Programme Offered, PO,PSO

RayatShikshan Sanstha’s

KarmaveerBhaurao Patil College Vashi, Navi Mumbai

Autonomous College

[University of Mumbai]

Department of Mathematics

(CBSC Pattern w.e.f. 2021-22)

CO-PO-PSO

F.Y.B.Sc. Mathematics

RayatShikshan Sanstha’s

KARMAVEER BHAURAO PATIL COLLEGE, VASHI.

NAVI MUMBAI (Autonomous)

Department of Mathematics

B. Sc. Mathematics

ProgramOutcomes(POs)

Learnersare able to–

PO-1

Disciplinary Knowledge

Understand the basic concepts, fundamental principles, theoretical formulations and experimental findings and the scientific theories related to Physics, Chemistry, Mathematics,Microbiology, Computer Science, Biotechnology, Information Technology and itsother fields related to the program.

PO-2

Communication Skills

Develop various communication skills such as reading, listening and speaking skills to express ideas and views clearlyand effectively.

PO-3

Critical Thinking

Propose novel ideas in explaining the scientific data, facts and figures related to science and technology.

PO-4

Analytical Reasoning and Problem Solving

Hypothesize, analyze, formulate and interpret the data systematically and solve theoretical and numerical problems in the diverse areas of science and technology.

PO-5

Sense of Inquiry

Curiouslyask relevant questions for better understanding of fundamental concepts and principles, scientific theories and applications related to the study.

PO-6

Use of Modern Tools

Operate modern tools, equipments, instruments and laboratory techniques to perform the experiments and write the programs in different languages(software).

PO-7

Research Skills

Understand to design, collect, analyze, interpret and evaluate information/data that is relevant to science and technology.

PO-8

Application of Knowledge

Develop scientific outlook and apply the knowledge with respect to subject.

PO-9

Ethical Awareness

Imbibe ethical, moral and social values and exercise it in day to day life.

PO-10

Teamwork

Work collectively and participate to take initiative for variousfield-based situations related to science, technology and society at large.

PO-11

Environment and Sustainability

Create social awareness about environment and develop sustainability for betterment of future.

PO-12

Lifelong Learning

Ability of self-driven to explore, learn and gainknowledge and new skills to improve the quality of life and sense of self-worth by paying attention to the ideas and goals throughout the life.

PSO-1

Recalling the concepts of mathematics and applying them to the various courses like algebra, analysis, Differential equations, statistics, etc to form mathematical models.

PSO-2

To apply knowledge of Mathematics for pursuing higher studies at reputed national and international institutes including higher research.

PSO-3

Apply Mathematics to interdisciplinary ways like statistician, mathematical finance, industry expertise and interpret quantitative ideas.

SEMISTER-I

UGMT101 Calculus-I

Course Outcomes: After successful completion of this course, students will beable to:

CO-1: State the properties of real numbers.

CO-2: Apply properties of real numbers to prove some inequalities.

CO-3: Define a sequence and classify different types of sequence.

CO-4: State and apply properties of convergence and divergence to sequences andseries

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS: 1)https://nptel.ac.in/courses/111/106/111106146/

2) https://nptel.ac.in/courses/111/104/111104144/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

1

2

1

1

-

-

-

-

-

-

-

CO2

2

2

-

2

-

-

-

-

-

-

-

-

CO3

2

1

2

1

-

-

-

-

-

-

-

-

CO4

2

2

-

2

-

-

-

-

-

-

-

-

*In CO-PO Mapping Matrix: a correlation is established between COs and POs in the scale of 1 to 3, 1 being the slight (low), 2 being moderate (medium), 3 being substantial (high) and ‘-’ indicate there is no correlation in respective CO and PO.

UGMT102Algebra-I

Course Outcomes:After successful completion of this course, students will be able to:

CO1:Define logic statements.

CO2:Identify and apply various properties relating to the integers.

CO3: Apply different methods of proof to verify mathematical assertions.

CO4:Apply Fundamental theorem of algebra for finding roots of given polynomial.

ICT Tools Used:Videos, PPT, Pen-Tablet

Students Centric Methods:Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM/MOOCS:

1) https://nptel.ac.in/courses/111/105/111105112/

2) https://nptel.ac.in/courses/111/106/111106113/

TheCO-POMappingMatrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

2

1

2

1

-

-

-

-

-

-

-

-

CO2

3

1

1

1

1

-

-

-

-

-

-

CO3

2

1

2

1

1

-

-

-

-

-

-

-

CO4

2

2

1

2

-

-

-

-

-

-

-

-

SEMESTER II

UGMT201 Calculus-II

Course Outcomes:After successful completion of this course, students will be able to:

CO1: Define limit, continuity and differentiability of real valued function

CO2:State and prove algebra of limits, continuous functions and differentiability.

CO3: Construct discontinuous function to continuous function

CO4: Apply continuous function State and prove algebra of limits, continuous functions and

differentiability.

CO5: Apply differentiation to graph of function functions, L-Hospital Rule, higher derivative and

Taylors Expansion.

ICT Tools Used:Videos, PPT, Chalk Board

Students Centric Methods:Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM/MOOCS:

1) https://nptel.ac.in/courses/111/104/111104144/

2) https://nptel.ac.in/courses/111/104/111104085/

TheCO-POMappingMatrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

2

2

-

-

-

-

-

-

-

-

-

CO2

2

2

3

-

-

-

-

-

-

-

-

-

CO3

2

1

1

2

-

-

-

-

-

-

-

-

CO4

-

2

-

-

-

-

-

1

-

-

-

-

CO5

2

2

-

3

-

-

-

2

-

-

-

-

UGMT201 Algebra-II

Course Outcomes:After successful completion of this course, students will be able to:

CO1:Solve systems of linear equations and interpret their results.

CO2:Compute and interpret determinants of matrices.

CO3:Use computational techniques and algebraic skills essential for the study of systems of linear

equations, matrix algebra.

CO4:Analyze and construct mathematical arguments that relate to the study of introductory group

theory. (Proof and Reasoning).

ICT Tools Used:Videos, PPT, Chalk Board

Students Centric Methods:Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM/MOOCS:

1) https://nptel.ac.in/courses/111/105/111105112/

2) https://nptel.ac.in/courses/111/106/111106113/

TheCO-POMappingMatrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

2

1

1

-

-

-

-

-

-

-

-

CO2

2

1

2

2

-

-

-

-

-

-

-

-

CO3

2

2

2

1

-

2

-

-

-

-

-

-

CO4

2

1

1

3

2

1

-

-

-

-

-

-

If o(a) = n and o(b) = m, ab = ba, (n, m) = 1 then o(ab) = nm.

Scheme of Examination

ForUGMT101, UGMT102, UGMT201 and UGMT202 (Semester I & II)

A. There will be a Semester end examination of 60 marks.

1. Duration: The examinations shall be of 2:30Hours duration.

2. Theory Question Paper Pattern:

a) There shall be FOUR questions. The questions first three questions shall be of 15 marks each based on the units I, II, III respectively. The fourth question shall be of 15 marks based on the entire syllabus.

b) All the questions shall be compulsory. The questions shall have internal choices within. Including the choices, the marks for each question shall be 30.

c) The questions may be subdivided into sub-questions and the allocation of marks depends on the weightage of the topic.

B. There will bea Continuous Internal Assessment (CIE)of 40 marks.

Paper

20 Marks

10 Marks

10 Marks

Paper I (Calculus)

Unit Test

Assignment/Seminar

Class Test on Unit II

Paper II (Algebra)

Unit Test

Assignment/Seminar

Class Test on Unit II

Question paper pattern for Unit Test of 20 marks:

The unit test for 20 marks will be conducted online. There shall be 20 compulsory multiple choice questions with single correct answer, each carrying one mark.

C. Practical Examination

1. There will be semester end practical examination of 100 marks.

2. Duration: The examinations shall be of 3Hours duration.

Practical Exam

Viva

Journal

Total

80

10

10

100

Question paper pattern for practical exam of 80 marks:

Part A: Based on Paper I (Total 40 marks)

Section I: Multiple Choice Questions (Total 16 marks, 2 marks each)

Attempt any 8 out of 12

Section II: Attempt any THREE out of FIVE (Total 24 marks, 8 marks each)

Part B: Based on Paper II (Total 40 marks)

Section I: Multiple Choice Questions (Total 16 marks, 2 marks each)

Attempt any 8 out of 12.

Section II: Attempt any THREE out of FIVE (Total 24 marks, 8 marks each)

Each Practical of every course of Semester-I andII shall contain10 problems out of which minimum 05 have to be written in the journal. A student musthavea certified journal before appearing for thepractical examination.

RayatShikshan Sanstha’s

KARMAVEER BHAURAO PATIL COLLEGE, VASHI,NAVI MUMBAI (Autonomous)

Department of Mathematics

M. Sc. Mathematics

(CBCS w.e.f. 2021-22 )

ProgramOutcomes(POs)

Learnersare able to:

PO-1

Disciplinary Knowledge and Skills

Acquire the comprehensive and in-depth knowledge of various subjects in sciences such as Physics, Chemistry, Mathematics, Microbiology, Bio-analytical Science, Computer Science, Data Science, Information Technology and disciplinary skills and ability to apply these skills in the field of science, technology and its allied branches.

PO-2

Communication and Presentation Skills

Develop various communication skills including presentation to express ideas evidently to achieve common goals of the organization.

PO-3

Creativity and Critical Judgement

Facilitatesolutions to current issues based on investigations, evaluation and justification using evidence-based approach.

PO-4

Analytical Reasoning and Problem Solving

Build critical and analytical attitude in handling the problems and situations.

PO-5

Sense of Inquiry

Curiouslyraiserelevant questions based on highly developed ideas, scientific theories and its applications including research.

PO-6

Use of Modern Tools

Use various digital technologies to explore information/data for business, scientific research and related purposes.

PO-7

Research Skills

Construct, collect, investigates, evaluate and interpret information/data relevant to science and technology to adapt, evolve and shape the future.

PO-8

Application of Knowledge

Develop scientific outlook to create consciousness against the social myths and blind faith.

PO-9

Moral and Ethical Reasoning

Imbibe ethical, moral and social values to develop virtues such as justice, generosity and charityas beneficial to individuals and society at large.

PO-10

Leadership and Teamwork

Work cooperatively and lead proactively to achieve the goals of the organization by implementing the plans and projects in various field-based situations related to science, technology and society at large.

PO-11

Environment and Sustainability

Create social awareness about environment and develop sustainability for betterment of future.

PO-12

Lifelong Learning

Realize that pursuit of knowledge is a lifelong activity and in combination with determined efforts, positive attitude and other qualities to lead a successful life.

ProgramSpecificOutcomes(PSO)

PSO1

Recalling the concepts of mathematics and applying them to the various courses like algebra, analysis, Differential equations, statistics, etc to form mathematical models.

PSO2

Apply Mathematics to interdisciplinary ways like statistician, mathematical finance, industry expertise and interpret quantitative ideas.

PSO3

Apply knowledge of Mathematics for research and engineering.

Choice Based Credit System (CBCS) Structure

Programme

SEM

Core Course (CC)

(6 credits per course)

Discipline Specific Elective (DSE)

(6 credits per course)

SEC

(4 credits per course)

MSC-I Mathematics

I

Algebra-I

Discrete Mathematics

Or

Elementary Probability Theory and Statistics

Introduction to R Programming-I

Analysis-I

Complex Analysis

II

Algebra-II

Differential Equation

Or

Optimization Techniques

Introduction to R Programming-II

Topology

Research Methodology

MSC-II Mathematics

III

Algebra-III

Numerical Methods

Or

Graph Theory

Or

Design Theory

IntegralTransform

Analysis-II

Differential Geometry

IV

Field Theory

Fourier Analysis

Or

Mathematical Modelling

Or

Calculus on Manifolds

Project

Functional Analysis

Partial Differential Equations

Note: 1. Blue Highlighted Topic / Course has focused on employability/ entrepreneurship/skill development

2. Yellow Highlighted Topic / Course is related to professional ethics, gender, human values, Environment & sustainability

3. Green HighlightedTopic / Course is related to local/national/regional & global development needs.

CO-PO Mapping Matrix

*In CO-PO Mapping Matrix:a correlation is established between COs and POs in the scale of 1 to 3, 1 being the slight (low), 2 being moderate (medium), 3 being substantial (high), and ‘-’ indicate there is no correlation in respective CO and PO.

PGMT101 - AlgebraI

Course Outcomes: After successful completion of this course, students will be able to:

CO-1:Define dual space and calculate the dual basis of a finite dimensional vector space.

CO-2: Explain the relation between matrices representing a linear transformation and its transpose.

CO-3:Explain different operators like normal, self-adjoint and symmetric operators.

CO4: Compute the Eigenvalue and Eigenvectors and minimal polynomials of a matrix.

CO5: Compute Jordan Canonical form of a matrix.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://onlinecourses.nptel.ac.in/noc20_ma34/preview
  2. https://onlinecourses.nptel.ac.in/noc19_ma23/preview
  3. https://onlinecourses.nptel.ac.in/noc21_ma50/preview

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

1

-

-

1

-

-

-

-

-

-

-

-

CO2

1

1

-

1

-

-

-

-

-

-

-

-

CO3

2

1

-

1

-

-

-

-

-

-

-

-

CO4

3

-

-

2

-

-

-

-

-

-

-

-

CO5

1

-

-

2

-

-

-

-

-

-

-

-

PGMT102- Analysis I

Course Outcomes: After successful completion of this course, students will be able to:

CO-1:Recall Inner product space, norm linear space and vector space.

CO-2: Distinguish among open and closed sets on different topologies of

CO-3: Determine whether a function is Riemann integrable using definition and Riemann criteria.

CO4: Demonstrate a working knowledge of Taylor’s theorem, mean value inequality and mean value theorem.

CO5: Find stationary points, saddle points, maxima and minima of a differentiable function by applying a second derivative test.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

1)Basic Calculus-1 - Coursehttps://onlinecourses.nptel.ac.in/noc20_ma34/preview

2)Basic real analysis - Coursehttps://onlinecourses.nptel.ac.in/noc19_ma23/preview

3)Multivariable calculus - Coursehttps://onlinecourses.nptel.ac.in/noc21_ma50/preview

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

-

-

-

-

-

-

-

-

-

-

CO2

-

-

2

1

-

-

-

-

-

-

-

-

CO3

-

-

1

2

-

-

-

-

-

-

-

-

CO4

1

-

-

2

1

-

-

-

-

-

-

-

CO5

2

-

-

2

2

-

-

-

-

-

-

-

PGMT103 - Complex Analysis

Course Outcomes: After successful completion of this course, students will be able to:

CO-1 :Represent complex numbers algebraically and geometrically.

CO-2 :Define and analyze limits, continuity for complex functions as well as consequences ofcontinuity.

CO-3 :Apply the Cauchy-Riemann equations and results on harmonic and entire functions including the

fundamental theorem of algebra.

CO-4 :Analyze sequences and series of analytic functions and types of convergence.

CO-5 :Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy

integral theorem in its various versions.

CO-6 :Represent functions as Taylor, power and Laurent series, classify singularities and poles,

find residues and evaluate complex integrals using the residue theorem.

ICT Tools Used:Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative(Experimental, Participative, problem Solving)

Links: SWAYAM / MOOCS:

  1. NOC:Complex Analysishttps://nptel.ac.in/courses/111/106/111106141/
  2. Complex Analysishttps://nptel.ac.in/courses/111/107/111107056/
  3. Advanced Complex Analysis https://nptel.ac.in/courses/111/106/111106084/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

1

1

-

-

-

-

-

-

-

-

-

CO2

1

-

-

2

-

-

-

-

-

-

-

-

CO3

1

-

2

3

1

-

-

-

-

-

-

-

CO4

2

-

-

2

-

-

-

-

-

-

-

-

CO5

1

-

2

1

1

-

-

-

-

-

-

-

CO6

1

1

2

-

-

-

-

-

-

-

-

-

PGMT104A - Discrete Mathematics

Course Outcomes: After successful completion of this course, students will be able to:

CO-1:Solve discrete mathematics problems that involve computing permutations and combinations of a set.

CO-2: Explain Polya’s theory of counting, Orbit stabilizer theorem, Burnside lemma and its

applications, applications of Polya’s formula.

CO-3: Apply the knowledge of Number theory to attain specific maturity.

CO4: Apply fundamental enumeration principles to solve appropriate problems.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

Mathematics - Discrete Mathematicshttps://nptel.ac.in/courses/111/107/111107058/

Mathematics - Number Theoryhttps://nptel.ac.in/courses/111/103/111103020/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

1

-

-

2

-

-

-

-

-

-

-

-

CO2

1

1

-

1

-

-

-

-

-

-

-

-

CO3

2

-

-

2

-

-

-

-

-

-

-

-

CO4

1

-

1

3

-

-

-

-

-

-

-

-

PGMT104B - ELEMENTARY PROBABILITY THEORY AND STATISTICS

Course Outcomes: After successful completion of this course, students will be able to:

CO-1:Define the principleconcepts about probability.

CO-2:Express the concept of probability with the concept of random variable and theprobabilitydistributions.

CO-3: Calculate the expected value and the moments.

CO4: Derive the probability density function of transformation of random variables.

CO5: Find basic theoretical and applied principles of statistics.

ICT Tools Used:Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/111/105/111105090/
  2. https://nptel.ac.in/courses/111/105/111105041/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

1

-

-

-

-

-

-

-

-

-

-

-

CO2

1

1

-

1

-

-

-

-

-

-

-

-

CO3

1

-

2

2

-

-

-

-

-

-

-

-

CO4

1

-

1

3

-

-

-

-

-

-

-

-

CO5

1

-

2

2

-

-

-

-

-

-

-

-

PGMT105: INTRODUCTION TO R PROGRAMMING -I

Course Outcomes: After successful completion of this course, students will be able to:

CO-1:Study of fundamentals of R.

CO-2:Use different functions, variables and operators in R

CO-3:Write and execute programming in R by using loop and string

CO-4:Analysed and visualized mathematical statistical functions using R.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative (Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/111/104/111104100/
  2. https://nptel.ac.in/courses/111/104/111104120/
  3. https://nptel.ac.in/courses/111/104/111104146/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

-

-

1

-

1

-

-

-

-

-

-

CO2

2

-

-

1

-

2

-

-

-

-

-

-

CO3

2

1

1

-

-

1

-

-

-

-

-

-

CO4

1

-

-

2

-

-

-

1

-

-

-

-

SEMESTER II

PGMT201 - ALGEBRA II

Course Outcomes: After successful completion of this course, students will be able to:

CO-1 :Understand the concept of group homomorphism, isomorphism and automorphism and apply it

for constructing groups.

CO-2 :Analyze Class equation, Sylow’s theorems and apply them for describing structures

of finite groups.

CO-3 :Demonstrate the knowledge of Rings, ideals of Rings and Quotient rings, Polynomial ring over

field and its extension.

CO-4 :Learn Fundamental theorem of algebra, Burnside theorem and Kronecker's theorem and solve the

problems.

CO-5 :Derive and apply Gauss Lemma, and Eisenstein criterion for irreducibility of Polynomials.

CO-6 :Demonstrate Field extensions and characterization of finite fields.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. NOC:Algebra _ II https://nptel.ac.in/courses/111/106/111106151/
  2. Basic Algebraic Geometryhttps://nptel.ac.in/courses/111/106/111106097/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

1

-

-

3

1

-

-

-

-

-

-

-

CO2

2

-

1

2

-

-

-

-

-

-

-

-

CO3

2

1

2

1

-

-

-

-

-

-

-

-

CO4

3

-

2

-

-

-

-

-

-

-

-

-

CO5

1

-

3

1

-

-

-

-

-

-

-

-

CO6

3

1

2

-

-

-

-

-

-

-

-

-

PGMT202– Topology

Course Outcomes: After successful completion of this course, students will be able to:

CO-1: Identify topologies and form a topological space using basis and sub-basis.

CO-2: Define connected space and find its components and path components of a topological space.

CO-3: Study of theorems on connectedness, compactness and completeness.

CO-4: State the first, second countability and separable axioms. List the results based on first and second countability.

CO-5: Apply metric space concept to compactness and completeness.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/111/106/111106054/#
  2. https://nptel.ac.in/courses/111/106/111106053/#

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

-

-

-

-

-

-

-

-

-

-

-

CO2

2

2

-

1

-

-

-

-

-

-

-

-

CO3

2

-

-

-

-

-

1

1

-

-

-

-

CO4

3

-

2

-

-

-

-

-

-

-

-

-

CO5

-

-

-

-

-

-

-

-

-

-

-

-

PGMT203– RESEARCH METHODOLOGY

Course Outcomes: After successful completion of this course, students will be able to:

CO-1: Understand fundamental concept of research and define appropriate hypothesis.

CO-2: Collect data and apply different methods for sampling data

CO-3: Analyse data and form report

CO-4:Understand IntellectualProperty Rights, patenting and copy right to develop research skill

CO-5:Construct project research report

ICT Tools Used: Videos, PPT, Sampling Data Analysis

Students Centric Methods: Problem Solving and Participative

(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/121/106/121106007/
  2. https://nptel.ac.in/courses/107/108/107108011/
  3. https://nptel.ac.in/courses/127/105/127105008/
  4. https://nptel.ac.in/courses/110/105/110105139/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

2

-

1

1

1

-

-

-

-

-

-

CO2

2

-

-

2

1

1

1

1

-

-

-

-

CO3

2

1

-

-

-

1

1

-

-

-

-

-

CO4

2

2

-

-

-

-

-

-

-

-

-

-

CO5

2

3

-

-

-

1

1

-

-

-

-

1

PGMT204A–Differential equations

Course Outcomes: After successful completion of this course, students will be able to:

CO-1: Apply Picard’s method for finding solutions of first order differential equations.

CO-2: Expresses the existence and uniqueness results for an order linear Ordinary Differential Equations.

CO-3: Apply the method of ‘variation of parameters’ to find solution of higher order linear differential equations with variable coefficients.

CO-4: Define Fourier series and apply for periodic functions.

CO-5: Construct Fourier analysis of daily life periodic functions.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative(Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

1. https://nptel.ac.in/courses/111/108/111108081/.

2. https://nptel.ac.in/courses/111/106/111106046/

3. https://nptel.ac.in/courses/111/104/111104031/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

2

-

-

-

1

-

-

1

-

-

-

-

CO2

2

-

-

3

-

-

1

-

-

-

-

-

CO3

2

-

1

1

-

-

2

-

-

-

-

-

CO4

-

-

-

2

1

-

-

-

-

-

-

-

CO5

-

-

1

2

-

-

-

-

-

-

-

-

PGMT204B– Optimization Techniques

Course Outcomes: After successful completion of this course, students will be able to:

CO-1: Formulate linear programming problems to determine the feasible solutions.

CO-2:Explain first and second order conditions for local optima.

CO-3:Use various methods such as one-dimensional search method, Golden section search,

Fibonacci search etc.

CO-4:Apply operation research to handle data in industry.

ICT Tools Used: Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative (Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/111/105/111105039/
  2. https://nptel.ac.in/courses/111/102/111102012/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

2

1

-

-

-

-

-

-

c

-

-

-

CO2

3

-

1

-

-

-

-

-

-

-

-

-

CO3

2

2

-

-

-

-

-

-

-

-

-

-

CO4

-

-

-

2

1

-

-

-

-

CO5

-

-

-

-

PGMT204A– INTRODUCTION TO R PROGRAMMING-II

Course Outcomes: After successful completion of this course, students will be able to:

CO-1: Create different types of data frames in R

CO-2: Handel and analyse various files in R

CO-3: Analyse and visualize statistical functions using R.

CO-4: Apply R programming to machine learning and big data analysis.

ICT Tools Used:Videos, PPT, Pen-Tablet

Students Centric Methods: Problem Solving and Participative (Experimental, Participative, Problem Solving)

Links: SWAYAM / MOOCS:

  1. https://nptel.ac.in/courses/111/104/111104100/
  2. https://nptel.ac.in/courses/110/105/110105142/
  3. https://nptel.ac.in/courses/111/104/111104120/
  4. https://nptel.ac.in/courses/111/104/111104146/

The CO-PO Mapping Matrix

CO\PO

PO1

PO2

PO3

PO4

PO5

PO6

PO7

PO8

PO9

PO10

PO11

PO12

CO1

3

-

-

1

-

1

-

-

-

-

-

CO2

2

-

-

1

-

2

-

1

-

-

-

-

CO3

2

1

1

-

-

-

-

1

-

-

-

-

CO4

1

-

-

2

-

-

-

1

-

-

-

-

Scheme of Examination

In each semester, the performance of the learners shall be evaluated into two parts. The learner’s performance in each course shall be assessed by Continuous Internal Assessment(CIE) with 40 marksand conducting the Semester End Examinations(SEE)with 60 marks.

Continuous Internal Assessment of 40 marks:

Paper Code

CIE

Unit Tests/Seminar

Total

PGMT101 to PGMT104 and

PGMT201 TO PGMT204

20 Marks

20 Marks

40 Marks

PGMT105 and PGMT205 (SEC)

Practical based on each unit

40 Marks

Project Work:

Evaluation of Project work: The evaluation of the Project submitted by a student shall be made by a Committee appointed by the Head of the Department of Mathematics of the college. The presentation of the project is to be made by the student in front of the committee appointed by the Head of the Department of Mathematics. This committee shall have two members, possibly with one external referee.

The Marks for the project are detailed below:

1. Monthly Project Report & Development: 30 Marks.

2. Power Point presentation: 10 Marks.

3. Viva- voce: 20 Marks.

4. Usage of modern tools/ technology: 10 Marks.

5. Innovativeness: 10 Marks.

6. Individual Contribution: 10 Marks.

7. Group activity: 10 Marks.

Semester End Examination of 60 marks:

(i) Duration: - Examination shall be of Two and Half hours duration.

(ii) Theory Question Paper Pattern: -

1. There shall be five questions each of 12 marks.

2. On each unit there will be one question and the fifth one will be based on entire syllabus.

3. All questions shall be compulsory with internal choice within each question.

4. Each question may be subdivided into sub-questions a, b, c, d and the allocation of marks dependon the weightage of the topic.

5. Each question will be of 24 marks when marks of all the sub-questions are added (including theoptions) in that question.

Questions

Marks

Q 1

Based on Unit I

12

Q 2

Based on Unit II

12

Q 3

Based on Unit III

12

Q 4

Based on Unit IV

12

Q 5

Based on All Units (I to IV)

12

Total Marks

60