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MSC in Pure Mathematics at Sant Gadge Baba Amravati University
Amravati, Maharashtra
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About the Specialization
What is Pure Mathematics at Sant Gadge Baba Amravati University Amravati?
This M.Sc. Pure Mathematics program at Sant Gadge Baba Amravati University focuses on advanced theoretical concepts in mathematics. It delves into the fundamental structures of algebra, analysis, topology, and differential equations, offering a rigorous foundation. The curriculum is designed to foster analytical thinking and problem-solving skills crucial for research and academia within the Indian scientific landscape, addressing a growing demand for advanced mathematical expertise.
Who Should Apply?
This program is ideal for Bachelor of Science graduates with a strong foundation in Mathematics, seeking to pursue higher education or research careers. It''''s suitable for aspiring university lecturers, researchers, or those aiming for Ph.D. studies in India or abroad. Fresh graduates passionate about abstract concepts and logical reasoning will find this program stimulating and intellectually rewarding, preparing them for advanced challenges in analytical fields.
Why Choose This Course?
Graduates of this program can expect career paths as Assistant Professors in colleges/universities, researchers in scientific organizations, or quantitative analysts in finance. Entry-level salaries in academia in India typically range from INR 4-7 lakhs per annum, with significant growth potential depending on qualifications and experience. This degree also provides a solid base for competitive exams like NET/SET for lectureship and various civil services examinations.
Student Success Practices
Foundation Stage
Master Core Concepts with Rigor- (Semester 1-2)
Focus intensely on understanding the foundational theories of Abstract Algebra, Real Analysis, and Complex Analysis. Engage deeply with lecture material, review proofs meticulously, and practice problem-solving using standard texts like Walter Rudin for Analysis or Contemporary Abstract Algebra by Joseph Gallian. Consistent practice is key to building a strong base.
Tools & Resources
University Library (recommended textbooks), NPTEL online lecture series, MIT OpenCourseware, Peer study groups
Career Connection
A strong theoretical base is critical for cracking competitive exams like NET/SET and Ph.D. entrance exams, leading to academic and research careers in India.
Develop Programming Skills for Numerical Applications- (Semester 1-2)
Actively participate in the C programming practicals and understand how mathematical algorithms translate into efficient code. Dedicate time to coding practice beyond assignments. Explore online platforms like GeeksforGeeks to solve numerical problems related to differential equations using C, enhancing computational thinking.
Tools & Resources
CodeBlocks IDE, GeeksforGeeks, HackerRank, University lab facilities
Career Connection
Essential for roles in quantitative analysis, computational mathematics, and data science, which are growing sectors in the Indian job market, offering diverse opportunities.
Engage in Peer Learning and Discussion Forums- (Semester 1-2)
Form study groups with classmates to discuss difficult topics, solve problems collaboratively, and clarify doubts. Regularly meet with peers to review lecture notes, work through challenging exercises, and present solutions to each other, fostering a deeper understanding and improving communication skills.
Tools & Resources
WhatsApp groups for quick queries, Google Meet for online discussions, University common rooms for study sessions
Career Connection
Enhances communication and teamwork skills, valuable in any professional or academic setting, and strengthens networking within your field, aiding future collaborations.
Intermediate Stage
Deepen Specialization through Electives and Advanced Studies- (Semester 3-4)
Carefully choose electives that align with your interest in Pure Mathematics (e.g., Graph Theory, Number Theory, Discrete Mathematics, Topology). Beyond coursework, delve into advanced literature and research papers in your chosen specialized areas. Seek out opportunities to apply theoretical knowledge to complex problems.
Tools & Resources
JSTOR and MathSciNet for research papers, Departmental research seminars, Faculty mentorship for advanced topics
Career Connection
This specialization helps define your research profile for Ph.D. applications and makes you a more attractive candidate for specialized academic or research roles, both nationally and internationally.
Participate in Workshops, Seminars, and Conferences- (Semester 3-4)
Actively attend national or regional workshops, seminars, and academic conferences related to mathematics. Look for opportunities within the university or other institutions in India to present minor research findings or participate in poster sessions, helping to build your academic presence and network.
Tools & Resources
Notices on department bulletin boards, University website for event listings, Online academic event calendars (e.g., those by Indian Mathematical Society)
Career Connection
Builds a professional network with peers and senior academics, exposes you to current research trends, and can lead to collaborative opportunities or mentorship, boosting your career trajectory.
Undertake a Mini-Project or Dissertation- (Semester 3-4)
Work with a faculty member on a small research problem, a detailed literature review, or a dissertation, even if not mandatory. Identify an area of interest within your core or elective subjects and approach a professor for guidance on a mini-project, aiming for a small presentation, report, or a publication in a student journal.
Tools & Resources
Faculty advisors, University library resources, Research databases, Academic writing guides
Career Connection
Develops independent research aptitude, critical for academic positions and Ph.D. applications; provides tangible research experience for your CV and portfolio, differentiating you in the job market.
Advanced Stage
Program Structure and Curriculum
Eligibility:
- Bachelor of Science (B.Sc.) with Mathematics as one of the subjects. (Source: SGBAU PG Admission Booklet 2023-24)
Duration: 4 semesters / 2 years
Credits: 72 Credits
Assessment: Internal: 20%, External: 80%
Semester-wise Curriculum Table
Semester 1
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MM101 | Advanced Abstract Algebra - I | Core | 4 | Group Theory, Sylow Theorems, Simple and Solvable Groups, Normal Series, Isomorphism Theorems |
| MM102 | Real Analysis - I | Core | 4 | Riemann Stieltjes Integral, Sequences and Series of Functions, Uniform Convergence, Power Series, Fourier Series |
| MM103 | Complex Analysis - I | Core | 4 | Complex Numbers and Functions, Analytic Functions, Complex Integration, Cauchy''''s Theorem, Residue Theorem |
| MM104 | Ordinary Differential Equations | Core | 4 | Linear Equations, Systems of ODEs, Phase Plane Analysis, Stability Theory, Boundary Value Problems |
| MM105 | Practical - I | Lab | 2 | Programming in C, Numerical Methods, Matrix Operations, Root Finding Algorithms, Differential Equation Solutions |
Semester 2
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MM201 | Advanced Abstract Algebra - II | Core | 4 | Ring Theory, Ideals and Factor Rings, Unique Factorization Domains, Modules, Field Extensions |
| MM202 | Real Analysis - II | Core | 4 | Lebesgue Measure, Measurable Functions, Lebesgue Integral, Modes of Convergence, Lp Spaces |
| MM203 | Complex Analysis - II | Core | 4 | Conformal Mapping, Riemann Mapping Theorem, Harmonic Functions, Entire Functions, Weierstrass Factorization Theorem |
| MM204 | Partial Differential Equations | Core | 4 | First Order PDEs, Second Order PDEs, Classification of PDEs, Wave Equation, Heat Equation, Laplace Equation |
| MM205 | Practical - II | Lab | 2 | Programming in C, Numerical Solutions to PDEs, Fourier Series Computations, Complex Function Visualization, Statistical Analysis |
Semester 3
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MM301 | Functional Analysis | Core | 4 | Normed Linear Spaces, Banach Spaces, Hilbert Spaces, Bounded Linear Operators, Dual Spaces |
| MM302 | Differential Geometry | Core | 4 | Curves in R3, Surfaces, First and Second Fundamental Forms, Gaussian Curvature, Geodesics |
| MM303 (A) | Graph Theory | Elective (Chosen for Pure Mathematics) | 4 | Graphs and Subgraphs, Paths and Cycles, Trees, Planarity and Dual Graphs, Coloring and Matchings |
| MM304 (A) | Analytical Number Theory | Elective (Chosen for Pure Mathematics) | 4 | Divisibility and Prime Numbers, Congruences, Arithmetic Functions, Diophantine Equations, Quadratic Residues |
| MM307 | Practical - III | Lab | 2 | Algorithms in Graph Theory, Number Theory Computations, Linear Algebra Applications, Optimization Problems, Statistical Programming |
Semester 4
| Subject Code | Subject Name | Subject Type | Credits | Key Topics |
|---|---|---|---|---|
| MM401 | Topology | Core | 4 | Topological Spaces, Open and Closed Sets, Continuous Functions, Connectedness, Compactness, Product Topology |
| MM402 | Measure Theory | Core | 4 | Measure Spaces, Outer Measure, Caratheodory Extension, Lebesgue Measure, Signed Measures, Radon-Nikodym Theorem |
| MM403 (A) | Advanced Discrete Mathematics | Elective (Chosen for Pure Mathematics) | 4 | Set Theory and Relations, Lattices and Boolean Algebra, Formal Languages and Grammars, Automata Theory, Combinatorics |
| MM404 (A) | Lattice Theory | Elective (Chosen for Pure Mathematics) | 4 | Lattices as Posets, Distributive Lattices, Modular Lattices, Boolean Lattices, Stone''''s Representation Theorem |
| MM407 | Practical - IV | Lab | 2 | Discrete Math Problems, Lattice Theory Properties, Topological Space Visualization, Measure Theory Applications, Advanced Programming Concepts |
