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      • About Instructorp

        Rahul Deshmukh is working as Assistant Professor in the Department of Mathematics at Sant Rawool Maharaj Mahavidyalaya, Kudal Dist- Sindhudurg State- Maharashtra (India). I have completed Master of Science in Mathematics from Shivaji University Kolhapur in 1998 and Master of Philosophy in Mathematics from Madurai Kamraj University, Madurai. My teaching and research interests include the many connections between Computer Science and Mathematics.


Available courses

TYBSC[2023-24]-USMT6C4-GRAPH THEORY & COMBINATORICS

About the course

The course covers the fundamentals of combinatorics and graph theory, as well as their applications. The study of graphs, trees, and networks is known as graph theory. Colouring of graphs, planar graphs, networking theory, applications of system of different representatives, and matching theory will all be explored. Combinatorics is the study of various ways for enumerating finite but massive sets. Applications of the principle of inclusion and exclusion, recurrence relations, generating functions, and equation-solving methods will all be covered.

Course Outcome

  • Understand and apply the basic concepts of graph theory, including colouring of graph, planar
  • graphs, networking theory, applications of system of distinct representative and matching theory
  • Use permutations and combinations to solve counting problems with sets and multisets
  • Compute a generating function and apply them to combinatorial problems
  • Set up and solve a linear recurrence relation and apply the inclusion/exclusion principle

TYBSC[2023-24]-USACCS601-I-Applet & AWT Prog

About the course

The Java Programming course is ideal for beginners like you drawn towards programming and software design. In this course you will learn about applets in java and AWT-Applet Window Toolkit i.e. the first step to enter into the world of graphics using java. You will also implement every program practically and will make an interesting applications at the end of the course.

Course Outcome

  • Write and run Java applications and Java applets.
  • Use data types for variables and constants in a Java applet or application and use conditional statements in a Java applet or application.
  • Implement a GUI using basic AWT Components and use Graphics


TYBSC[2023-24]-USACCS601-AC-Python Programming

About the course

This course introduces you to programming and the Python programming language. Data management, conditionals, loops, variables, and functions, as well as lists and dictionaries, are all introduced to students. This course provides a review of the many tools available for writing and running Python, as well as an introduction to the Anaconda and SymPy packages with programming, to begin students working immediately. It also includes hands-on coding assignments that include developing custom functions, reading and writing to files, and using commonly used data structures. Because it digs deeper into certain important programming principles, this course may be more robust than some other beginner python courses.

Course Outcome

  • To acquire programming skills in core Python and to understand why Python is a useful scripting language for developers.
  • To learn how to use lists, tuples, and dictionaries, indexing and slicing to access data  in Python programs.
  • To learn how to write loops and decision statements, how to write functions and pass arguments in Python.
  • To develop the skill of designing Mathematical user Interfaces with SymPy package in Python

SYBSC[2023-24]-SEM-IV-USMT403A-Numerical Methods(Elective A)

About the course 

      This course introduces the fundamental concepts and techniques of numerical solution of algebraic equations, systems of algebraic equations, numerical solution of differentiation, integration, and their interrelationships, as well as their applications in engineering and science. It also develops problem-solving skills with both theoretical and computational oriented problems. It is crucial in the solution of different engineering and science challenges. This course also includes an advanced introduction to numerical analysis using Scilab Open Source Software, with a focus on the accuracy and efficiency of numerical algorithms.

Course Outcome:

  1. Apply numerical methods to find our solution of algebraic equations using different methods under different conditions, and numerical solution of system of algebraic equations.
  2. Apply various interpolation methods and finite difference concepts
  3. Understand the main features of the SCILAB program development environment to enable their usage in the higher learning.
  4. Implement simple mathematical functions/equations in numerical computing environment such as SCILAB.

TYBSC[2023-24]-USACCS501-I-RDBMS

About this Course

Are you ready to dive into the world of data Science? You will need a understanding of how data is stored, processed, and accessed. You’ll need to identify the different types of database that are appropriate for the kind of data you are working with and what processing the data requires.

In this course, you will learn the basic concepts about relational databases and Relational Database Management Systems (RDBMS). You’ll study relational data models and discover how they are created. You’ll be introduced to standard relational databases Oracle 10g. This course incorporates hands-on, practical exercises to help you demonstrate your learning. You will work with real databases and explore real-world datasets. You will create database instances and practised them with tables. No prior knowledge of databases or programming is required. 

Course Outcome 

  • Fundamental Relational Database concepts. Types of RDBMS objects. Popular database systems.
  • Design a relational database and its schema. Create Entity Relationship Diagrams (ERD). 
  • Work hands-on with Relational Databases such ORACLE 10g using command line and app.
  • Create tables and load data. Use of SQL functions and executing SQL queries.

TYBSC[2023-24]-USACCS501-II-PLSQL

About this Course

Are you ready to dive into the world of data Science? You will need a understanding of how data is stored, processed, and accessed. You’ll need to identify the different types of database that are appropriate for the kind of data you are working with and what processing the data requires.

In this course, you will learn the basic concepts about procedural extension language for SQL (PL/SQL). This course introduces students to PL/SQL, Oracle’s procedural extension language for SQL and the Oracle relational database with programming to handle data. You will explore the differences between SQL and PL/SQL. 

Course Outcome 
    • Basic PL/SQL block and programming concepts
    • Conditionally control code flow (loops, control structures).
    • Declare PL/SQL variables.
    • Create anonymous PL/SQL blocks, stored procedures and functions.
    • Describe stored procedures and functions.
    • Work with different data types.
    • Declare identifiers and trap exceptions.

TYBSC[2023-24]USACCA501-JAVA PROGRAMMING

About this Course

     This course provides an overview of Java syntax and how it differs from those of other languages, as well as an introduction to Java and object-oriented programming. This specialisation is for students with no prior programming experience who wish to learn Java programming skills as well as the underlying computer science concepts that will enable them learn other programming languages quickly. Students will learn how to write their own Java classes and methods, as well as unit test their code. After finishing this course, you will be able to create simple Java classes that exemplify the concept of encapsulation, import other classes for use, work with strings, print output, and apply sophisticated math functions. You'll also be able to arrange and access classes, as well as use some of the Java runtime environment's standard classes.

Course Outcome 

  • Identify core aspects of object-oriented programming and features of the Java language.
  • Develop programs that use Java collections and apply core object-oriented programming concepts using classes, polymorphism, and method overloading.
  • Write, compile, and execute Java programs that may include basic data types and control flow constructs using Integrated Development Environments (IDEs) 
  • Write, compile, and execute Java programs using arrays and recursion.
  • Write, compile and execute Java programs using object oriented class structures with parameters, constructors, and utility and calculations methods, including inheritance, test classes and exception handling.

TYBSC[2023-24]-USMT5C4-GRAPH THEORY

About the course

This is a course for a one-semester (USMT5C4) at the T.Y.B.Sc. of Mumbai University. What are graphs? What do we need them for? This week we'll see that a graph is a simple pictorial way to represent almost any relations between objects. We'll see that we use graph applications daily! We'll learn what graphs are, when and how to use them, how to draw graphs, and we'll also see the most important graph classes. We will use interactive puzzles in this course. While they may be hard, they demonstrate the power of graph theory very well! If you don't find these puzzles easy, please see the videos and reading materials after them.

Course Outcome

  • To understand and apply the fundamental concepts in graph theory
  • To learn the basic terminology and some of the theory associated with graphs.
  • To improve the proof writing skills
  • To learn to model problems using graphs and to solve these problems algorithmically.
  • To apply graph theory based tools in solving practical problems
  • Modern applications of graph theory will be explored


SYBSC[2023-24]-USMT303-SYBSC-ORDINARY DIFFERENTIAL EQUATIONS

About Course

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on Higher Order linear Differential Equations, Systems of First Order Linear differential equations and Numerical Solutions of Ordinary Differential Equations.

Course outcome

  • Find the solution of higher-order linear differential equations and to solve the homogeneous and non-homogeneous linear differential equations with constant coefficients, method of undetermined coefficients and method of variations of parameters.
  • To solve systems of linear differential equations, determine the type of a linear differential equation systems.
  • Use the operator method to solve linear systems with constant coefficients, solve the linear systems in normal form and to solve the homogeneous linear systems with constant coefficients.
  • Demonstrate understanding of common numerical methods and how they are used to obtain approximate solutions, 
  • Derive numerical methods for various mathematical operations and tasks, such as Taylor's series method, Picard's method for successive approximation and its convergence, Euler's method, Modified Euler's Method, Runge-Kutta methods and solving first order ordinary differential equation
  • Derive Numerical solution of simultaneous and higher order ordinary differential equation using: Runge-Kutta fourth order method for solving simultaneous ODE and Finite difference method for the solution of two point linear boundary value problem.

MSC-II[2023-24]-SEM-III-PSMT305-GRAPH THEORY

About the Course

This is a standard course in graph theory, assuming little introductory knowledge of graphs. It aim is to present all usual basic concepts of graph theory, graph properties (with simplified proofs) and formulations of typical graph problems. This is also supplemented with some abstract-level algorithms for the presented problems, and with some advanced graph theory topics. The results in graph theory, in addition to their theoretical value, are increasingly being applied to understand and analyze systems across a broad domain of enquiry, including natural sciences, social sciences and engineering. The course does not require any background of the learner in graph theory. The emphasis will be on the axiomatic foundations and formal definitions, together with the proofs of some of the central theorems. Few applications of these results to other disciplines would be discussed.

Course Outcome

The students should be able to 

  • Solve problems using basic graph theory and to write precise and accurate mathematical definitions of objects in graph theory. 
  • Determine whether graphs are Hamiltonian and/or Eulerian 
  • Apply theories and concepts to test and validate intuition and independent mathematical thinking in problem solving. 
  • Integrate core theoretical knowledge of graph theory to solve problems. 
  • Reason from definitions to construct mathematical proofs 
  • Model real world problems using graph theory


M.Sc-I[2022-23]-PSMT204-Partial Differential Equation

About the Course

Partial Differential Equations (PDEs) appear as mathematical models for many a physical phenomena. Closed-form solutions to most of these PDEs cannot be found. One of the possible ways to understand the models is by studying the qualitative properties exhibited by their solutions. In this course, we study first order partial differential equations in two independent variables, Semilinear and Quasilinear equations in two independent variables, method of characteristics, the Characteristics Cauchy Problem and its solutions as well as Non-linear equations in two independent variables including Monge Strip and Charpit Equations, Solution of Cauchy problem, Determination of Complete integral. After we Classifications of second order partial differential equations in two and more than two independent variables, method of reduction to normal form, the Cauchy problem. Potential theory and elliptic differential equations, boundary value problems and Cauchy problem, Poisson's theorem, the mean value and the Maximum-Minimum properties

Course Outcome

  • Classify different types of PDEs
  • Define different notions of solutions
  • Analyze the properties of solutions of PDEs

MSC-I[2022-23]-PSMT104-ORDINARY DIFFERENTIA EQUATION

About Course

One of the most essential components of each discipline of research has been the building of mathematical models to solve real-world problems. These mathematical models are frequently expressed in the form of equations involving functions and their derivatives. Differential equations are the name given to such equations. Ordinary differential equations are those in which only one independent variable, usually time, is involved. The course will show how ordinary differential equations can be used to model physical and other events. Analytical methods and graphical analysis will be provided as complementary mathematical approaches to their solution. Scientists and engineers must be able to model the world using differential equations, as well as solve and interpret such equations. Linear differential equations and their applications in science and engineering are the emphasis of this course.

Course Outcomes

1. Through this course students are expected to understand the basic concepts of existence and uniqueness of solutions of Ordinary Differential Equations (ODEs).

2. In case of nonlinear ODEs, students will learn how to construct the sequence of approximate solutions converges to the exact solution if exact solution is not possible.

3. Students will be able to understand the qualitative features of solutions.

4. Students will be able to identify Sturm Liouville problems and to understand the special functions like Legendre's polynomials and Bessel's function.

5. Students will be to understand the applicability of the above concepts in different disciplines of Technology.