# Programme Overview Mathematics

March 18, 2021**Programme****Overview**

**Mathematics**

**Department of Mathematics**

**Year of Establishment: **1974

**Programme Offered: **UG

**No. of Teaching Posts**

Sanctioned: 3

Filled: 3

**Faculty Profile:**

Sl. No. | Name | Qualification | Designation | Teaching experience |

01 | Mr. Som Krishna Sharma | M.Sc. , M.Phil. | Associate Professor | 23 Years |

02 | Mrs. Priyanka Randhava | M.Sc. , M.Phil. CSIR-NET | Assistant Professor | 10 Years |

03 | Mrs. Pooja Sohal | M.Sc. , M.Ed. , SET | Assistant Professor | 2 Years |

**Course Structure**

**U.G. Yearly Programme (w.e.f. 2018–19)**

Year | Course Type | Course Code | Title | Credits |

1st | Core Course Core Course | MATH101TH MATH102TH | Differential Calculus Differential Equations | 6 6 |

2nd | Core Course Core Course SEC I (Choose any one from the given three) SEC 2 (Choose any one from the given three) | MATH201TH MATH202TH MATH307TH MATH308TH MATH309TH MATH310TH MATH311TH MATH312TH | Real Analysis Algebra Logic and Sets Analytic Geometry Integral Calculus Vector Calculus Boolean Algebra Number Theory | 6 4 4 |

3rd | DSE 3A (Choose any one from the given three) DSE 3B (Choose any one from the given three) SEC 3 (Choose any one from the given three) SEC 4 (Choose any one from the given three) | MATH301TH MATH302TH MATH303TH MATH304TH MATH305TH MATH306TH MATH313TH MATH314TH MATH315TH MATH316TH MATH317TH MATH318TH | Matrices Mechanics Linear Algebra Numerical Methods Complex Analysis Linear Programming Probability and Statistics Mathematical Finance Mathematical Modelling Theory of Equations Transportation and Game Theory Graph Theory | 6 6 4 4 |

**Name of Programme: (B.Sc. Mathematics / B.A. Mathematics)**

**Mathematics Programme:**

According to German Mathematician Carl Friedrich Gauss “Mathematics is the queen of the science”. Mathematics is a fundamental part of human thought, logic and integral to attempts at understanding the world and ourselves. Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. It provides foundational knowledge and skills for other subjects such as sciences, art, economy, etc.Thus there arises the need for its detailed study by adopting a systematic programme.

**Programme Objectives:**

- Develop the ability to think critically, logically and analytically and hence use mathematical reasoning in everyday life.
- Create deep interest in learning mathematics.
- Communicate mathematics effectively by written, computational and graphic means.
- Develop broad and balanced knowledge and understanding of definitions, concepts, principles and theorems.
- The program covers the full range of mathematics from Classical Calculus to modern Number Theory thus, providing learners sufficient knowledge and skills enabling them to undertake further studies in mathematics and its allied areas on multiple disciplines concerned with mathematics.
- Pursuing a degree in mathematics introduces the students to a number of interesting and useful ideas in preparations for a number of mathematics careers in education, research, government sector, business sector and industry.

**Programme Outcomes and Graduate Attributes:**

**Disciplinary** **knowledge**: Capability of demonstrating comprehensive knowledge of mathematics and understanding of one or more disciplines which form a part of an undergraduate programme of study.

**Communications** **skills**:

- Ability to communicate various concepts of mathematics effectively using examples and their geometrical visualizations.
- Ability to use mathematics as a precise language of communication in other branches of human knowledge.
- Ability to communicate long standing unsolved problems in mathematics.
- Ability to show the importance of mathematics as precursor to various scientific developments since the beginning of the civilization.
- Ability to explain the development of mathematics in the civilizational context and its role as queen of all sciences.

**Critical** **thinking** **and** **analytical** **reasoning**:

- Ability to employ critical thinking in understanding the concepts in every area of mathematics.
- Ability to analyze the results and apply them in various problems appearing in different branches of mathematics.

**Problem** **solving**:

- Capability to solve problems in computer graphics using concepts of linear algebra.
- Capability to solve various models such as growth and decay models, radioactive decay model, drug assimilation, LCR circuits and population models using techniques of differential equations.
- Ability to solve linear system of equations, linear programming problems and network flow problems.
- Ability to provide new solutions using the domain knowledge of mathematics acquired during this programme.

**Research-related** **skills:**

- Capability for inquiring about appropriate questions relating to the concepts in various fields of mathematics.
- To know about the advances in various branches of mathematics.

**Information/digital** **literacy:**

- Capability to use appropriate softwares to solve system of equations and differential equations.

**Self-directed** **learning:**

Ability to work independently and do in-depth study of various notions of mathematics.

**Moral** **and** **ethical** **awareness/reasoning:**

Ability to identify unethical behavior such as fabrication, falsification or misrepresentation of data and adopting objective, unbiased and truthful actions in all aspects.

**Lifelong** **learning:**

Ability to think, acquire knowledge and skills through logical reasoning and to inculcate the habit of self-learning.

**Programme Specific Outcomes:**

**DSE (Discipline Specific Elective):**

Choices from DSE provide the students with liberty of exploring his interest within the Mathematics. They enhance the ability of learners to apply the knowledge and skills acquired by themthemk during the programme to solve specific theoretical and applied problems in mathematics.

**SEC (Skill Enhancement Courses):**

These courses enable the student to acquire the skill relevant to Mathematics. They familiarize the students with suitable tools of mathematical analysis to handle issue and problems in mathematics and related sciences.

Let us have a look on different courses of this programme: –

**MATH101TH: Differential Calculus: –**

This course will enable the students to assimilate the notions of limits, continuity, differentiability of functions at a point. Sketch curves in Cartesian and Polar co-ordinate systems, expansion of functions using Maclurin’s and Taylor’s theorems, curvature, asymptotes and curve tracing.

**MATH102TH: Differential Equations: –**

It will enable learners to learn various techniques of getting exact solutions of solvable first order differential equations and linear differential equations of higher order. They will be introduced to partial differential equations and their solutions.

**MATH201TH: Real Analysis: –**

Learners will get concept of real line, completeness property, real sequences, infinite series, uniform convergence and power series.

**MATH202TH: Algebra: –**

Students will learn about algebraic structures, groups, subgroups, their types; They will be also introduced to rings, subrings, integral domains and fields.

**MATH309TH: Integral Calculus: –**

This SEC will lead expertise in integration, rectification and quadrature. Students will learn to handle double and triple integrals.

**MATH310TH: Vector Calculus: –**

It will teach students to find gradient divergence, curl, vector integration and provides a peep into the beautiful world of Gauss, Green and Stokes theorem.

**MATH301TH: Matrices: –**

It will enable students to read different types of matrices, corelate matrices and linear transformation, compute eigen values, eigen vectors, concept of vector spaces, subspaces,solution of linear equation using matrices.

**MATH304TH: Numerical Methods: –**

This course will help in administering numerical methods for solutions of non-linear equations, iterative methods for solution of linear equations. Students will know about interpolation, differential operators, numerical differentiation and numerical integration methods.

**MATH313TH: Probability and Statistics: –**

This course will change one’s sight of viewing different experiments by defining sample space, probability, providing in depth knowledge of different probability distributions and joint probability distribution functions.

**MATH317TH: Transportation and Game Theory: –**

No mathematics programme is complete without operations research. Operations research is that branch of mathematics which helps in optical decision making in various business situations. So, this SEC deals with solution of transportation problems, assignment problems and game theory.