorem
• Gram-Schmidt Orthogonalisation Process
• Least Squares Approximation
• Orthogonal Projections and Spectral Theorem

#### Discipline Specific Elective-3

##### Theory of Equations
• General Properties of Polynomials
• General Properties of Equations
• Descarte’s Rile of Signs Positive and Negative Rule
• Symmetric Functions
• Applications of Symmetric Function of the Roots
• Transformation of Equations
• Solutions of Reciprocal and Binomial Equations
• Properties of the Derived Functions
• Symmetric Functions of the Roots
• Limits of the Roots of Equations
• Separation of the Roots of Equations
• Applications of Strum’s Theorem
• Solution of Numerical Equations
##### Bio-Mathematics
• Mathematical Biology and The Modeling Process
• Continuous Models
• Qualitative Analysis of Continuous Models
• Spatial Models
• Discrete Models
• Host-Parasitoid Systems
• Optimal Exploitationtion Models
• Models in Genetics
• Stage Structure Models
• Age Structure Models
##### Linear Programming
• Introduction to Linear Programming Problem
• Theory of Simplex Method
• Optimality and Unboundedness
• Simplex Method in Tableau Format
• Introduction to Artificial Variables
• Big-M method and Their Comparison
• Duality
• Transportation Problem and Its Mathematical Formulation
• Assignment Problem and Its Mathematical Formulation
• Game Theory
• Linear Programming Solution of Games

#### Discipline Specific Elective-4

##### Mathematical Modeling
• Bessel’s Equation and Legendre’s Equation
• Laplace Transform and Inverse Transform
• Monte Carlo Simulation Modeling
• Generating Random Numbers
• Queuing Models
• Linear Programming Model
##### Mechanics
• Laws of Coulomb Friction
• Transmission of Power Through Belts
• Theorem of Pappus-Guldinus
• Polar Moment of Area
• Conservative Force Field
• Conservation for Mechanical Energy
• Translation and Rotation of Rigid Bodies
• Chasles’ Theorem
• Acceleration of Particles for Different References
##### Differential Geometry
• Theory of Space Curves
• Osculating Circles and Spheres
• Existence of Space Curves
• Evolutes and Involutes of Curves
• Theory of Surfaces
• First and Second Fundamental Forms
• Principal and Gaussian Curvatures
• Euler’s Theorem
• Rodrigue’s Formula
• Developables
• Geodesics
• Tensors