# BSc 1st Year Maths Syllabus and Subjects 2023-24 (with PDF)

Want to know about the syllabus of B.Sc Maths 1st year course? If yes, and browsing the syllabus, don’t worry because you landed at the right place. In this post, I will share the complete BSc maths 1st-year syllabus as per the University Grants Commission (UGC).

Bachelor of Science in maths stream comprises core subjects, ability enhancement subjects, skill enhancement subjects, and generic elective subjects. In 1st year BSc maths, the course has two core papers and one ability enhancement and generic elective paper respectively.

BSc Maths is a 3 to 4 years undergraduate-level degree course which deals with the study of various aspects of mathematics. It is also one of the popular UG courses among students who are interested in mathematics. The minimum qualification required to take admission in this course is 12th pass from the science stream.

The syllabus of BSc 1st year maths may vary from university to university. So, it is not necessary that the syllabus of your university and the syllabus mentioned below are exactly the same. However, I tried also to cover some popular university syllabi.

Without any further delay, let’s move toward the syllabus.

## BSc Mathematics 1st Year: Overview

### BSc 1st Semester Maths Syllabus

#### Calculus

• Hyperbolic Functions
• Higher Order Derivatives
• Leibniz Rule and Its Application
• Concavity and Inflection Points
• Asymptotes
• Curve Tracing in Cartesian Coordinates
• Tracing in Polar Coordinates of Standard Curves
• Reduction Formulae
• Volumes By Slicing
• Disks and Washers Methods
• Volumes By Cylindrical Shells
• Parametric Equations
• Parameterizing a Curve
• Arc Length of Parametric Curves
• Area of Surface of Revolution
• Techniques of Sketching Conics
• Polar Equations of Conics
• Triple Product
• Introduction to Vector Functions
• Differentiation and Integration of Vector Functions
• Modeling Ballistics and Planetary Motion
• Kepler’s Second Law
##### Algebra
• Polar Representation of Complex Numbers
• De Moivre’s Theorem for Rational Indices and Its Applications
• Equivalence Relations
• Composition of Functions
• Invertible Functions
• Well-ordering Property of Positive Integers
• Division Algorithm
• Principles of Mathematical Induction
• Systems of Linear Equations
• Solution Sets of Linear Systems
• Applications of Linear Systems
• Introduction to Linear Transformations
• Matrix of a Linear Transformation
• Characterizations of Invertible Matrices
• Eigen Vectors and Characteristic Equation of a Matrix

#### Generic Electives

##### 1. Object Oriented Programming in C++
• Object-based Programming Languages C++
• Enumeration
• Arrays and Pointer
• Implementing Oops Concepts in C++
• Polymorphism
• Default Parameter Value
• Using Reference Variables with Functions
• Abstract Data Types
• Access Modifiers
• Concepts of Namespaces
##### 2. Finite Element Methods
• Introduction to Finite Element Methods
• Methods of Weighted Residuals
• Least Squares and Galerkin’s Method
• Linear
• Solution of Assembled System
• Simplex Elements in Two and Three Dimensions
• Discretization with Curved Boundaries
• Interpolation Functions
• Numerical Integration
• Modelling Considerations

### BSc Maths 2nd Semester Syllabus

#### Real Analysis

• Review of Algebraic and Order Properties of R
• Idea of Countable Sets
• Uncountable Sets and Uncountability of R
• The Archimedean Property
• Density of Rational Numbers in R
• iNTERVALS
• Illustrations of Bolzano-Weierstrass Theorem for Sets
• Sequences
• Limit of a Sequence
• Limit Theorems
• Monotone Convergence Theorem
• Bolzano Weierstrass Theorem for Sequences
• Cauchy’s Convergence Criterion
• Leibniz Test
• Absolute and Conditional Convergence

#### Differential Equations

• Differential Equations and Mathematical Models
• Exact Differential Equations and Integrating Factors
• Linear Equation and Bernoulli Equations
• Introduction to Compartmental Model
• Exponential Growth of Population
• Limited Growth with Harvesting
• Principle of Super Position for Homogeneous Equation
• Wronskian
• Euler’s Equation
• Method of Undetermined Coefficients
• Method of Variation of Parameters
• Equilibrium Points
• Predatory-prey Model and Its Analysis
• Epidemic Model of Influenza and Its Analysis
• Battle Model and Its Analysis

#### Generic Electives

##### 1. Mathematical Finance
• Basic Principles
• Arbitrage and Risk Aversion
• Time Value of Money
• Comparison of NPV and IRR
• Bond Prices and Yields
• Macaulay and Modified Duration
• Term Structure of Interest Rates
• Putable and Callable Bonds
• Portfolio Mean Return and Variances
• Diversification
• Markowitz Model
• Two Fund Theorem
• Capital Asset Pricing Model
• Betas of Stocks and Portfolios
• Jensen’s Index
##### 2. Econometrics
• Statistical concepts Normal Distribution
• Estimation of Parameters
• Properties of Estimators
• Testing of Hypothesis
• Defining Statistical Hypothesis
• Type I and Type II Errors
• Power of a Test
• Simple Linear Regression Model
• Properties of Estimators
• Scaling and Units of Measurement
• Gauss-Markov Theorem
• Functional Forms of Regression Models
• Violations of Classical Assumptions
• Heteroscedasticity
• Specification Analysis Omission of a Relevant Variable
• Test of Specification Errors

Also Read:- BSc 2nd Year Maths Syllabus

### BSc 1st Year Maths Syllabus Agra University

#### Algebra and Trigonometry

• Sequence and Its Convergence
• Cauchy’s Condensation Test
• Alternating Series
• Leibnitz Test
• Equivalence Relations and Partitions
• Centre and Normalizer
• Coset Decomposition
• Lagrange’s Theorem and Its Consequence
• Homomorphism and Isomorphism
• Cayley’s Theorem
• Fundamental Theorem of Homomorphism
• Introduction to Rings
• Characteristic of a Ring
• Homomorphism of Rings
• Direct and Inverse Trigonometric
• Hyperbolic Functions
• Logarithmic Function
• Gregory’s Series

#### Calculus

• Definition of the Limit of a Function
• Continuous Functions and Classification of Discontinuities
• Differentiability
• Rolle’s Theorem
• Successive Differentiation and Leibnitz’s Theorem
• Expansion of Functions
• Partial Differentiation and Euler’s Theorem
• Maxima and Minima
• Tangents and Normals
• Enveloped and Evolutes
• Asymptotes
• Tests for Concavity and Convexity
• Pappus Theorem
• Dirichlet’s and Liouville’s Integral Formulae

#### Geometry and Vector Calculus

• General Equation of Second Degree
• Three-Dimensional System of Co-ordinates
• Projection and Direction Cosines
• Sphere, Cone and Cylinder
• Central Conicoids
• Conjugate Diameters
• Vector Differentiation and Integration
• Theorems of Gauss
• Green and Stokes and Problems Based on These