About Instructor
| 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. |
About the course
A machine learning course teaches students how to build computer systems that learn from data to make predictions or decisions. Topics cover supervised and unsupervised learning, neural networks, and data evaluation using programming languages like Python
About the Course
Computational Machine Learning is an online Moodle course designed to provide students with a strong foundation in Machine Learning, Python programming, statistics, and data analysis. The course covers the basic concepts and applications of Machine Learning, types of learning, datasets, data preprocessing, and the Machine Learning workflow. Students will use Python tools such as Pandas for data manipulation and Matplotlib for visualization, along with descriptive statistics, probability distributions, hypothesis testing, and ANOVA for data analysis and interpretation. The course also introduces the Gradient Descent algorithm and Scikit-Learn for building, training, evaluating, and validating Machine Learning models using different datasets. Moodle will provide structured learning resources, lecture materials, practical exercises, quizzes, assignments, datasets, and assessment activities to support self-paced and continuous learning. The course is intended to develop practical computational skills and prepare students to apply Machine Learning and statistical techniques to real-world data-driven problems.
This practical course introduces participants to the creation, management, and delivery of Massive Open Online Courses (MOOCs) and digital learning content using the Moodle Learning Management System (LMS) hosted through Gnomio.com. Gnomio provides educators with a Moodle-based online learning environment where they can create virtual classrooms, organize courses, upload learning resources, conduct assessments, and monitor learner progress.
Key Topics:
Learning Outcome:
By the end of the course, participants will be able to create and manage a structured online course, develop digital learning materials, integrate assessments and activities, and deliver a complete MOOC through a Moodle platform hosted on Gnomio.com.
About the Course
R Programming is a comprehensive course designed to introduce postgraduate students to statistical computing, data manipulation, visualization, and exploratory data analysis using the R programming language. The course emphasizes practical implementation of statistical techniques along with programming skills required for data-driven research.
Students learn how to import, clean, transform, visualize, and analyze data using modern R packages such as dplyr, tidyverse, and ggplot2. The course also covers hypothesis testing, ANOVA, probability distributions, and exploratory data analysis, enabling students to perform complete statistical analyses for academic research and industrial applications.
Laboratory sessions reinforce theoretical concepts through hands-on programming exercises, preparing students for advanced research in mathematics, statistics, data science, machine learning, and related disciplines.
Algorithm and Basic Python Programming form the cornerstone of computer science and software development. Algorithms offer structured methods for solving problems efficiently, while Python provides an intuitive and flexible programming language to implement these methods. Mastering algorithms leads to optimized, high-performance software solutions, and Python’s clarity and simplicity make it an ideal language for writing and testing these solutions.
Algorithms are widely used in areas such as sorting, searching, graph theory, cryptography, and machine learning. At the same time, Python plays a crucial role in web development, artificial intelligence, data science, and process automation—demonstrating its broad utility. For those who enjoy logical thinking and strategy, understanding algorithms is both intellectually rewarding and practically valuable. Python’s beginner-friendly syntax makes it especially appealing to newcomers and experienced developers alike.
Developing proficiency in both algorithm design and Python opens up a wide range of career opportunities. Professionals with these skills can excel as software developers, data analysts, algorithm engineers, machine learning specialists, and research scientists. In essence, gaining expertise in these areas provides a solid foundation for success in the rapidly evolving world of technology and enhances one’s ability to solve real-world computational problems effectively.
This course is designed to provide a comprehensive introduction to the Java programming language. Java is a versatile, high-level, and object-oriented programming language widely used in various applications, including web development, mobile applications, and large-scale enterprise systems. This course will cover the fundamental concepts of Java, including basic syntax, data types, control structures, object-oriented programming (OOP), and key features such as inheritance and exception handling. Additionally, students will be introduced to basic graphics programming to create simple graphical applications. Whether you are new to programming or transitioning from another language, this course will equip you with the knowledge and skills to develop basic Java programs and understand core programming principles.
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
This course will equip undergraduate students with essential skills in numerical and scientific computing using Python, preparing them for careers in data science, engineering, and applied sciences. It focuses on four essential libraries—NumPy (for array-based numerical computations), SciPy (for advanced scientific functions including problem solving in mathematics), Pandas (for data manipulation and analysis) and Matplotlib (for creating visual representations of data). Students will gain practical experience in using four libraries to solve real-world problems, including numerical equation solving, performing matrices and system of equations, and applying statistical methods for data analysis. The course emphasizes the application of these techniques to data science, showing how numerical computing can be applied to fields such as engineering, economics, and research. Additionally, the course covers basic statistical analysis to help interpret data and solve real-world data science problems. By the end of the course, students will have the skills needed to efficiently perform numerical computations, analyze complex datasets, and visualize data effectively, making this course a valuable foundation for anyone working in data science or related fields.
AComputing with Python and Doing Mathematics with Python are closely related yet distinct ways of using Python in computer science and mathematics. Python is widely used in both areas because of its simplicity, flexibility, and rich library support. Its readable syntax makes it ideal for expressing both computational procedures and mathematical ideas. In computing, Python is commonly applied to software development, automation, and data handling. In mathematics, it supports numerical computation, symbolic processing, and graphical visualization. Applications of mathematical computing with Python include numerical methods, statistical modeling, and scientific computing. Skills in Python programming are highly valued in the technology sector, while computational mathematics expertise is increasingly in demand in research and data-driven fields. Together, these complementary skills prepare individuals for diverse and rewarding careers across technology, data science, and academia.
The course is designed to provide learners with a clear understanding of research methodology, including the meaning of research, the process of defining research problems, and the techniques of reviewing literature and preparing research reports. It also focuses on equipping students with practical skills in LaTeX for writing theses, reports, resumes, question papers, and creating beamer presentations, as well as using LaTeX to draw diagrams and plot graphs. Additionally, the course introduces learners to mathematical software for enhanced comprehension of mathematical concepts. By the end of the course, students will be able to initiate independent research projects, write literature reviews and research reports, effectively use LaTeX for academic writing and presentations, and apply mathematical software tools to support and strengthen their understanding of mathematical ideas.
This course is designed to provide a comprehensive introduction to the Java programming language. Java is a versatile, high-level, and object-oriented programming language widely used in various applications, including web development, mobile applications, and large-scale enterprise systems. This course will cover the fundamental concepts of Java, including basic syntax, data types, control structures, object-oriented programming (OOP), and key features such as inheritance and exception handling. Additionally, students will be introduced to basic graphics programming to create simple graphical applications. Whether you are new to programming or transitioning from another language, this course will equip you with the knowledge and skills to develop basic Java programs and understand core programming principles.
Algorithm and Basic Python Programming form the cornerstone of computer science and software development. Algorithms offer structured methods for solving problems efficiently, while Python provides an intuitive and flexible programming language to implement these methods. Mastering algorithms leads to optimized, high-performance software solutions, and Python’s clarity and simplicity make it an ideal language for writing and testing these solutions.
Algorithms are widely used in areas such as sorting, searching, graph theory, cryptography, and machine learning. At the same time, Python plays a crucial role in web development, artificial intelligence, data science, and process automation—demonstrating its broad utility. For those who enjoy logical thinking and strategy, understanding algorithms is both intellectually rewarding and practically valuable. Python’s beginner-friendly syntax makes it especially appealing to newcomers and experienced developers alike.
Developing proficiency in both algorithm design and Python opens up a wide range of career opportunities. Professionals with these skills can excel as software developers, data analysts, algorithm engineers, machine learning specialists, and research scientists. In essence, gaining expertise in these areas provides a solid foundation for success in the rapidly evolving world of technology and enhances one’s ability to solve real-world computational problems effectively.
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
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
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
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
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
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
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
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:
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
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
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
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.
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
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
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
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
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:
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.
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
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
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
About this Course
In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modelling problems, which can be handled by the methods introduced in this course. The course is mainly delivered through video lectures. At the end of each module, there will be a quiz consisting of several problems related to the lecture of the week. Next we shall provide a quick introduction to SageMath software along with demonstration. The main focus will be on using SageMath to explore topics in Differential Equation along with several applications.
Course Outcome
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
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