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1 Semester - 2024 - Batch | Course Code |
Course |
Type |
Hours Per Week |
Credits |
Marks |
MTH111 | RESEARCH METHODOLOGY | Skill Enhancement Courses | 2 | 2 | 0 |
MTH112 | STATISTICS | Skill Enhancement Courses | 2 | 2 | 0 |
MTH131 | ABSTRACT ALGEBRA | Core Courses | 4 | 4 | 100 |
MTH132 | REAL ANALYSIS | Core Courses | 4 | 4 | 100 |
MTH133 | ORDINARY DIFFERENTIAL EQUATIONS | Core Courses | 4 | 4 | 100 |
MTH134 | LINEAR ALGEBRA | Core Courses | 4 | 4 | 100 |
MTH135 | DISCRETE MATHEMATICS | Core Courses | 4 | 4 | 100 |
MTH151 | INTRODUCTORY COURSE ON PYTHON PROGRAMMING | Core Courses | 2 | 2 | 50 |
2 Semester - 2024 - Batch | Course Code |
Course |
Type |
Hours Per Week |
Credits |
Marks |
MTH211 | TEACHING TECHNOLOGY AND SERVICE LEARNING | - | 2 | 2 | 0 |
MTH212 | RESEARCH AND DEVELOPMENT IN MATHEMATICS | - | 2 | 1 | 0 |
MTH231 | GENERAL TOPOLOGY | - | 4 | 4 | 100 |
MTH232 | COMPLEX ANALYSIS | - | 4 | 4 | 100 |
MTH233 | PARTIAL DIFFERENTIAL EQUATIONS | - | 4 | 4 | 100 |
MTH234 | GRAPH THEORY | - | 4 | 4 | 100 |
MTH235 | INTRODUCTORY FLUID MECHANICS | - | 4 | 4 | 100 |
MTH236 | PRINCIPLES OF DATA SCIENCE | - | 4 | 4 | 100 |
3 Semester - 2023 - Batch | Course Code |
Course |
Type |
Hours Per Week |
Credits |
Marks |
MTH311 | PRACTICE TEACHING | Skill Enhancement Courses | 2 | 2 | 0 |
MTH312 | CALCULUS OF VARIATIONS AND INTEGRAL EQUATIONS | Discipline Specific Elective Courses | 2 | 2 | 0 |
MTH331 | MEASURE THEORY AND LEBESGUE INTEGRATION | Core Courses | 4 | 4 | 100 |
MTH332 | NUMERICAL ANALYSIS | Core Courses | 4 | 4 | 100 |
MTH333 | NUMBER THEORY AND CRYPTOGRAPHY | Core Courses | 4 | 4 | 100 |
MTH334 | MACHINE LEARNING AND ARTIFICIAL INTELLIGENCE | Core Courses | 4 | 4 | 100 |
MTH341A | ADVANCED FLUID MECHANICS | Discipline Specific Elective Courses | 4 | 4 | 100 |
MTH341B | ADVANCED GRAPH THEORY | Discipline Specific Elective Courses | 4 | 4 | 100 |
MTH341C | NUMERICAL LINEAR ALGEBRA | Discipline Specific Elective Courses | 4 | 4 | 100 |
MTH381 | INTERNSHIP | Skill Enhancement Courses | 4 | 3 | 0 |
4 Semester - 2023 - Batch | Course Code |
Course |
Type |
Hours Per Week |
Credits |
Marks |
MTH431 | CLASSICAL MECHANICS | - | 4 | 4 | 100 |
MTH432 | FUNCTIONAL ANALYSIS | - | 4 | 4 | 100 |
MTH433 | DIFFERENTIAL GEOMETRY | - | 4 | 4 | 100 |
MTH434 | NEURAL NETWORKS AND DEEP LEARNING | - | 4 | 4 | 100 |
MTH441A | COMPUTATIONAL FLUID DYNAMICS | - | 4 | 4 | 100 |
MTH441B | ALGEBRAIC GRAPH THEORY | - | 4 | 4 | 100 |
MTH441C | ADVANCED ANALYSIS | - | 4 | 4 | 100 |
MTH451 | PROGRAMMING FOR DATA SCIENCE USING R | - | 2 | 2 | 50 |
MTH481 | PROJECT | - | 4 | 4 | 100 |
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Introduction to Program: | ||||||||||||||||||||||||||||||||||||||||||||||||||||
The MSc course in Mathematics aims at developing mathematical ability in students with acute and abstract reasoning. The course will enable students to cultivate a mathematician’s habit of thought and reasoning and will enlighten students with mathematical ideas relevant for oneself and for the course itself. Course Design: Masters in Mathematics is a two year programme spreading over four semesters. In the first two semesters focus is on the basic courses in mathematics such as Algebra, Topology, Analysis and Graph Theory along with the basic applied course ordinary and partial differential equations. In the third and fourth semester focus is on the special courses, elective courses and skill-based courses including Measure Theory and Lebesgue Integration, Functional Analysis, Computational Fluid Dynamics, Advanced Graph Theory, Numerical Analysis and courses on Data Science . Important feature of the curriculum is that students can specialize in any one of areas (i) Fluid Mechanics, (ii) Graph Theory and (iii) Data Science, with a project on these topics in the fourth semester, which will help the students to pursue research in these topics or grab the opportunities in the industry. To gain proficiency in software skills, four Mathematics Lab papers are introduced, one in each semester. viz. Python Programming for Mathematics, Computational Mathematics using Python, Numerical Methods using Python and Numerical Methods for Boundary Value Problem using Python / Network Science with Python and NetworkX / Programming for Data Science in R / Numerical Linear Algebra using MATLAB respectively. Special importance is given to the skill enhancement courses: Research Methodology, Machine Learning (during 2024-2025 for 2023-2024 batch) and Teaching Technology and Service learning. | ||||||||||||||||||||||||||||||||||||||||||||||||||||
Programme Outcome/Programme Learning Goals/Programme Learning Outcome: PO1: Engage in continuous reflective learning in the context of technology and scientific advancementPO2: Identify the need and scope of the Interdisciplinary research PO3: Enhance research culture and uphold the scientific integrity and objectivity PO4: Understand the professional, ethical and social responsibilities PO5: Understand the importance and the judicious use of technology for the sustainability of the environment PO6: Enhance disciplinary competency, employability and leadership skills Programme Specific Outcome: PSO1: Attain mastery over pure and applied branches of Mathematics and its applications in multidisciplinary fieldsPSO2: Demonstrate problem solving, analytical and logical skills to provide solutions for the scientific requirements PSO3: Develop critical thinking with scientific temper PSO4: Communicate the subject effectively and express proficiency in oral and written communications to appreciate innovations in research PSO5: Understand the importance and judicious use of mathematical software's for the sustainable growth of mankind PSO6: Enhance the research culture in three areas viz. Graph theory, Fluid Mechanics and Data Science and uphold the research integrity and objectivity | ||||||||||||||||||||||||||||||||||||||||||||||||||||
Assesment Pattern | ||||||||||||||||||||||||||||||||||||||||||||||||||||
Assessment Pattern
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Examination And Assesments | ||||||||||||||||||||||||||||||||||||||||||||||||||||
EXAMINATION AND ASSESSMENTS (Theory)
EXAMINATION AND ASSESSMENTS (Practicals) The course is evaluated based on continuous internal assessment (CIA). The parameters for evaluation under each component and the mode of assessment are given below:
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MTH111 - RESEARCH METHODOLOGY (2024 Batch) | |
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
Max Marks:0 |
Credits:2 |
Course Objectives/Course Description |
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Course Description: This course is intended to assist students in acquiring necessary skills on the use of research methodology. Also, the students are exposed to the principles, procedures and techniques of planning and implementing a research project. Course Objectives: This course will help the learner to COBJ 1. Know the general research methods. COBJ 2. Get hands on experience in methods of research that can be employed for research in mathematics. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to foster a clear understanding about research design that enables students in analyzing and evaluating the published research. CO2: On successful completion of the course, the students should be able to obtain necessary skills in understanding the mathematics research articles. CO3: On successful completion of the course, the students should be able to acquire skills in preparing scientific documents using MS Word, Origin, LaTeX and Tikz Library. |
Unit-1 |
Teaching Hours:10 |
Research Methodology
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Introduction to research and research methodology, Scientific methods, Choice of research problem, Literature survey and statement of research problem, Reporting of results, Roles and responsibilities of research student and guide. | |
Unit-2 |
Teaching Hours:10 |
Mathematical research methodology
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Introducing mathematics Journals, reading a Journal article, Ethics in Research and publications, Mathematics writing skills - Standard Notations and Symbols, Using Symbols and Words, organizing a paper, Defining variables, Symbols and notations, Different Citation Styles, IEEE Referencing Style in detail, Tools for checking Grammar and Plagiarism, IPR, Patents/Trademarks and Copyrights, Procedure to apply Patents/Trademarks and Copyrights, The Patent/Trademarks Agent Examinations. | |
Unit-3 |
Teaching Hours:10 |
Type Setting research articles
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Packages for Documentation - MS Word, LaTeX, Overleaf, Tikz Library, Origin, Pictures and Graphs, producing various types of documents using TeX. | |
Text Books And Reference Books: C. R. Kothari and G Garg, Research methodology methods and techniques, 4 th ed., New Age International Publishers, New Delhi, 2019. | |
Essential Reading / Recommended Reading
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Evaluation Pattern The course is evaluated based on continuous internal assessment (CIA). The parameters for evaluation under each component and the mode of assessment are given below: < marks to be converted to credits > | |
MTH112 - STATISTICS (2024 Batch) | |
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
Max Marks:0 |
Credits:2 |
Course Objectives/Course Description |
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Course Description: This course aims at teaching the students the idea of discrete and continuous random variables, Probability theory, in-depth treatment of discrete random variables and distributions, with some introduction to continuous random variables and introduction to estimation and hypothesis testing. Course Objectives: This course will help the learner to COBJ1: be proficient in understanding and solving problems on random variables COBJ2: efficiently solve problems involving probability distributions. COBJ3: Acquire proficiency in hypothesis testing. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to understand random variables and probability distributions. CO2: On successful completion of the course, the students should be able to distinguish between discrete and continuous random variables. CO3: On successful completion of the course, the students should be able to acquire knowledge in using Binomial distribution, Poisson distribution. |
Unit-1 |
Teaching Hours:10 |
Random variables and Distributions
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Introduction to Random variables: Distribution functions, probability mass function and probability density function, Chebyshev's inequality, law of large numbers, central limit theorem, moments and moment generating functions, Binomial, Poisson, Negative binomial, Geometric, Hypergeometric, Discrete uniform. Uniform, Exponential, Gamma, Beta, Weibull, Normal, Lognormal and replacement, t , chi-square, F distribution. | |
Unit-2 |
Teaching Hours:10 |
Theory of estimation
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Basic concepts of estimation, point estimation, methods of estimation, method of moments, method of interval estimation, Maximum likelihood estimates. | |
Unit-3 |
Teaching Hours:10 |
Testing of hypothesis
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Null and alternative hypothesis, type I and II errors, power function, t, chi-square, F test method of finding tests, likelihood ratio test, Neyman Pearson lemma, uniformly most powerful tests, some results based on normal population. | |
Text Books And Reference Books: Gupta S.C. and Kapoor V.K., Fundamentals of Mathematical Statistics, Sultan Chand and Sons, New Delhi, 2001. | |
Essential Reading / Recommended Reading
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Evaluation Pattern SKILL ENHANCEMENT COURSE The course is evaluated based on continuous internal assessment (CIA). The parameters for evaluation under each component and the mode of assessment are given below: | |
MTH131 - ABSTRACT ALGEBRA (2024 Batch) | |
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
Max Marks:100 |
Credits:4 |
Course Objectives/Course Description |
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Course Description: This course enables students to understand the intricacies of advanced areas in algebra. This includes a study of advanced group theory, Euclidean rings, polynomial rings and Galois theory. Course objectives: This course will help the learner to COBJ1. Enhance the knowledge of advanced-level algebra. COBJ2. Understand the proof techniques for the theorems on advanced group theory, rings and Galois theory. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to demonstrate knowledge of conjugates, the Class Equation and Sylow theorems. CO2: On successful completion of the course, the students should be able to demonstrate knowledge of polynomial rings and associated properties. CO3: On successful completion of the course, the students should be able to derive and apply Gauss Lemma, Eisenstein criterion for the irreducibility of rationals. CO4: On successful completion of the course, the students should be able to demonstrate the characteristic of a field and the prime subfield. CO5: On successful completion of the course, the students should be able to demonstrate factorisation and ideal theory in the polynomial ring; the structure of primitive polynomials; field extensions and characterization of finite normal extensions as splitting fields; the structure and construction of finite fields; radical field extensions; Galois group and Galois theory. |
Unit-1 |
Teaching Hours:15 |
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Advanced Group Theory
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Automorphisms, Cayley’s theorem, Cauchy’s theorem, permutation groups, symmetric groups, alternating groups, simple groups, conjugate elements and class equations of finite groups, Sylow theorems, direct products, finite Abelian groups, solvable groups. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Rings
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Euclidean Ring, polynomial rings, polynomials rings over the rational field, polynomial rings over commutative rings. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Fields
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Extension fields, roots of polynomials, construction with straightedge and compass, more about roots. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Galois theory
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The elements of Galois theory, solvability by radicals, Galois group over the rationals, finite fields. | |||||||||||||||||||||||||||||
Text Books And Reference Books: I. N. Herstein, Topics in algebra, Second Edition, John Wiley and Sons, 2007. | |||||||||||||||||||||||||||||
Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH132 - REAL ANALYSIS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This course will help students to understand the concepts of functions of single and several variables. This course includes such concepts as Riemann-Stieltjes integral, sequences and series of functions, Special Functions, and the Implicit Function Theorem.
Course objectives: This course will help the learner to COBJ1. develop in a rigorous and self-contained manner the elements of real variable functions COBJ2. integrate functions of a real variable in the sense of Riemann – Stieltjes COBJ3. classify sequences and series of functions which are pointwise convergent and uniform Convergent COBJ4. explore the properties of special functions COBJ5. understand and apply the functions of several variables. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to determine the Riemann-Stieltjes integrability of a bounded function. CO2: On successful completion of the course, the students should be able to recognize the difference between pointwise and uniform convergence of sequence/series of functions. CO3: On successful completion of the course, the students should be able to illustrate the effect of uniform convergence on the limit function with respect to continuity, differentiability, and integrability. CO4: On successful completion of the course, the students should be able to analyze and interpret the special functions such as exponential, logarithmic, trigonometric and Gamma functions. CO5: On successful completion of the course, the students should be able to gain in depth knowledge on functions of several variables and the use of Implicit Function Theorem. |
UNIT 1 |
Teaching Hours:15 |
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The Riemann-Stieltjes Integration
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Definition and Existence of Riemann-Stieltjes Integral, Linearity Properties of Riemann-Stieltjes Integral, The Riemann-Stieltjes Integral as the Limit of Sums, Integration and Differentiation, Integration of Vector-valued Functions, Rectifiable Curves. | |||||||||||||||||||||||||||||
UNIT 2 |
Teaching Hours:15 |
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Sequences and Series of Functions
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Pointwise and uniform convergence, Uniform Convergence: Continuity, Integration and Differentiation, Equicontinuous Families of Functions, The Stone-Weierstrass Theorem | |||||||||||||||||||||||||||||
UNIT 3 |
Teaching Hours:15 |
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Some Special Functions
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Power Series, The Exponential and Logarithmic Functions, The Trigonometric Functions, The Algebraic Completeness of the Complex Field, Fourier Series, The Gamma Function. | |||||||||||||||||||||||||||||
UNIT 4 |
Teaching Hours:15 |
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Functions of Several Variables
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Linear Transformations, Differentiation, The Contraction Principle, The Inverse Function Theorem, The Implicit Function Theorem. | |||||||||||||||||||||||||||||
Text Books And Reference Books: W. Rudin, Principles of Mathematical Analysis, 3rd ed., New Delhi: McGraw-Hill (India), 2016. | |||||||||||||||||||||||||||||
Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH133 - ORDINARY DIFFERENTIAL EQUATIONS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This helps students understand the beauty of the important branch of mathematics, namely, differential equations. This course includes a study of second order linear differential equations, adjoint and self-adjoint equations, existence and uniqueness of solutions, Eigenvalues and Eigenvectors of the equations, power series method for solving differential equations. Non-linear autonomous system of equations. Course Objectives: This course will help the learner to COBJ1. solve adjoint differential equations and understand the zeros of solutions.
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to understand concept of linear differential equation, Fundamental set Wronskian. CO2: On successful completion of the course, the students should be able to understand the existence and uniqueness of solutions of differential equations and to solve the Strum-Liouville problems. CO3: On successful completion of the course, the students should be able to identify ordinary and singular points by Frobenius Method, Hyper geometric differential equation and its polynomial.
CO4: On successful completion of the course, the students should be able to understand the basic concepts of the existence and uniqueness of solutions. CO5: On successful completion of the course, the students should be able to understand basic concept of solving the linear and non-linear autonomous systems of equations. CO6: On successful completion of the course, the students should be able to understand the concept of critical point and stability of the system. |
Unit-1 |
Teaching Hours:15 |
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Linear Differential Equations
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Linear differential equations, fundamental sets of solutions, Wronskian, Liouville’s theorem, adjoint and self-adjoint equations, Lagrange identity, Green’s formula, zeros of solutions, comparison and separation theorems. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Existence and Uniqueness of solutions
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Fundamental existence and uniqueness theorem, Dependence of solutions on initial conditions, existence and uniqueness theorem for higher order and system of differential equations, Eigenvalue Problems, Strum-Liouville problems, Orthogonality of eigenfunctions. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Power series solutions
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Ordinary and singular points of the differential equations, Classification of singular points, Solution near an ordinary point and a regular singular point by Frobenius method, solution near irregular singular point, Hermite, Laguerre, Chebyshev and Hypergeometric differential equation and its polynomial solutions, standard properties. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Linear and non-linear Autonomous differential equations
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Linear system of homogeneous and non-homogeneous equations, Non-linear autonomous sysem of equations, Phase plane, Critical points, Stability, Liapunov direct method, limit cycle and periodic solutions, Bifurcation of plane autonomous systems. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH134 - LINEAR ALGEBRA (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This course aims at introducing elementary notions on linear transformations, canonical forms, rational forms, Jordan forms, inner product space and bilinear forms. Course Objectives: This course will help the learner to COBJ 1. have thorough understanding of Linear transformations and its properties. COBJ 2. understand and apply the elementary canonical forms, rational and Jordan forms in real life problems. COBJ 3. gain knowledge on Inner product space and the orthogonalisation process. COBJ 4. explore different types of bilinear forms and their properties. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to gain in-depth knowledge on Linear transformations. CO2: On successful completion of the course, the students should be able to demonstrate the elementary canonical forms, rational and Jordan forms. CO3: On successful completion of the course, the students should be able to apply the inner product space in orthogonality. CO4: On successful completion of the course, the students should be able to gain familiarity in using bilinear forms. |
Unit-1 |
Teaching Hours:15 |
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Linear Transformations and Determinants
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Linear transformations, algebra of linear transformations, isomorphism, representation of transformation by matrices, linear functionals, the transpose of a linear transformation, determinants: commutative rings, determinant functions, permutation and the uniqueness of determinants, additional properties of determinants. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:20 |
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Elementary Canonical Forms, Rational and Jordan Forms
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Elementary canonical forms: characteristic values, annihilating polynomials, invariant subspaces, simultaneous triangulation and diagonalization, direct sum decomposition, invariant dual sums, the primary decomposition theorem. the rational and Jordan forms: cyclic subspaces and annihilators, cyclic decompositions and the rational form, the Jordan form, computation of invariant factors, semi-simple operators. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Inner Product Spaces
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Inner products, Inner product spaces, Linear functionals and adjoints, Unitary operators – Normal operators, Forms on Inner product spaces, Positive forms, Spectral theory, Properties of Normal operators. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:10 |
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Bilinear Forms
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Bilinear forms, Symmetric Bilinear forms, Skew-Symmetric Bilinear forms, Groups preserving Bilinear forms. | |||||||||||||||||||||||||||||
Text Books And Reference Books: K. Hoffman and R. Kunze, Linear Algebra, 2nd ed. New Delhi, India: PHI Learning Private Limited, 2011. | |||||||||||||||||||||||||||||
Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH135 - DISCRETE MATHEMATICS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This course will discuss the fundamental concepts and tools in discrete mathematics with emphasis on their applications to mathematical writing, enumeration and recurrence relations. Course Objectives: The course will help the learner to COBJ 1. develop logical foundations to understand and create mathematical arguments.. COBJ 2. implement enumeration techniques in a variety of real-life problems. COBJ 3. analyze the order and efficiency of algorithms. COBJ 4. communicate the basic and advanced concepts of the topic precisely and effectively.
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to demonstrate mathematical logic to write mathematical proofs and solve problems. CO2: On successful completion of the course, the students should be able to apply the concepts of sets, relations, functions and related discrete structures in practical situations. CO3: On successful completion of the course, the students should be able to understand and apply basic and advanced counting techniques in real-life problems CO4: On successful completion of the course, the students should be able to analyse algorithms, determine their efficiency and gain proficiency in preparing efficient algorithms |
Unit-1 |
Teaching Hours:15 |
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Set Theory and Mathematical Logic
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Sets: Cardinality and countability, recursively defined sets, relations, equivalence relations and equivalence classes, partial and total ordering, representation of relations, closure of relations, functions, bijection, inverse functions. Logic: Propositions, logical equivalences, rules of inference, predicates, quantifiers, nested quantifiers, arguments, formal proof methods and strategies. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Enumeration Techniques
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Fundamental principles, pigeon-hole principle, permutations – with and without repetitions, combinations- with and without repetitions, binomial theorem, binomial coefficients, principle of inclusion and exclusion, derangements, arrangements with forbidden positions, rook polynomial. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Generating Functions and Recurrence Relations
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Ordinary and exponential generating functions, recurrence relations, first order linear recurrence relations, higher order linear homogeneous recurrence relations, non-homogeneous recurrence relations, solving recurrence relations using generating functions. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Analysis of Algorithms
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Real-valued functions, big-O, big-Omega and big-Theta notations, orders of power functions, orders of polynomial functions, analysis of algorithm efficiency, the sequential search algorithm, exponential and logarithmic orders, binary search algorithm. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH151 - INTRODUCTORY COURSE ON PYTHON PROGRAMMING (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
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Max Marks:50 |
Credits:2 |
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Course Objectives/Course Description |
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This course aims at introducing the programming language Python andits uses in solving problems on discrete mathematics and differential equations. Course Objectives: This course will help the learner to COBJ1. gain proficiency in using Python for programming. COBJ2. acquire skills in usage of suitable functions/packages of Python to solve mathematical problems. COBJ3. acquaint with Sympy and Numpy packages for solving concepts of calculus, linear algebra and Differential equations. COBJ4. illustrates use of built-in functions of Pandas and Matplotlib packages for visualizing of data and plotting of graphs. |
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Course Outcome |
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CO1: acquire proficiency in using different functions of Python to compute solutions of basic mathematical problems. CO2: demonstrate the use of Python to solve differential equations along with visualize the solutions. CO3: be familiar with manipulating and visualizing data using pandas. |
Unit-1 |
Teaching Hours:10 |
Basic of Python
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Installation, IDE, variables, built-in functions, input and output, modules and packages, data types and data structures, use of mathematical operators and mathematical functions, programming structures (conditional structure, the for loop, the while loop, nested statements) | |
Unit-2 |
Teaching Hours:10 |
Symbolic and Numeric Computations
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Use of Sympy package, Symbols, Calculus, Differential Equations, Series expressions, Linear and non-linear equations, List, Tuples and Arrays. | |
Unit-3 |
Teaching Hours:10 |
Data Visualization
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Standard plots (2D, 3D), Scatter plots, Slope fields, Vector fields, Contour plots, streamlines, Manipulating and data visualizing data with Pandas, Mini Project. | |
Text Books And Reference Books: Svein Linge & Hans Petter Langtangen, Programming for computations- Python -A gentle Introduction to Numerical Simulations with Python 3.6, Springer Open, Second Edn. 2020. | |
Essential Reading / Recommended Reading
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Evaluation Pattern The course is evaluated based on continuous internal assessments (CIA) and the lab e-record. The parameters for evaluation under each component and the mode of assessment are given below. | |
MTH211 - TEACHING TECHNOLOGY AND SERVICE LEARNING (2024 Batch) | |
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
Max Marks:0 |
Credits:2 |
Course Objectives/Course Description |
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Course Description: This course is intended to assist the students in acquiring necessary skills for the use of modern technology in teaching. They are exposed to the principles, procedures, techniques of planning and implementing teaching techniques. Through service learning, they will apply the knowledge in real-world situations and serve the community. Course objectives: This course will help the learner to COBJ 1: understand the pedagogy of teaching. COBJ 2: able to use various ICT tools for effective teaching. COBJ 3: apply the knowledge in real-world situations. COBJ 4: enhances academic comprehension through experiential learning. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to gain necessary skills on the use of modern technology in teaching.
CO2: On successful completion of the course, the students should be able to understand the components and techniques of effective teaching. CO3: On successful completion of the course, the students should be able to obtain necessary skills for pursuing mathematics teaching. CO4: On successful completion of the course, the students should be able to strengthen personal character and attain the sense of social responsibility through service-learning module. CO5: On successful completion of the course, the students should be able to contribute to the community by addressing and meeting the community needs. |
Unit-1 |
Teaching Hours:10 |
Teaching Technology
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Development of concept of teaching, Teaching skills, Chalk board skills, Teaching practices, Effective teaching, Models of teaching, Teaching aids (Audio-Visual), Teaching aids (projected and non-projected), Communication skills, Feedback in teaching, Teacher’s role and responsibilities, Information technology for teaching. | |
Unit-2 |
Teaching Hours:5 |
Service Learning
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Concept of difference between social service and service learning, Case study of best practices, understanding contemporary societal issues, Intervention in the community, Assessing need and demand of the chosen community. | |
Unit-3 |
Teaching Hours:15 |
Community Service
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A minimum of fifteen (15) hours documented service is required during the semester. A student must keep a log of the volunteered time and write the activities of the day and the services performed. A student must write a reflective journal containing an analysis of the learning objectives. | |
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern The course is evaluated based on continuous internal assessment (CIA). The parameters for evaluation under each component and the mode of assessment are given below: < marks to be converted to credits > | |
MTH212 - RESEARCH AND DEVELOPMENT IN MATHEMATICS (2024 Batch) | |
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
Max Marks:0 |
Credits:1 |
Course Objectives/Course Description |
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This course aims at strengthening students by providing exposure to analyze and understand the literature from mathematics journals of their choice and present it among peers. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to demonstrate their ability to understand the research articles published in journals.
CO2: On successful completion of the course, the students should be able to explain the research articles to the mathematics fraternity. CO3: On successful completion of the course, the students should be able to handle the queries on the research articles that are presented. |
Unit-1 |
Teaching Hours:30 |
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Text Books And Reference Books: . | |
Essential Reading / Recommended Reading . | |
Evaluation Pattern Assessment Criteria:
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MTH231 - GENERAL TOPOLOGY (2024 Batch) | |
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
Max Marks:100 |
Credits:4 |
Course Objectives/Course Description |
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Course Description: This course deals with the essentials of topological spaces and their properties in terms of continuity, connectedness, compactness etc. Course objectives: This course will help the learner to: COBJ1. understand precise definitions and appropriate examples and counter examples of fundamental concepts in general topology. COBJ2. acquire knowledge about generalization of the concept of continuity, product topology, metric topology and related results. COBJ3. appreciate the beauty of deep mathematical results such as Uryzohn’s metrization theorem and understand and apply various proof techniques. |
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Course Outcome |
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CO1: On successful completion of the course define topological spaces, give examples and counterexamples on core concepts like open sets, basis and subspaces and other related concepts in topology. CO2: On successful completion of the course, establish equivalent definitions of continuity and apply the same in proving theorems, analyse product/metric spaces. CO3: On successful completion of the course, understand the concepts of connectedness and compactness and prove the related theorems. Analyze the proof techniques involved in proving Urysohn Metrization Theorem and Titetze Extension Theorem |
Unit-1 |
Teaching Hours:15 |
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Topological Spaces
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Elements of topological spaces, basis for a topology, the order topology, the product topology on X x Y, the subspace topology, Closed sets and limit points. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Continuous Functions
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Continuous functions, the product topology, metric topology. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Connectedness and Compactness
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Connected spaces, connected subspaces of the Real line, components and local connectedness, compact spaces, Compact Subspaces of the Real line, limit point compactness, local compactness. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Countability and Separation Axioms
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The countability axioms, the separation axioms, normal spaces, the Urysohn lemma, the Urysohn metrization theorem, Tietze extension theorem. | |||||||||||||||||||||||||||||
Text Books And Reference Books: J.R. Munkres,Topology, Second Edition, Prentice Hall of India, 2007. | |||||||||||||||||||||||||||||
Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH232 - COMPLEX ANALYSIS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description:This course will help students learn about the essentials of complex analysis. This course includes important concepts such as power series, analytic functions, linear transformations, Laurent’s series, Cauchy’s theorem, Cauchy’s integral formula, Cauchy’s residue theorem, argument principle, Schwarz lemma and theorems on meromorphic functions. Course objectives: This course will help the learner to COBJ1. enhance the understanding the advanced concepts in complex Analysis COBJ2. acquire problem solving skills in complex Analysis. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to apply the concept and consequences of analyticity and related theorems. CO2: On successful completion of the course, the students should be able to represent functions as Taylor and Laurent series, classify singularities and poles, find residues, and evaluate complex integrals using the residue theorem and understand conformal mappings.
CO3: On successful completion of the course, the students should be able to understand meromorphic functions and simple theorems concerning them.
CO4: On successful completion of the course, the students should be able to understand advanced theorems on meromorphic functions. |
Unit-1 |
Teaching Hours:15 |
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Analytic functions and singularities
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Morera’s theorem, Gauss mean value theorem, Cauchy inequality for derivatives, Liouville’s theorem, fundamental theorem of algebra, maximum and minimum modulus theorems. Taylor’s series, Laurent’s series, zeros of analytical functions, singularities, classification of singularities, characterization of removable singularities and poles. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Mappings
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Rational functions, behavior of functions in the neighborhood of an essential singularity, Cauchy’s residue theorem, contour integration problems, Mobius transformation, conformal mappings. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Meromorphic functions - 1
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Meromorphic functions and argument principle, Schwarz lemma, Rouche’s theorem, convex functions and their properties, Hadamard 3-circles theorem. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Meromorphic functions - 2
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Phragmen-Lindelöf theorem, Riemann mapping theorem, Weierstrass factorization theorem, Harmonic functions, Poisson formula, Poisson integral formula, Jensen’s formula, Poisson-Jensen formula. | |||||||||||||||||||||||||||||
Text Books And Reference Books: J. B. Conway, Functions of One Complex Variable, 2nd ed., New York: Springer, 2000. | |||||||||||||||||||||||||||||
Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH233 - PARTIAL DIFFERENTIAL EQUATIONS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This helps students understand the beauty of the important branch of mathematics, namely, partial differential equations. This course includes a study of first and second order linear and non-linear partial differential equations, existence and uniqueness of solutions to various boundary conditions, classification of second order partial differential equations, wave equation, heat equation, Laplace equations and their solutions by Eigenfunction method and Integral Transform Method. Course Objectives: This course will help the learner to COBJ 1. understand the occurrence of partial differential equations in physics and its applications. COBJ 2. solve partial differential equation of the type heat equation, wave equation and Laplace equations. COBJ 3. also solving initial boundary value problems. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to understand the basic concepts and definition of PDE and mathematical models representing stretched string, vibrating membrane, heat conduction in rod. CO2: On successful completion of the course, the students should be able to demonstrate the canonical form of second order PDE. CO3: On successful completion of the course, the students should be able to demonstrate initial value boundary problem for homogeneous and non-homogeneous PDE. CO4: On successful completion of the course, the students should be able to demonstrate on boundary value problem by Dirichlet and Neumann problem. |
UNIT 1 |
Teaching Hours:10 |
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First Order Partial differential equations
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Formation of PDE, initial value problems (IVP), boundary value problems (BVP) and IBVP, solutions of first, methods of characteristics for first order PDE, linear and quasi, linear, method of characteristics for one-dimensional wave equations and other hyperbolic equations. | |||||||||||||||||||||||||||||
UNIT 2 |
Teaching Hours:15 |
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Second order Partial Differential Equations
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Origin of second order PDE, Classification of second order PDE, Initial value problems (IVP), Boundary value problems (BVP) and IBVP, Mathematical models representing stretched string, vibrating membrane, heat conduction in solids, second-order equations in two independent variables. Cauchy’s problem for second order PDE, Canonical forms, General solutions. | |||||||||||||||||||||||||||||
UNIT 3 |
Teaching Hours:15 |
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Solutions of Parabolic PDE
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Occurrence of heat equation in Physics, resolution of boundary value problem, elementary solutions, method of separation of variables, method of eigen function expansion, Integral transforms method, Green’s function. | |||||||||||||||||||||||||||||
UNIT 4 |
Teaching Hours:20 |
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Solutions of Hyperbolic and Elliptic PDE
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Occurrence of wave and Laplace equations in Physics, Jury problems, elementary solutions of wave and Laplace equations, methods of separation of variables,, the theory of Green’s function for wave and Laplace equations. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH234 - GRAPH THEORY (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This course is an introductory course to the basic concepts of Graph Theory. This includes definition of graphs, vertex degrees, directed graphs, trees, distances, connectivity and paths. Course objectives: This course will help the learner to COBJ 1: know the history and development of Graph Theory COBJ 2: understand all the elementary concepts and results COBJ 3: learn proof techniques and algorithms in Graph Theory |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to write precise and accurate mathematical definitions of basics concepts in Graph Theory. CO2: On successful completion of the course, the students should be able to provide appropriate examples and counterexamples to illustrate the basic concepts. CO3: On successful completion of the course, the students should be able to demonstrate various proof techniques in proving theorems. CO4: On successful completion of the course, the students should be able to use algorithms to investigate Graph theoretic parameters. |
Unit-1 |
Teaching Hours:15 |
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Introduction to Graphs
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Graphs as models, degree sequences, classes of graphs, matrices, isomorphism, distances in graphs, connectivity, Eulerian and Hamiltonian graphs, Chinese postman problems, travelling salesman problem and Dijkstra’s algorithm. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:15 |
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Trees
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Properties of trees, rooted trees, spanning trees, algorithms on trees- Prufer’s code, Huffmans coding, searching, and sorting algorithms, spanning tree algorithms. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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Planarity
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Graphical embedding, Euler’s formula, platonic bodies, homeomorphic graphs, Kuratowski’s theorem, geometric duality. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:15 |
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Graph Invariants
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Vertex and edge coloring, chromatic polynomial and index, matching, decomposition, independent sets and cliques, vertex and edge covers, clique covers, digraphs and networks. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH235 - INTRODUCTORY FLUID MECHANICS (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Course Description: This course aims at introducing the fundamental aspects of fluid mechanics. They will have a deep insight and general comprehension on tensors, kinematics of fluid, incompressible flow, boundary layer flows and classification of non-Newtonian fluids. Course Objectives: This course will help the learner to COBJ1: understand the basic concept of tensors and their representations. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to confidently manipulate tensor expressions using index notation and use the divergence theorem and the transport theorem. CO2: On successful completion of the course, the students should be able to understand the basics laws of Fluid mechanics and their physical interpretations. CO3: On successful completion of the course, the students should be able to comprehend two and three dimension flows incompressible flows. CO4: On successful completion of the course, the students should be able to appreciate the concepts of the viscous flows, their mathematical modelling and physical interpretations. |
Unit-1 |
Teaching Hours:15 |
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Cartesian tensors and continuum hypothesis
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Cartesian tensors: Cartesian tensors, basic properties, transpose, symmetric and skew symmetric tensors, gradient, divergence and curl in tensor calculus, integral theorems. Continuum hypothesis: deformation gradient, strain tensors, infinitesimal strain, compatibility relations, principal strains, material and local time derivatives, transport formulas, streamlines, path lines. | |||||||||||||||||||||||||||||
Unit-2 |
Teaching Hours:20 |
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Stress, Strain and basic physical laws
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Stress and Rate of Strain: stress components and stress tensor, normal and shear stresses, principal stresses, transformation of the rate of strain and stress, relation between stress and rate of strain. Fundamental basic physical laws: The equations of conservation of mass, linear momentum (Navier-Stokes equations), and energy. | |||||||||||||||||||||||||||||
Unit-3 |
Teaching Hours:15 |
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One-, two- and three-Dimensional inviscid incompressible Flow
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Bernoulli equation, applications of Bernoulli equation, Concept of circulation, Kelvin circulation theorem, constancy of circulation, Laplace equations, stream functions in two- and three-dimensional motion. Two dimensional flow: Rectilinear flow, source and sink, the theorem of Blasius. | |||||||||||||||||||||||||||||
Unit-4 |
Teaching Hours:10 |
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Two-dimensional flows of viscous fluid
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Flow between parallel flat plates, Couette flow, plane Poiseuille flow, the Hagen Poiseuille flow, flow between two concentric rotating cylinders. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern Examination and Assessments
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MTH236 - PRINCIPLES OF DATA SCIENCE (2024 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:60 |
No of Lecture Hours/Week:4 |
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Max Marks:100 |
Credits:4 |
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Course Objectives/Course Description |
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Data Science is an interdisciplinary, problem-solving oriented subject that learns to apply scientific techniques to practical problems. This course provides a strong foundation for data science and application area related to information technology and understand the underlying core concepts and emerging technologies in data science. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to have the managerial understanding of the tools and techniques used in Data Science process. CO2: On successful completion of the course, the students should be able to analyze data analysis techniques for applications handling large data.
CO3: On successful completion of the course, the students should be able to apply techniques used in Data Science and Machine Learning algorithms to make data driven, real time, day to day organizational decisions. CO4: On successful completion of the course, the students should be able to present the inference using various Visualization tools. CO5: On successful completion of the course, the students should be able to learn to think through the ethics surrounding privacy, data sharing and algorithmic decision-making |
UNIT 1 |
Teaching Hours:12 |
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Introduction to Data Science
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Definition, big data and data science hype, why data science, getting past the hype, the current landscape, who is data scientist? - data science process overview, defining goals, retrieving data, data preparation, data exploration, data modeling, presentation. | |||||||||||||||||||||||||||||
UNIT 2 |
Teaching Hours:12 |
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Big Data
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Problems when handling large data, General techniques for handling large data, Case study, Steps in big data, Distributing data storage and processing with Frameworks, Case study. | |||||||||||||||||||||||||||||
UNIT 3 |
Teaching Hours:14 |
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Machine Learning
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Machine learning, modeling process, training model, validating model, predicting new observations, supervised learning algorithms, unsupervised learning algorithms. introduction to deep learning. | |||||||||||||||||||||||||||||
UNIT 4 |
Teaching Hours:12 |
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Data Visualization
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The characteristic polynomial, eigenvalues and graph parameters, eigenvalues of regular graphs, eigenvalues and expanders, strongly regular graphs. | |||||||||||||||||||||||||||||
Unit-5 |
Teaching Hours:10 |
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Ethics and Recent Trends
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Data Science Ethics – Doing good data science – Owners of the data - Valuing different aspects of privacy - Getting informed consent - The Five Cs – Diversity – Inclusion – Future Trends. | |||||||||||||||||||||||||||||
Text Books And Reference Books:
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Essential Reading / Recommended Reading
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Evaluation Pattern
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MTH311 - PRACTICE TEACHING (2023 Batch) | |||||||||||||||||||||||||||||
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
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Max Marks:0 |
Credits:2 |
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Course Objectives/Course Description |
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This course is designed to prepare students for real class room situation under the supervision of faculty mentors. It provides experiences in the actual teaching and learning environment. · Fifteen hours of teaching assignments for UG classes shall be undertaken by each student during the 3rd and 4th semester. · Each student shall be under the supervision of a faculty mentor/guide. · The 15 hours may be distributed among 1 or 2 subjects- which shall be a combination of theory and problem based papers. · A Structured Plan stating the Topic- Objectives- Methodology and Evaluation shall be prepared in advance by the student for each class session and submitted to the faculty mentor/guide. · Faculty guides shall maintain an assessment register for their respective students and record assessment for each session on the given parameters. |
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Course Outcome |
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CO1: On successful completion of the course, the students should be able to demonstrate and use various teaching pedagogies. CO2: On successful completion of the course, the students should be able to develop content and material for classroom teaching. CO3: On successful completion of the course, the students should be able to manage classroom sessions effectively. CO4: On successful completion of the course, the students should be able to assist the teachers in internal assessments. CO5: On successful completion of the course, the students should be able to articulate and communicate in an effective way. |
Unit-1 |
Teaching Hours:15 |
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Practice Teaching
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This course is designed to prepare students for real class room situation under the supervision of faculty mentors. It provides experiences in the actual teaching and learning environment.
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Text Books And Reference Books: NA | ||||||||||||||||
Essential Reading / Recommended Reading NA | ||||||||||||||||
Evaluation Pattern
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MTH312 - CALCULUS OF VARIATIONS AND INTEGRAL EQUATIONS (2023 Batch) | ||||||||||||||||
Total Teaching Hours for Semester:30 |
No of Lecture Hours/Week:2 |
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Max Marks:0 |
Credits:2 |
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Course Objectives/Course Description |
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