### Department of Mathematics

##### Program Outcomes (POs):

Students applying admission to the four year undergraduate B.Sc. programme are projected to get equipped with the followings:

PO1: Describing the fundamental concepts and procedures of science.

PO2: Encourage students to think critically and be aware of science.

PO3: Being able to solve a problem critically and handle an unexpected situation.

PO4: Recognizing the problems with nature, environmental contexts, and sustainable development.

##### Program Specific Outcomes (PSOs):

Students applying admission to the four year undergraduate B.Sc. programme in Mathematics are expected to acquire the followings:

PSO1: Students will be able to model and solve mathematical problems by applying their theoretical and analytical knowledge, as well as their understanding of the common body of knowledge in mathematics.

PSO2: Being able to write proofs that are both clear and concise requires an understanding of the nature of mathematical proofs.

PSO3: Possess the ability to create simple computer programs to carry out the mathematical competition.

PSO4:  Develop mathematical modelling skills while learning about how mathematics is used in other fields.

PSO5: The student gains the ability to articulate ideas clearly and to independently assimilate new knowledge and concepts.

PSO6: Students are encouraged to grow intellectually and get involved in career organizations.

PSO7: Try to solve challenging math problems and communicate mathematical ideas both orally and in writing.

### Semester-I (Major)

Course Title: Calculus and Classical Algebra

Course Code: MTHC1

Course Description: The course covers the concept of the De Moivre’s Theorem, sequential differentiation, Leibnitz theorem, different techniques for finding limit, various types of reduction formula for integration and system of linear equations and their solutions.

Course Outcome (COs): As a result of successfully completing this course, students will be able to:

CO1: Apply calculus to practical issues.

CO2: Create mathematical simulations.

CO3: Evaluate the area of surface of revolution.

CO4: List the algebraic elements that can be found in the various scientific disciplines.

CO5: Solve different types of system of linear equations by using different method.

##### MINOR:

Semester-I (Minor)

Course Title: Differential Calculus

Course Code: MINMTH1

Course Description: The course covers the concept of limits, continuity, differentiability, applications of the Rolle’s theorem, Mean value theorem and Taylor’s theorem.

Course Outcome (COs): The student will be capable of the following after completing this course:

CO1: Differentiate between functions.

CO2: Apply the continuity and differentiability in real problems.

CO3: Identify the tangent, normal, curvature, asymptotes, and other properties of a given curve.

CO4: Take into account the requirements of shifting functions.

### Semester-II (Major)

Course Title: Real Analysis and Differential Equations

Course Code: MTHC2

Course Description: The course covers the deep understanding of real line and of important terms to prove the results about convergence and divergence of sequences and series of real numbers. Also, this course the concept of Differential Equations, and develop the skill to solve differential equation of different order.

Course Outcomes (COs): The student will be capable of the following after completing this course:

CO1: Identify the properties of the number system.

CO2: Describe various analytical properties of the real number system.

CO3: Able to understand the Countable and Uncountable sets.

CO4: Identify the convergence and divergence sequences.

CO5: Use the techniques to solve differential equations.

CO6: Identify the homogeneous and non-homogeneous linear differential equations.

CO7: Apply these techniques in various mathematical models used in real life problems.

##### MINOR

Semester-II (Minor):

Title of Course: Real Analysis

Course Code: MINMTH2

Course Description: This course covers the real line R and of important terms to prove the results about convergence and divergence of sequences and series of real numbers. Also, this course contains the theory of different types of infinite series and their convergency test.

Course Outcomes (COs): The student will be capable of the following after completing this course:

CO1: Analyse the properties of the number line.

CO2: Describe various analytical properties of the real number system.

CO3: Able to understand the concept of Infinite series and their properties.

CO4: Apply the different techniques to test the convergency of the different sequences and series.

### Semester-III (Major)

Course Title: Theory of Real Functions

Course Code: MTHC3

Course description: This course covers the concepts of function, namely, limits, continuity, differentiability and their applications. Also, this course contains the applications of the Rolle’s theorem, mean value theorem, Darboux’s theorem, Taylor’s theorem and Cauchy’s mean value theorem.

Course Outcomes (COs): As a result of successfully completing this course, students will be able to:

CO1: Apply limit, continuity and differentiability of real valued functions.

CO2: Apply Mean Value Theorem to inequalities.

CO3: Able to know the algebra of differentiable function with their importance.

CO4: Able to expand functions in series and different form of remainders.

CO5: Able to apply the Taylor & Maclaurin series and their applications to simple problems.

Course Title: Group Theory I

Corse Code: MTHC4

Course Description: This course introduces the concept of fundamental theory of groups with its various types and their homomorphisms. Also, it contains the study of the Fermat’s Little theorem as a consequence of the Lagrange’s theorem on finite groups.

Course Outcomes (COs): As a result of successfully completing this course, students will be able to:

CO1: Describe various group structures onsets.

CO2: Able to understand the subgroups and their examples.

CO3: Able to understand the classification of subgroups of cyclic group.

CO4:  Able to apply External Direct Products of finite number of groups.

CO5: Identify the group structures present in different branches of sciences.

MINOR

Semester-III (Minor)

Course Title: Differential Equations

Course Code: MINMTH3

Course Description: This course introduces the concept of Differential Equations, Mathematical Modeling and their applications. Also, it explains the solution technique of ordinary and partial differential equations.

Course Outcomes (COs): The student will be capable of the following after completing this course:

CO1: Able to understand the rules for finding integrating factors.

CO2: Able to solve higher order differential equations by reducing its order.

CO3: Able to classify the linear and non-linear ordinary differential equations.

CO4: Able to distinguish the order and degree of differential equations.

CO5: Able to classify the second-order differential equations into elliptic, parabolic and hyperbolic form.

#### GENERIC ELECTIVE COURSE:

##### Semester-I [GEC (Any one)]

Title of Course: Foundation in Mathematics-I

Course Code: GECMTH1A

Course Description:

The course contains the basic concept of sets and mathematical logic in order to develop the critical and logical thinking in solving the problems and the idea of calculus along with their applications.

Course Outcome (COs):

The student will be capable of the following after completing this course:

CO1: List element of a finite set and illustration of set using Venn diagram.

CO2: Use the critical and rational approach for the solution of a problem.

CO3: Identify the Mathematical objects to describe social and physical systems.

CO4: Describe various algebraic structures onsets.

CO5: Apply Calculus in real life problems.

Course Title: History of Mathematics

Course Code: GECMTH1B

Course Description: This course introduces the historical perspective of mathematics such as numerical symbol, word numerals, place value notation. To explain the arithmetic algorithms, construction of sine tables and Diophantine equation in ancient and medieval India.

Course Outcomes (COs):

The student will be capable of the following after completing this course:

CO1: Able to explain how mathematics has evolved in India.

CO2: Able to analyze and critically reflect on ancient and modern mathematical issues.

CO3: Conduct historical research on ancient Indian mathematical ideas with the texts of classical mathematics and their historical interpretation.

CO4: Explain some of the mathematical concepts developed in ancient time and evaluate the relevance in modern mathematics and sciences.

##### Semester-II [GEC (Any one)]

Course Title: Foundation in Mathematics-II

Course Code: GECMTH2A

Course Description:

This course introduces the basic concept of difference operator with their relation and interpolation of function for the set of tabulated points. Also, it contains the study of the basic concepts of probability, random variables and the measure of central tendency.

Course Outcomes (COs): After the completion of this course, the learner will be able to:

CO1: Able to know the Counting principles and their applications in real problems.

CO2: Able to understand the theory of probability and apply in real situations.

CO3: Able to apply the concept of statistics in  different branches of science.

CO4: Able to build up a strong foundation of the basic Mathematical tools.

CO5: Identify the Mathematical objects to describe social and physical systems.

Course Code: GECMTH2B

Course Description:

This course introduces the basic concept of matrix and determinant with their applications in business and economic problems. Also, it explains the graphical solution of linear programming problem with two variables.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Able to understand the concept of algebra of matrices and determinants and their applications in economic problems.

CO2: Able to apply the differentiation in supply and demand problems which is related to cost revenue and profits.

CO3: Evaluate the simple interest and compound interest in real life problems.

CO4: Formulating linear programming and solve in graphically.

CO5: Familiarize students with the applications of mathematics in business decision-making.

##### Semester-III [GEC (Any one)]

Course Title: Mathematical Finance

Course Code: GECMTH3A

Course Description:

This course introduces the concept of finance in mathematics. To apply mathematics in the financial world, which enables the student to understand some computational and quantitative techniques required for working in the financial markets.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Apply models to financial mathematics/industries.

CO2: Able to understand the mechanism of the investment and market.

CO3: Ability to use mathematical tools to market economy.

CO4: Able to understand the basics of interest.

Course Title: Combinatorial Mathematics

Course Code: GECMTH3B

Course Description:

This course analyzes the Binomial theorem, Multinomial theorem, Necklace problem, Burnside’s lemma, Poly’s theorem and application. To study the principles of counting, principles of inclusion and exclusion, permutations and combinations, generating functions, recurrence relations, partition etc.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Use combinatorial approach in solving algebraic problems

CO2: Explain counting principles.

#### SKILL ENHANCEMENT COURSE:

Semester-I (SEC)

Title of Course: Computer Laboratory-I

Course Code: SEC115

Course Description:

The course covers the concept of different mathematical software namely MATLAB, MATHEMATICA or Open Source software that are very momentous in different physical fields.

Course Outcome (COs):

After the completion of this course, the learner will be able to:

CO1: Basic knowledge on MATLAB or MATHEMATICA through command window or creating programming files.

CO2: Solve different algebraic and trigonometric problems through the help of MATLAB or MATHEMATICA.

CO3: Sketching conics, polar equations of conics and polynomial of higher degree.

##### Semester-II (SEC)

Course Title: Computer Laboratory-II

Course Code: SEC214

Course Description:

This course offers the concept of the model in various real-life problems namely exponential decay model, lake pollution model etc. using MATHEMATICA /MATLAB/Open-source softwares etc. To plot the recursive sequences, sequence of partial sum using Mathematica /MATLAB.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Able to use MATLAB or Mathematica software through command window or creating programing files for various mathematical modelling problem.

CO2: Plotting of second order solution family of differential equation.

CO3: Able to sketch different recursive sequences.

##### Semester-III (SEC)

Course Title: Mathematical Logic

Course Code: SEC315

Course Description:

This course introduces the basic concept of sets and mathematical logic. To develop the critical and logical thinking in solving the problems.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Analyze the truth and falsity of a logical statement.

CO2: Differentiate between a logical statement and an ordinary statement.

CO3: Define and describe various properties of sets.

#### ABILITY ENHANCEMENT COURSE

##### Semester-III  (AEC)

Course Title: Mathematical Ability

Course Code: AECMTH3

Course Description:

This course offers the basic mathematics skills and logical reasoning which required in day-to-day life. To analyze and draw conclusions from the data, which may be presented in the form of tables or graphs.

Course Outcomes (COs):

After the completion of this course, the learner will be able to:

CO1: Able to solve the problem based on critical thinking with logic and reasoning.

CO2: Able to use basic mathematics as a tool to understand and solve the real-life problems.

CO3: Able to use basic mathematics for competitive examinations.