gogate-college

Department of Mathematics

Department of Mathematics

Established in 1945

T.Y.B.Sc. started in 1985

M.Sc. began in 1992

 UG

Class and Semester Course Nomenclature Type (Optional, Elective, Compulsory, etc)
F.Y.B.Sc. (SEM I & II) Calculus I & II Compulsory
Algebra I & II Compulsory
S.Y.B.Sc. (SEM III & IV) Calculus III Compulsory
Algebra III Compulsory
Introduction to computing & Problem solving Compulsory
T.Y.B.Sc. (SEM V) Integral Calculus Compulsory
Linear Algebra Compulsory
Topological Metric Spaces Compulsory
Graph Theory Elective
Computer Programming & System analysis Compulsory
T.Y.B.Sc. (SEM VI) Real & Complex Analysis Compulsory
Algebra Compulsory
Metric Topology Compulsory
Graph Theory & Combinatorics Elective
Computer Programming & System analysis Compulsory

 PG

Class and Semester Course Nomenclature Type (Optional, Elective, Compulsory, etc)
M.Sc. (SEM I) Algebra-I Compulsory
Analysis-I Compulsory
Complex analysis Compulsory
Discrete Mathematics Compulsory
Set theory and Logic Compulsory
M.Sc. (SEM II) Algebra-II Compulsory
Topology Compulsory
Analysis-II Compulsory
Differential Equations Compulsory
Probability Theory Compulsory
M.Sc. (SEM III) Algebra-III Compulsory
Analysis-II Compulsory
Differential Geometry Compulsory
Numerical Analysis-I Optional
Graph Theory-I Optional
M.Sc. (SEM IV) Field Theory Compulsory
Fourier Analysis Compulsory
FunctionalAnalysis Compulsory
Numerical Analysis-II Optional
Graph Theory-II Optional

 Add on Courses

Add on Course in Applied Mathematics
dr-r-g-sapre
Dr. R. G. Sapre
Associate Professor, HOD
M.Sc. M. Phil, Ph.D.
mr-c-g-patwardhan
Mr. C. G. Patwardhan
Associate Professor
M.Sc. M. Phil, NET
mr-d-p-karwanje
Mr. D. P. Karwanje
Assistant Professor
M.Sc. M. Phil
mrs-g-r-patwardhan
Mrs. G. R. Patwardhan
Assistant Professor (Contract Basis)
M.Sc. B.Ed.
mrs-u-e-joshi
Mrs. Uma Joshi
Assistant Professor
M.Sc.(Mathematics)
ms-s-v-surve
Ms. S. V. Surve
Assistant Professor (Contract Basis)
M.Sc.
mr-p-r-shitut
Mr. P. R. Shitut
Assistant Professor (Contract Basis)
M.Sc.
ms-d-v-wakankar
Ms. D. V. Wakankar
Assistant Professor (Contract Basis)
M.Sc. B.Ed
Visiting Faculty Details
Staff Member
Dr. Mrs. Thakkar
M.Sc. Ph.D.Shivaji University
Staff Member
Dr. Selby Jose
M.Sc. Ph.D.Mumbai University
Staff Member
Dr. S Shende
M.Sc. Ph.D.Mumbai University
Staff Member
Dr. M. S. Bapat
M.Sc. Ph.D.
Staff Member
Dr. Sanjeev Sabnis
M.Sc. Ph.DIIT Mumbai

Computer Lab with 15 Machines

Lokmanya Tilak Ganit Pradnya Pariksha for 11th STD students.

International Olympiad Exam for 11th& 12th STD Students.

PG to UG Program.

Power Point Presentation Competition (Internal & State Level).

Research Project Competition (State Level).

Mathematics Wallpaper display on Independence & Republic Day.

Mathematics Exhibition in students Annual Program (ZEP).

Extension activities

School Teaching: UG & PG Students of the department conducts lectures on 8th&10th STD students in various schools.

Departmental Library with 400 books

Every year Bridge course for the new T.Y.B.Sc. students in month of April

Dr. S.B. Kulkarni(HOD of Applied Science & Humanities in Finolex Academy of Management & Technology)

Departmental staff & student representative.

Name Organization Special Achievements
Farha Vanu 1st Rank in Mumbai University for all subjects (2013)
Santosh Kulkarni Manager – Bank of Maharashtra
Pralhad Soman Assistant Professor – Finolex Academy of Management & Technology
Madhavi Parab Probationary Officer – IDBI bank
Meera Mainkar Ph.D guide in Michigan University USA
UG:

To develop numerical aptitude among students.
To develop preciseness and thinking abilities in students.
To develop their logical reasoning.
To develop research aptitude among the students.

PG:

To develop numeric aptitude among students.
To develop preciseness and thinking abilities in students
To develop their logical reasoning.
To develop research aptitude among the students.
To develop abstract thinking among the students.

Class Course Code Nomenclature Outcomes
F.Y.B.Sc USMT 101 CALCULUS I
  1. Students get knowledge of fundamental principles, tools and methods in Mathematics.
  2. Logical thinking abilities are developed.
USMT 102 ALGEBRA I
  1. Students get knowledge of numbers and operations on numbers.
  2. Students know the various mathematical ideas and tools.
  3. Students know how to use the mathematical tools by modeling, solving and interpreting.
USMT 201 CALCULUS II
  1. Students know the various mathematical ideas and tools
  2. Students know how to use the mathematical tools by modeling, solving and interpreting.
USMT 202 LINEAR ALGEBRA
  1. Students know the various mathematical ideas and tools
  2. Students know how to use the mathematical tools by modeling, solving and interpreting.
S.Y.B.Sc. USMT 301 CALCULUS III
  1. Students get the broad view of the subject and develop the mathematical tools.
  2. Students can think in abstract manner.
USMT 302 ALGEBRA III
  1. Abstract thinking abilities are developed.
  2. Students know the real life applications of mathematical concepts.
USMT 303 INTRODUCTION TO COMPUTING & PROBLEM SOLVING- I
  1. Students can deal with numerical problems very well.
  2. Numerical abilities are enhanced.
USMT 401 CALCULUS IV
  1. Students are exposed to broader mathematical concepts
  2. They develop the ability to use the mathematical tools for further studies of science and Mathematics.
USMT 402 ORDINARY DIFFERENTIAL EQUATIONS
  1. Students get exposed to the applied branch of Mathematics.
  2. They know the applications of differential equations in various other fields.
USMT 403 INTRODUCTION TO COMPUTING & PROBLEM SOLVING- II
  1. Students are exposed to programming for Mathematics.
  2. Computer related abilities are enhanced.
T.Y.B.Sc USMT 501 INTEGRAL CALCULUS
  1. Problem solving skills are enhanced.
  2. Mathematical modeling abilities are focused.
  3. Abstract thinking level is uplifted.
USMT 502 LINEAR ALGEBRA
  1. Knowledge of shapes and rotations reflections is made further concrete.
  2. Students can relate mathematics to real life.
USMT 503 TOPOLOGY OF METRIC SPACES
  1. Logical thinking is developed.
  2. Problem solving skill and mathematical modeling skill are enhanced.
USMT 5C4 GRAPH THEORY
  1. Students get known to the applied branch of Mathematics.
  2. Many real life problems are related to graphs and can be solved using these techniques.
USACCA501 COMPUTER PROGRAMMING AND SYSTEM ANALYSIS I
  1. Improved Logical Thinking
  2. Enhanced programming skills
USMT 601 REAL AND COMPLEX ANALYSIS
  1. Students know new number system and their properties.
  2. They are exposed to new field of the subject
USMT 602 ALGEBRA
  1. Problem solving skills are enhanced.
  2. Students get ideas of different algebraic structures.
USMT 603 METRIC TOPOLOGY
  1. Problem solving and mathematical modeling skills are enhanced.
  2. Different new concepts are made familiar to the students.
USMT 6C4 GRAPH THEORY AND COMINATORICS
  1. Different counting techniques and their uses are made known to the students.
  2. Students get knowledge about networking.
  3. Students are now able to apply their knowledge of the subject into real life.
USACCA601 COMPUTER PROGRAMMING AND SYSTEM ANALYSIS II
  1. Improved Logical Thinking
  2. Enhanced programming skills
M.Sc – I
Semester I
PSMT 101 Algebra I
  1. Use computational techniques and algebraic skills essential for the study of systems of linear equations, matrix algebra, vector spaces, eigenvalues and eigenvectors, orthogonality and diagonalization. (Computational and Algebraic Skills).
  2. Critically analyze and construct mathematical arguments that relate to the study of introductory linear algebra. (Proof and Reasoning).
PSMT 102 Analysis I
  1. Describe the real line as a complete, ordered field
  2. Determine the basic topological properties of subsets of the real numbers
  3. Use the definitions of convergence as they apply to sequences, series, and functions
  4. Determine the continuity, differentiability, and integrability of functions defined on subsets of the real line,Apply the Mean Value Theorem and the Fundamental Theorem of Calculus to problems in the context of real analysis
  5. Produce rigorous proofs of results that arise in the context of real analysis.
PSMT 103 Complex Analysis
  1. how complex numbers provide a satisfying extension of the real numbers
  2. Appreciate how throwing problems into a more general context may enlighten one about a specific context (e.g. solving real integrals by doing complex integration; Taylor series of a complex variable illuminating the relationship between real function that seem unrelated — e.g. exponentials and trignometric functions);
  3. Learn techniques of complex analysis that make practical problems easy (e.g. graphical rotation and scaling as an example of complex multiplication)
PSMT 104 DISCRETE MATHEMATICS
  1. Solve counting problems by applying elementary counting techniques using the product and sum rules, permutations, combinations, the pigeon-hole principle, and binomial expansion.
  2. Solve discrete probability problems and use sets to solve problems in combinatorics and probability theory.
  3. Describe binary relations between two sets; determine if a binary relation is reflexive, symmetric, or transitive or is an equivalence relation; combine relations using set operations and composition.
PSMT 105 Set Theory and Logic
  1. Simplify and evaluate basic logic statements including compound statements, implications, inverses, converses, and contrapositives using truth tables and the properties of logic.
  2. Express a logic sentence in terms of predicates, quantifiers, and logical connectives
  3. Apply the operations of sets and use Venn diagrams to solve applied problems
  4. solve problems using the principle of inclusion-exclusion.
M.Sc – I
Sem II
PSMT301 Algebra II The student is able to

  1. Demonstrate knowledge and Understanding of fundamental concepts including groups, subgroups , normal subgroups, homomorphism and isomorphism.
  2. Demonstrate knowledge and understanding of rings, fields and their properties.
  3. Apply algebraic ways of thinking
  4. Understand and prove fundamental results and solve algebraic problems using appropriate techniques.
PSMT202 TOPOLOGY A student will be able to:

  1. Define and illustrate the concept of topological spaces and continuous functions.
  2. Define and illustrate the concept of product topology and quotient topology.
  3. Prove a selection of theorems concerning topological spaces, continuous functions, product topologies and quotient topologies.
  4. Define and illustrate the concept of the seperation axioms.
  5. Define connectedness and compactness and prove a selection of related theorems.
PSMT203 ANALYSIS II A student will be able to:

  1. understand how Lebesgue measure on R is defined
  2. understand basic properties are measurable functions
  3. understand how measures may be used to construct integrals
  4. know the basic convergence theorems for the Lebesgue integral
  5. understand the relation between differentiation and Lebesgue integration.
PSMT204 DIFFERENTIAL EQUATIONS A student will be able to:

  1. Learn how the differential equations are used to study various physical problems such as mass attached to spring and electric circuit problem etc.
  2. Obtain power series solutions of several important classes of ordinary differential equations including Bessel’s, Legendre, and Chebyshev’s differential equations.
  3. Understand the Sturm-Liouville problem and analyze stability of linear and non-linear systems.
  4. Solve the first-order linear differential equations.
PSMT205 PROBABILITY THEORY A student will be able to

  1. demonstrate understanding the random variable, expectation, variance and distributions.
  2. explain the large sample properties of sample mean.
  3. understand the concept of the sampling distribution of a statistic, and in particular describe the behaviour of the sample mean
  4. analyse the correlated data and fit the linear regression models.
  5. demonstrate understanding the estimation of mean and variance and respective one sample and two-sample hypothesis tests.
M.Sc II-
Sem III
PSMT301 Algebra III
  1. Demonstrate understanding of the concepts of a module and their role in mathematics.
  2. Demonstrate familiarity with a range of examples of these structures.
  3. Demonstrate familiarity with a range of examples of these structures.
  4. Explain the structure theorem for finitely generated modules over a principal ring and its applications to abelian groups and matrices.
  5. Demonstrate skills in communicating mathematics orally and in writing.
PSMT302 Functional Analysis
  1. Verify the axioms of normed vector spaces, Banach spaces and Hilbert spaces in specific examples, applying relevant tests for completeness or the existence of an inner product
  2. Compute the norms and spectra of (certain classes of) operators
  3. Use completeness arguments to produce existence proofs for operators and linear functionals with desired properties
  4. Establish well-known isometric isomorphisms between sequence spaces and their dual spaces.
PSMT303 Differential Geometry
  1. The course aims to give a proper background in differential geometry for applications in theoretical physics and for further studies in geometry/geometrical analysis
  2. The course introduces the fundamentals of differential geometry primarily by focussing on the theory of curves and surfaces in three space. The theory of curves studies global properties of curves such as the four vertex theorem.
  3. The theory of surfaces introduces the fundamental quadratic forms of a surface, intrinsic and extrinsic geometry of surfaces.
PSMT304 Numerical Analysis
  1. Derive appropriate numerical methods to solve algebraic and transcendental equations
  2. Develop appropriate numerical methods to approximate a function
  3. Develop appropriate numerical methods to solve a differential equation
  4. Derive appropriate numerical methods to evaluate a derivative at a value
  5. Derive appropriate numerical methods to solve a linear system of equations
  6. Perform an error analysis for various numerical methods
  7. Prove results for various numerical root finding methods
  8. Derive appropriate numerical methods to calculate a definite integral
  9. Code various numerical methods in a modern computer language
PSMT305 Graph Theory
  1. Demonstrate knowledge of the syllabus material
  2. Write precise and accurate mathematical definitions of objects in graph theory
  3. Use mathematical definitions to identify and construct examples and to distinguish examples from non-examples
  4. Validate and critically assess a mathematical proof
  5. Use a combination of theoretical knowledge and independent mathematical thinking in creative investigation of questions in graph theory
  6. Reason from definitions to construct mathematical proofs
M.Sc IV
sem IV
PSMT401 Field Theory
  1. Explain the fundamental concepts of field extensions and Galois theory and their role in Modern mathematics
  2. Demonstrate accurate and efficient use of field extensions and Galois theory
  3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from field extensions and Galois theory
PSMT402 Fourier Analysis
  1. In-depth knowledge of Fourier analysis and its applications to problems in engineering.
  2. An ability to communicate reasoned arguments of a mathematical nature in both written and oral form.
  3. An ability to read and construct rigorous mathematical arguments.
PSMT403 Calculus on Manifolds
  1. The student having seen basic analysis and linear algebra is expected to learn how these topics play a significant role, first in multi-variate calculus which then naturally leads to calculus on manifolds.
  2. The intimate relationship between analysis and geometry should become apparent at the end of this course.
PSMT404 Linear Programming, Optimisation
  1. Identify and express a decision problem in mathematical form and solve it graphically and by Simplex method
  2. Recognize and formulate transportation, assignment problems and drive their optimal solution
  3. Identify parameters that will influence the optimal solution of an LP problem and derive feasible solution using a technique of O R.
  4. Feasibility study for solving an optimization problem
PSMT404 Linear Programming, Optimisation
  1. Identify and express a decision problem in mathematical form and solve it graphically and by Simplex method
  2. Recognize and formulate transportation, assignment problems and drive their optimal solution
  3. Identify parameters that will influence the optimal solution of an LP problem and derive feasible solution using a technique of O R.
  4. Feasibility study for solving an optimization problem
PSMT405 Project Course
  1. Use mathematical ideas to model real-world problems
  2. Communicate mathematical ideas with others
  3. Utilize technology to address mathematical ideas