MATHEMATICS

PROFILE

Vision

• To remedy math-phobia through authentic learning based on hands-on experience with computers.

• To foster experimental, problem-oriented learning of mathematics.

• To show that ICT can be a panacea for quality and efficient education when properly integrated and accepted.

• To prove that the activity-centered mathematics laboratory places the student in a problem solving situation and then through self exploration and discovery habituates the student into providing a solution to the problem based on his or her experience, needs, and interests.

• To provide greater scope for individual participation in the process of learning and becoming autonomous learners.

• To ultimately see that the learning of mathematics becomes more alive, vibrant, relevant and meaningful; a program that paves the way to seek and understand the world around them. A possible by-product of such an exercise is that math-phobia can be gradually reduced amongst students.

• To help the student build interest and confidence in learning the subject

mission

• Improve retention of mathematical concepts in the student.

• To develop a spirit of inquiry in the student. • To improve the perspective of students on mathematics as per modern requirement.

• To initiate students to enjoy mathematics, and solve meaningful problems. To use abstraction to perceive relationships and structure and to understand the basic structure of mathematics.

• To enable the teacher to demonstrate, explain and reinforce abstract mathematical ideas by using concrete objects, models, charts, graphs, pictures, and posters with the help of FOSS tools on a computer.

• To make the learning process student-friendly by having a shift in focus in mathematical teaching, especially in the mathematical learning environment. Exploit techno-savvy nature in the student to overcome math-phobia.

• Propagate FOSS (Free and open source software) tools amongst students and teachers as per the vision of the National Mission for Education.

COURSE OUTCOME

SEMESTER/ TITLE OF THE COURSE LEARNING OUTCOME PROGRAM SPECIFIC OUTCOME
I Semester- MAT 1.1 

Matrices, Differential calculus, Integral calculus, Theory of equations
• Relate an augmented matrix to a system of linear equations.

• Apply the Cayley-Hamilton Theorem to compute powers of a given square matrix.

• Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions.

• Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution.

• Applied to solve higher degree polynomials.
At the end of the three year program in History the students will able to:

• This course is intended to expose you to the basic ideas of Differential Equations combined with some ideas from Linear Algebra. To be successful, a student must be able to, at the end of the class, solve the majority of the problems with no external help. All assignments and exams are geared towards and measure how much this goal has been accomplished.

• Use mathematical ideas to model real-world problems

• Utilize technology to address mathematical ideas

• Demonstrate the effective use of mathematical skills to solve quantitative problems from a wide array of authentic contexts

• Demonstrate the ability to make rigorous mathematical arguments in axiomatic and non-axiomatic systems

• Demonstrate effective written communication of mathematical concepts
II Semester – MAT 2.1

Groups, Differential Calculus, Integral Calculus, Differential equations-I
• Construct and describe groups. They will learn basic properties of groups and get familiar with important classes of groups. They will understand the crucial concept of simple groups.

• Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.

• Develop the ability to apply differential equations to significant applied and/or theoretical problems
III Semester – MAT 3.1

Groups, Sequences and Series of Real Numbers, Differential Calculus
• Understand the proof, statement and simple uses of Lagrange’s Theorem.

• Recognize the embedded infinite geometric series in geometric applications.

• Understand the consequences of the intermediate value theorem for continuous functions.
IV Semester – MAT 4.1

Groups, Fourier series, Mathematical Methods-I, Differential Equations-II
• Demonstrate familiarity with permutation groups and be able to decompose permutations into 2-cycles. Familiar with Fourier series and their applications and be notionally aware of their convergence.

• Laplace transforms is used to simplify calculations in system modeling.

• Demonstrate an understanding of solution techniques for second and higher order differential equations; be familiar with qualitative tools for linear equations applications.
V Semester – MAT5.1

Rings, Integral domains, Fields, Vector Differential calculus,

Numerical methods-I
• Demonstrate familiarity with some of the applications of algebra to other fields, e.g. cryptography.

• Apply derivative concepts to find tangent lines to level curves and to solve optimization.

• Analyze the error incumbent in any such numerical approximation.
MAT5.2

Calculus of variation, Line and multiple integral, Integral theorems
• Compute the curl and the divergence of vector field

• Apply triple integrals to find volumes and center of mass

• Compute the area of parametric surfaces in 3-dimensional space
VI Semester – MAT 6.1

Linear algebra, PDE
• Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization

• Be familiar with the modeling assumptions and derivations that lead to PDEs
MAT6.2

Complex analysis, Numerical methods-II
• Applications in many scientific areas, including signal processing, control theory, electro magnetism etc. • Implement a variety of numerical algorithms using appropriate technology.
SEMESTER/ TITLE OF THE COURSE LEARNING OUTCOME
I Semester- MAT 1.1 

Matrices, Differential calculus, Integral calculus, Theory of equations
• Relate an augmented matrix to a system of linear equations.

• Apply the Cayley-Hamilton Theorem to compute powers of a given square matrix.

• Compute limits, derivatives, and definite & indefinite integrals of algebraic, logarithmic and exponential functions.

• Compute definite and indefinite integrals of algebraic and trigonometric functions using formulas and substitution.

• Applied to solve higher degree polynomials.
II Semester – MAT 2.1

Groups, Differential Calculus, Integral Calculus, Differential equations-I
• Construct and describe groups. They will learn basic properties of groups and get familiar with important classes of groups. They will understand the crucial concept of simple groups.

• Use technological tools such as computer algebra systems or graphing calculators for visualization and calculation of multivariable calculus concepts.

• Develop the ability to apply differential equations to significant applied and/or theoretical problems
III Semester – MAT 3.1

Groups, Sequences and Series of Real Numbers, Differential Calculus
• Understand the proof, statement and simple uses of Lagrange’s Theorem.

• Recognize the embedded infinite geometric series in geometric applications.

• Understand the consequences of the intermediate value theorem for continuous functions.
IV Semester – MAT 4.1

Groups, Fourier series, Mathematical Methods-I, Differential Equations-II
• Demonstrate familiarity with permutation groups and be able to decompose permutations into 2-cycles. Familiar with Fourier series and their applications and be notionally aware of their convergence.

• Laplace transforms is used to simplify calculations in system modeling.

• Demonstrate an understanding of solution techniques for second and higher order differential equations; be familiar with qualitative tools for linear equations applications.
V Semester – MAT5.1

Rings, Integral domains, Fields, Vector Differential calculus,

Numerical methods-I
• Demonstrate familiarity with some of the applications of algebra to other fields, e.g. cryptography.

• Apply derivative concepts to find tangent lines to level curves and to solve optimization.

• Analyze the error incumbent in any such numerical approximation.
MAT5.2

Calculus of variation, Line and multiple integral, Integral theorems
• Compute the curl and the divergence of vector field

• Apply triple integrals to find volumes and center of mass

• Compute the area of parametric surfaces in 3-dimensional space
VI Semester – MAT 6.1

Linear algebra, PDE
• Compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization

• Be familiar with the modeling assumptions and derivations that lead to PDEs
MAT6.2

Complex analysis, Numerical methods-II
• Applications in many scientific areas, including signal processing, control theory, electro magnetism etc. • Implement a variety of numerical algorithms using appropriate technology.
PROGRAM SPECIFIC OUTCOME
At the end of the three year program in History the students will able to:
• This course is intended to expose you to the basic ideas of Differential Equations combined with some ideas from Linear Algebra. To be successful, a student must be able to, at the end of the class, solve the majority of the problems with no external help. All assignments and exams are geared towards and measure how much this goal has been accomplished.

• Use mathematical ideas to model real-world problems

• Utilize technology to address mathematical ideas

• Demonstrate the effective use of mathematical skills to solve quantitative problems from a wide array of authentic contexts

• Demonstrate the ability to make rigorous mathematical arguments in axiomatic and non-axiomatic systems

• Demonstrate effective written communication of mathematical concepts

FACULTY

Dr. Bhagya S

Associate Professor

M.Sc., Ph.D
Bhagyas.nmkrv@rvei.edu.in

Dr. Sheeba S

Assistant Professor

M.Sc., Ph.D.
Sheeba.nmkrv@rvei.edu.in

Dr. Saba Tarannum

Assistant Professor

M.Sc., Ph.D.
Sabatarnnum.nmkrv@rvei.edu.in

Mrs. Radharani V

Assistant Professor

M.Sc.,
radharaniv.nmkrv@rvei.edu.in