**Name of the Department: Mathematics**

**Year of Establishment: June 1996**

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**About the Department:**

Department of Mathematics started from June 1996 is one of the premiere department of the college. It is primarily providing subject of Mathematics at undergraduate Science Degree course.

The college was established in the year 1981. Department of Mathematics being started in June 1996, since then Mathematics is taught at under graduate level for Science streams. The department in the courses offered by other departments viz. Computer Science. The Department aims to create a solid foundation for the assimilation of mathematical concepts and structures and build mathematical skills like creative, logical and analytical thinking. Software such as Maxima, Scilab and Python etc. are used to increase the understanding of the fundamental mathematical concepts.

The Department has been organizing activities like celebration of National Mathematics Day, Celebration of Birth anniversary of Mathematician D.R.Kaprekar, Quiz, Essay & Poster Competition that promotes student’s interests in the subject with their enthusiastic involvement. Department also encourages students to participate in Avishhkar Research Project Competition and Madhava competition.

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**Vision of the Department: **

- To motivate students in developing their skills in applying Mathematical method to real life situations.
- We envision our students as excellent not only in the field of science and technology, but also in good citizenship and discipline.

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**Mission Statement of the Department: **

- To provide a conducive environment for learning and teaching where students can learn, become competent users of mathematics, and understand the use of mathematics in other disciplines.
- To provide quality education to students in the subject so as to increase their employability.
- To popularize the subject among students.
- To impart updated technical education and knowledge.

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** ****Goals: **

- Remove the fear of Mathematics at an early stage and to create strong interest among the students in this vital subject .
- Encourage the students to participate actively in various activities like Avishhkar Research Project Competition, Departmental activities (poster, quiz and essay Competition ) etc.
- Encourage students to learn Mathematical concepts geometrically using various Mathematical Software namely Maxima, Scilab, Python etc.
- To inculcate analytical, logical and critical thinking among the students.

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**Subjects Taught at Various Programmes: **

## Sr. No. |
## Name of the Programme |
## Subjects |

## 1 |
## F.Y.B.Sc.## S.Y.B.Sc. |
## Mathematics## Mathematics |

## 2 |
## F.Y.B.Sc.## F.Y.B.Sc.## S.Y.B.Sc. |
## Mathematics## Statistics## Mathematics |

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**POs/COs/PSOs**

**Programme Outcomes: **

- Enabling students to develop a positive attitude towards mathematics as an interesting and valuable subject of study.
- Understand the basic concepts, fundamental principles and scientific theories related to various scientific phenomena and their relevance in the day-to-day life.
- Ability to analyze a problem, identify and define the computing requirements, which may be appropriate to its solution.
- Enhancing students’ overall development and to equip them with mathematical modelling abilities, problem solving skills, creative talent and power of communication necessary for various kinds of employment.
- Understand application mathematics in different fields
- Ability to pursue advanced studies and research in pure and applied mathematical science.
- Be prepared for life-long learning.

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**Programme Specific Outcomes: **

- Think in a critical manner.
- Be familiar with different areas of Mathematics
- Know when there is a need for information, to be able to identify, locate, evaluate, and effectively use that information for the issue or problem at hand.
- Formulate and develop mathematical arguments in a logical manner.
- Acquire good knowledge and understanding in advanced areas of mathematics and software like maxima, chosen by the student from the given courses.
- Be prepared to use Mathematics, not only in the discipline of Mathematics, but also in other disciplines and in their future endeavours
- Identify suitable existing methods of analysis, if any, and assess his/her strengths and weaknesses in the context of the problem being considered.

**Course Outcomes: **

__F.Y.B.Sc. (Computer Science)-Mathematics__

**(1) MTC-111: Matrix Algebra**

** **After completion of this course, the student will be able to:

- Perform basic Matrix operation.
- Define special matrices: diagonal, triangular, and symmetric.
- Basics of solving systems of linear equations.
- Understand determinants and their properties.
- Factorization of any square matrix in simpler LU-form.

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**(2) MTC-112: Discrete Mathematics**

** **After completion of this course, the student will be able to:

- Understanding the concepts of discrete mathematics.
- To provide overview of theory of discrete objects, starting with relations and partially ordered sets.
- Learning applications of discrete structures in Computer Science.
- Express a logic sentence in terms of predicates, quantifiers, and logical connectives.
- Study about recurrence relations, generating function and operations on them.

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**(3) MTC-113: Mathematics Practical**

** **This course will enable the students to:

- Learn Maxima software.
- Students will be able to compute matrix calculation using Maxima software
- Use appropriate modern technology to explore calculus concepts.
- Solve applied problems using matrices
- Solve systems of linear equations by use of the matrix.
- Students will be able to formulate problems in the language of sets and perform set operations, and will be able apply the Fundamental Principle of Counting, Multiplication Principle
- Knowledge of application of mathematics

**(4) MTC-121: Linear Algebra**

After completion of this course, the student will be able to:

- Solve systems of linear equations using various methods including Gaussian and Gauss Jordan elimination and inverse matrices.
- Perform matrix algebra, invertibility, and the transpose and understand vector algebra in Rn.
- Compute linear transformations, kernel and range, and inverse linear transformations, and find matrices of general linear transformations
- Compute inner products on a real vector space and compute angle and orthogonality in inner product spaces.
- Prove basic results in linear algebra using appropriate proof-writing techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues.

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** (5) MTC-122: Graph Theory**

After completion of this course, the student will be able

- Explain basic concepts in graph theory
- Define how graphs serve as models for many standard problems.
- Account for the theory of paths and degree of connectedness of graph.
- Learn the use of spanning tree.
- Discuss the concept of graph, tree, and Euler graph.
- See the applications of graphs in science, business and industry.
- To present a survey of essential topics for computer science students who will encounter some of them again in more advanced courses.

**(6) MTC-123: Mathematics Practical**

This course will enable the students to:

- Students will be able to find eigen values and eigen vectors using Maxima software.
- Students will be able to perform operations on orthogonality and quadratic forms.
- Use appropriate modern technology to explore calculus concepts.

__F.Y.B.Sc. (Computer Science)-Statistics__

**(1) CSST-111: Descriptive Statistics**

** **After completion of this course, the student will be able to:

- Enable learners to know descriptive statistical concepts.
- The main purpose of descriptive statistics is to provide a brief summary of the samples and the measures done on a particular study.
- Understand Data types, their representations and Aggregations; also be able to solve problems related to it
- Solve problems related to Frequency distribution, data presentation and Measures of central tendency
- Perform frequency distribution, Data presentation
- Understand and solve problems related to Moments, Measures of Skewness, and Kurtosis, Correlation and Regression and Linear regression.

**(2) CSST-112: Mathematical Statistics**

** **After completion of this course, the student will be able to:

- It will help students develop skills in thinking and analyzing problems from a probabilistic and statistical point of view.
- Enable study of probability concept required for Computer learners.
- Understand and solve problems based on Probability and operations of events.
- Get the knowledge of Probability definition and Elementary Theorems of probability.
- It will provide difference between Discrete and continuous distributions.

**(3) CSST-113: Statistics Practical**

** **At the end of the course students are expected to be able:

- To tabulate and make frequency distribution of the given data.
- To use of Statistical tools in Ms-Excel.
- To use various graphical and diagrammatic techniques and interpret.
- To compute various measures of central tendency, dispersion, Skewness and kurtosis.
- To fit the Binomial and Poisson distributions.
- To compute the measures of attributes.
- The process of collection of data, its condensation and representation for real life data.
- To study free statistical softwares and use them for data analysis in project.

**(4) CSST-121: Methods of Applied Statistics**

After completion of this course, the student will be able to:

- To create a mathematical model that can be used to predict the values.
- Study data related to time and predict its future behaviour.
- To study different models of forecasting.
- To Handle large data and analyze it by statistical tools.

**(5) CSST-123: Statistics Practical**

** **At the end of the course students are expected to be able:

- To understand the relationship between two variables using scatter plot.
- To compute coefficient of correlation, coefficient of regression.
- To fit various regression models and to find best fit.
- To fit the Normal distribution.
- To understand the trend in time series and how to remove it.
- To apply inferential methods for real data sets.
- To generate model sample from given distributions.
- To understand the importance and functions of different statistical organizations in the development of nation.

__S.Y.B.Sc. (Computer Science)-Mathematics__

**(1) MTC-231: Groups and Coding Theory**

At the end of the course students are expected to be able:

- Use the division algorithm, Euclidian algorithm to find G.C.D. of integers.
- Learn about some important results in the theory of numbers including the prime number theorem, describe the properties of prime numbers,
- To define congruence and describe the properties of congruence.
- To define groups and its properties.
- To defines subgroups, cyclic groups and to find generators.
- To defines permutation of groups, its type, inverse and order of permutation.
- To understand cosets and its properties.
- To understand concept of decoding and error correction.

**(2) MTC-232: Numerical Techniques**

After completion of this course, the student will be able to:

- Obtain numerical solutions of algebraic and transcendental equations.
- Learn about various interpolating and extrapolating methods.
- Understand the relation between the operators ∆,Ε, ∇
- Solve problems using Newton forward and Newton backward difference interpolation formula.
- Apply Lagrange’s Interpolation formula when difference interval is unequal.
- Understand the concept divided difference.
- Solve problems using Newton’s divided difference.
- Apply various numerical methods in real life problems.
- To solve problems of Trapezoidal rule, Simpson’s 1/3 and 3/8 rules.
- Find the solution of ordinary differential equation of first by Euler method, Modified Euler’s methods and Runge-Kutta methods.

**(3) MTC-233: Mathematics Practical (Python Programming Language – I)**

After completion of this course, the student will be able to:

- To develop logic for problem solving.
- To be familiar about the basic constructs of programming such as data, operations, conditions, loops, functions etc.
- To be familiar with string and its operation.
- To develop basic concepts of function and terminology.
- To determine the methods to create and develop Python programs by utilizing the data structures like lists and tuples.
- To write python program and develop maps using dictionary
- To develop logic for 2D graphics.
- Demonstrate the use of Python in mathematics such as matrix algebra
- To be familiar about basic math built in functions such as sine, cosine, etc.
- To write Python programs to handle matrices and vectors using NumPy.
- Find the root of the equation by using Newton’s Raphson method and Regula Falsi Method, Trapezoidal rule, Simpson’s (1/3)rd rule, Simpson’s (3/8)th rule.

**(4) MTC-241: Computational Geometry**

After completion of this course, the student will be able to:

- In 2D & 3D, learn Scaling, Shearing, reflection and rotation transformation.
- Understand the term Projection, Bezier’s curve
- Acquainted with the typical problems of computational geometry.
- Understand the existing solutions and their applications in computer graphics and machine vision.
- Get a deeper knowledge of mathematics.
- Learn the principles of geometric algebra including its application in graphics and vision-related tasks.

**(5) MTC-242: Operations Research**

After completion of this course, the student will be able to:

- Define a LPP in standard form and Canonical form
- Identify a feasible solution, a basic feasible solution and an optimal solution using simplex method
- Understand the new term LPP
- Formulate and model a linear programming problem from a word problem and solve them graphically in 2 and 3 dimensions, while employing some convex analysis
- Place a Primal linear programming problem into standard form and use the Simplex Method or The Big M Method to solve it
- Use dual simplex method to find optimal solutions
- Understand duality theorems and dual simplex method
- Identify the advantages of duality method
- Apply the theorems on duality to problems appropriately
- Use dual simplex method to find optimal solutions
- Find the dual, and identify and interpret the solution of the Dual Problem from the final tableau of the Primal problem
- Explain the concept of complementary slackness and its role in solving primal / dual problem pairs
- Be able to modify a Primal Problem, and use the Fundamental Insight of Linear Programming to identify the new solution, or use the Dual Simplex Method to restore feasibility.

**(6) MTC-243: Mathematics Practical (Python Programming Language – II)**

After completion of this course, the student will be able to:

- Learn how to draw 2D and 3D graphs by using various commands of the graph.
- Solve examples of linear entities.
- Representing polygons in python.
- Draw various attributes of the polygon.
- Solve transformation of a point.
- Solve Linear Programming in Python.
- Solve transportation Problem.