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:
-
https://onlinecourses.nptel.ac.in/noc20_ma34/preview
- https://onlinecourses.nptel.ac.in/noc19_ma23/preview
- 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:
- NOC:Complex Analysishttps://nptel.ac.in/courses/111/106/111106141/
- Complex
Analysishttps://nptel.ac.in/courses/111/107/111107056/
- 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:
- https://nptel.ac.in/courses/111/105/111105090/
- 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:
- https://nptel.ac.in/courses/111/104/111104100/
- https://nptel.ac.in/courses/111/104/111104120/
- 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:
- NOC:Algebra
_ II https://nptel.ac.in/courses/111/106/111106151/
- 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:
- https://nptel.ac.in/courses/111/106/111106054/#
- 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
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
-
|
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:
- https://nptel.ac.in/courses/111/105/111105039/
- 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
|
|
|
|
|
|
|
|
|
-
|
-
|
-
|
-
|
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
|