Government College Bhoranj(Tarkwari)
District Hamirpur, Himachal Pradesh
Tel. No. 01972-287505, 287287 , e.mail: gcbhoranj-hp@nic.in
B. Sc. with Mathematics
&
B.A. with Mathematics
Program Specific Outcomes (PSOs)
Students will be able to do the following by the end of the program:
PSO1 Use mathematics to address theoretical and applied problems through critical thinking, analysis, and synthesis.
PSO2 Able to learn Algebra, Calculus, Geometry, Differential Equations, and a variety of other fields of Mathematics. This also leads to the study of allied fields like computer science, physical science, chemistry, and biology. As a result, this Program assists students in laying a solid basis for future study in mathematics.
PSO3 Capable of sharing thoughts and insights while seeking and benefiting from the expertise and insight of others. This teaches students how to be responsible in a quickly changing interconnected society.
PSO4 Model real-world situations mathematically and use the ensuing inferences to improve one's quality of life.
PSO5 Create mathematical ideas from basic axioms.
PSO6 Able to present Mathematics clearly and precisely, make vague ideas precise by formulating them in the language of mathematics, describe mathematical ideas from multiple perspectives, and explain fundamental concepts of Mathematics to non-mathematicians.
PSO7 Undergraduate students are expected to be deeply engaged in initial learning to think differently as agents of new knowledge, understanding, and applying new concepts to gain employability/self-employment.
PSO8 Able to qualify for National-level exams including Banking exams, CDS, JAM, TIFR, HPPSC, UPSC, and others.
Program Outcomes (POs)
B.Sc. (Mathematics) First Year
Course Code: MATH101TH
Course Type: CORE COURSE
Name of the Course: Differential Calculus
Course Learning Outcomes:
After completing this course the learner should be able to
CO1 Find the higher-order derivative of the product of two functions.
CO2 Expand a function using Taylor’s and Maclaurin’s series.
CO3 Conceive the concept of asymptotes and obtain their equations.
CO4 I Have learned the method of finding the nth derivative and to use the Leibnitz theorem.
CO5 Understood effectively the geometrical aspects of curvature, radius of curvature, involutes, and evolutes of plane curves which are essential and elegant applications of differential calculus.
CO6 Understanding in handling functions of more than one variable for finding the maxima and minima of functions of two variables and Lagrange’s multipliers for finding maxima and minima along with the given constants.
B.Sc. (Mathematics) First Year
Course Code: MATH102TH
Course Type: CORE COURSE
Name of the Course: Differential Equations
Course Learning Outcomes:
On successful completion of this course, the student will be able to
CO1 Obtain an integrating factor that may reduce a given differential equation into an exact one and eventually provide its solution.
CO2 Identify and obtain the solution of Clairaut’s equation.
CO3 Find the complementary function and particular integrals of the linear differential equation.
CO4 Describe the origin of the partial differential equation and distinguish the integrals of the first-order linear partial differential equation into complete, general, and singular integrals.
CO5 Use Lagrange’s method for solving the first-order linear partial differential equation.
CO6 Solve and apply linear differential equations of second order (and higher).
CO7 To solve simultaneous and total differential equations, Lagrange’s method.
CO8 To classify the second-order partial differential equations: Parabolic, Elliptic and
Hyperbolic.
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Sc. ( Mathematics) Second Year
Course Code: MATH201TH
Course Type: DISCIPLINE SPECIFIC ELECTIVE
Name of course: Real Analysis
Course Learning Outcomes: On completion of the course, students will be able to
CO1 Identify the difference between lub and glb.
CO2 Understand the concepts of convergent sequence and Cauchy sequence.
CO3 Tests for absolute convergence and conditional convergence.
CO4 Develop the idea about the limit of a function on the real line.
CO5 Apply the concepts of open sets and closed sets.
B. Sc. ( Mathematics) Second Year
Course Code: MATH202TH
Course Type: DISCIPLINE SPECIFIC ELECTIVE
Name of course: ALGEBRA
Course Learning Outcomes: After completing this course the learner should be able to
CO1 Assess properties implied by the definitions of groups.
CO2 Use various canonical types of groups (including cyclic groups and groups of permutations).
CO3 Analyze and demonstrate examples of subgroups, normal subgroups, and quotient groups.
CO4 Analyze and demonstrate examples of ideals and quotient Groups.
CO5 Demonstrate understanding of the importance of homomorphism and isomorphism in groups.
CO6 Develop the idea about the rings, integral domain, field, and ideal.
Class: B. Sc. Second Year (Major Mathematics)
Subject: Mathematics
Course Type: Skill Enhancement Course
Paper Code: MATH309TH
Title of Paper: Integral Calculus
Course Learning Outcomes
After the completion of the course, Students will be able to:
CO1 Demonstrate the ability to integrate knowledge and ideas of definite and indefinite integrals in a coherent and meaningful manner and use appropriate techniques for solving such problems.
CO2 To Calculate the areas of curved regions by using integration methods.
CO3 To Find the volume of a solid of revolution using various methods.
CO4To Compare different integration methods for determining volume.
CO5 To Calculate the arc length of a curve and the surface area of a solid of revolution.
CO6 To evaluate double and triple integrals.
CO7 Apply the change variable method to find the value of double and triple integrals.
B.Sc. ( Mathematics) Second Year
Course Code: MATH310TH
Course Type: Skill Enhancement Course
Name of course: Vector Calculus
Course Learning Outcomes: On completion of this area of course, students will be able to
CO1 Find the Triple Product of Products and their Applications.
CO2 Deduce the Vector equations subject to different conditions.
CO3 Understand the applications of vector algebra (particularly, vector products) to geometry and mechanics — concurrent forces in a plane, theory of couples, and system of parallel forces.
CO4 Learn operations with vector-valued functions.
CO5 Find the limits and verify the continuity of vector functions.
CO6 Differentiate and integrate vector functions of one variable.
B.Sc. (Mathematics) Third Year
Course Code: MATH303TH
Course Type: DISCIPLINE SPECIFIC ELECTIVE
Name of the Course: LINEAR ALGEBRA
Course Learning Outcomes: Upon completion of this course, students should be able to:
CO1 Understand the idea of vector space and metric space.
CO2 Analyze finite and infinite dimensional vector spaces and subspaces over a field and their properties, including the basis structure of vector spaces.
CO3 Compute with the characteristic polynomial, eigenvectors, eigenvalues, and Eigenspaces.
B.Sc. (Mathematics) Third Year
Course Code: MATH304TH
Course Type: DISCIPLINE SPECIFIC ELECTIVE
Name of the Course: Numerical Methods
Course Learning Outcomes: On successful completion of this course, the student will be able to
CO1. Understand numerical techniques to find the roots of nonlinear equations and the solution of a system of linear equations.
CO2. Understand the different operators and the use of interpolation.
CO3. Understand numerical differentiation and integration and numerical solutions of
ordinary and partial differential equations.
CO4. Demonstrate understanding of common numerical methods and how they are used to obtain approximate solutions to otherwise intractable mathematical problems.
CO5. Apply numerical methods to obtain approximate solutions to mathematical problems.
CO6. Derive numerical methods for various mathematical operations and tasks, such as interpolation, differentiation, integration, the solution of linear and nonlinear equations, and the solution of differential equations.
CO7. Analyse and evaluate the accuracy of common numerical methods.
B.Sc. (Mathematics) Third Year
Course Code: MATH313TH
Course Type: Skill Enhancement Course
Name of the Course: Probability and Statistics
Course Learning Outcomes:
After the successful completion of this course, it is indented that a student will be able to:
CO1 Use the basic probability rules, including additive and multiplicative law by using the Concept of probability set function, random variable, and the probability density function.
CO2 Distribution function and use this concept for calculating probabilities and drive the marginal/conditional distribution and their respective mean, variance, and standard deviation.
CO3 Mathematical expectation, moments, moment generating function, characteristic
function, discrete distributions: uniform.
CO4 Applications of Binomial distribution, Poisson distribution, continuous distribution, normal distribution, and exponential distribution.
CO5 Problems on Joint cumulative distribution function and its properties.
CO6 Problems on joint probability density functions, marginal and conditional distributions.
CO7 Problems on the expectation of a function of two random variables, conditional expectations, and independent random variables.
B.Sc. (Mathematics) Third Year
Course Code: MATH316TH
Name of the Course: Theory of Equations
Course Type: Skill Enhancement Course
Course Learning Outcomes: On successful completion of this course, the student will be able to
CO1 Describe the relation between roots and coefficients.
CO2 Find the sum of the power of the roots of an equation using Newton’s Method.
CO3 Transform the equation through roots multiplied by a given number, increase the roots, decrease the roots, remove terms
CO4 Solve the reciprocal equations.
CO5 Analyse the location and describe the nature of the roots of an equation.