B.Sc Mathematics - ANR College of Arts & Science, Vadamavandal

Course Overview

The Department of Mathematics is one of the important departments of our college. It is a fully equipped Department. In addition to a rigorous curriculum, the department offers a vibrant environment of students. The department not only nurtures the talents and skills in the subjects offered in the curriculum but also focuses on the subjects that help them to choose a career. It is one of the organs to all other neighboring departments like Commerce, Corporate Secretaryship, Computer Science and its application. There are both Mathematics and Statistics as an allied papers of all the above disciplines. The cherished goal of the department to inculcate in the students a desire to excel, to prepare for competitive exams and register for online courses, to demonstrate originality and to develop a sense of responsibility towards the society.

Courses Offered

UG Course - B.Sc Mathematics

Vision & Mission

Our Vision

We share the vision of developing our intellectually vigorous community of students and faculty, together engaging in research, teaching, and learning that advance knowledge in diverse areas of mathematics and support current progress in science.
We envision our students as excellent engineers, not only in the field of science and technology, but also in good citizenship and discipline. We would like to foster positive attitudes, fascination and excitement of discovery through the teaching and learning of mathematical concepts.

Our Mission

To excel in providing high quality Mathematical skills to undergraduate students.
To attend the mathematical needs of the institute and the community.
To provide students (UG/PG) with a wide spectrum of valuable courses with rigorous training/tutorials that enables them to pursue their future.
To employ effective educational tools for our undergraduate and graduate courses, informed by the scholarship of teaching and learning of college-level mathematics.
To prepare our undergraduate students to develop the attitude and ability to apply mathematical methods and ideas in a wide variety of careers.

Programme Outcomes

PO1 : Disciplinary Knowledge: Capable of demonstrating comprehensive knowledge and understanding of one or more disciplines that form a part of an undergraduate programme of study.

PO2 : Critical Thinking: Capability to apply analytic thought to a body of knowledge; analyse and evaluate evidence, arguments, claims, beliefs on the basis of empirical evidence; identify relevant assumptions or implications; formulate coherent arguments; critically evaluate practices, policies and theories by following scientific approach to knowledge development.

PO3 : Problem Solving: Capacity to extrapolate from what one has learned and apply their competencies to solve different kinds of non-familiar problems, rather than replicate curriculum content knowledge; and apply one’s earning to real life situations.

PO4 : Analytical Reasoning: Ability to evaluate the reliability and relevance of evidence; identify logical flaws and holes in the arguments of others; analyze and synthesize data from a variety of sources; draw valid conclusions and support them with evidence and examples and addressing opposing viewpoints.

PO5 : Scientific Reasoning: Ability to analyse, interpret and draw conclusions from quantitative / qualitative data; and critically evaluate ideas, evidence, and experiences from an open minded and reasoned perspective.

PO6 : Self-directed & Lifelong Learning: Ability to work independently, identify and manage a project. Ability to acquire knowledge and skills, including “learning how to learn”, through self-placed and self-directed learning aimed at personal development, meeting economic, social and cultural objectives.

Programme Specific Outcomes

Acquire good knowledge and understanding, to solve specific theoretical & applied problems in different area of mathematics & statistics.
Understand, formulate, develop mathematical arguments, logically and use quantitative models to address issues arising in social sciences, business and other context /fields.
To prepare the students who will demonstrate respectful engagement with other’s ideas, behaviors, beliefs and apply diverse frames of references to decisions and actions. To create effective entrepreneurs by enhancing their critical thinking, problem solving, decision making and leadership skill that will facilitate startups and high potential organizations.

B.Sc MATHEMATICS COURSE DETAILS

COURSE CODE	SEMESTER	TITLE OF THE PAPER	COURSE OUTCOMES
CC-I	I	ALGEBRA& TRIGONOMETRY	Classify and solve reciprocal equations. Find the sum of binomial, exponential and logarithmic series. Find Eigen values, Eigen vectors, verify Cayley-Hamilton theorem and diagonalize a given matrix. Expand the powers and multiples of trigonometric functions in terms of sine and cosine. Determine the relationship between circular and hyperbolic functions and the summation of trigonometric series.
CC-II	I	DIFFERENTIAL CALCULUS	Find the nth derivative, form equations involving derivatives, and apply Leibnitz formula. Find the partial derivative and total derivative coefficient. Determine maxima and minima of functions of two variables and use Lagrange’s method of undetermined multipliers. Find the envelope of a given family of curves. Find the evolutes and involutes and determine the radius of curvature using polar coordinates.
ECC-I	I	NUMERICAL METHODS WITH APPLICATIONS -I	Will be able to solve Iteration method, Regular – False method, Newton – Raphson method. Will be able to calculate interpolation values by applying Gauss – Elimination method, Gauss – Jordan method. Will be able to calculate Differences of a polynomial and Factorial polynomials. Will be able to estimate central Differences formulae. Will be able to estimate the interpolation value for unequal intervals based on Lagrange’s formula of inverse interpolation.
FC-1	I	BRIDGE MATHEMATICS	Prove the binomial theorem and apply it to find the expansions of any (x + y)ⁿ and also solve the related problems. Find the various sequences and series and solve the problems related to them. Explain the principle of counting. Find the number of permutations and combinations in different cases. Apply the principle of counting to solve the problems on permutations and combinations. Explain the various trigonometric ratios and find them for different angles, including sum of the angles, multiple and submultiple angles, etc. Find the limit and derivative of a function at a point, the definite and indefinite integral of a function, and the points of minimum or maximum of a function.
SEC-I	I	MATHEMATICS FOR COMPETITIVE EXAMINATIONS -I	Solve mathematical problems using mathematical formulas. Understand the knowledge of application of mathematics. Understand the concepts of simplification. Calculate the square root and cube root. Solve problems on age.
CC -III	II	ANALYTICAL GEOMETRY	Understand and apply the concept of homogeneous equations of second degree to represent straight lines in different forms. Derive polar equations for straight lines, circles, and conic sections, and analyze their geometric properties. Formulate general equations of planes, calculate angles between two planes, and determine perpendicular distances. Calculate the angle between a line and a plane, determine the length of perpendiculars, and analyze coplanar and skew lines. Formulate equations of spheres, determine lengths of tangents, and analyze sections of spheres.
CC – IV	II	INTEGRAL CALCULUS	Determine the integrals of algebraic, trigonometric, and logarithmic functions and to find the reduction formulae. Evaluate double and triple integrals and problems using change of order of integration. Solve multiple integrals and to find the areas of curved surfaces and volumes of solids of revolution. Explain beta and gamma functions and to use them in solving problems of integration. Explain geometric and physical applications of integral calculus.
EC– II	II	NUMERICAL METHODS WITH APPLICATIONS -II	Will be able to evaluate derivatives by applying Newton’s forward and backward differences formulae. Will be able to evaluate integrations by applying the trapezoidal rule, Simpson’s rules, and Waddle’s rule. Will be able to find a complete solution to linear difference equations. Will be able to estimate approximate numerical solutions of ordinary differential equations by Euler, Picard, and Taylor. Will be able to estimate approximate numerical solutions of ordinary differential equations by Runge-Kutta methods.
SEC - II	II	MATHEMATICS FOR COMPETITIVE EXAMINATIONS-II	Make critique of quantitative information using proportional reasoning. Interpret and compare weighted averages, indices, ranking. Identify uses and misuse of percentage related to a proper understanding of the bases. Examine and estimate percentages as rates per 100. Solve for an unknown quantity in proportional situations.
SEC-III	II	GEOGEBRA	Proficiency Matrix and Trigonometry Mastery Understanding Limits and continuity Geogebra Scripting and Advanced Tasks Critical Thinking and Mathematical Problem-Solving Effective communication of Mathematical Ideas Independent Learning and Exploration
C-V	III	VECTOR CALCULUS	Find the derivative of vector and sum of vectors, product of scalar and vector point function and to determine derivatives of scalar and vector products Applications of the operator ‘del’ and to Explain solenoid and ir-rotational vectors Solve simple line integrals Solve surface integrals and volume integrals Verify the theorems of Gauss, Stokes and Green’s (Two Dimension)
CC- VI	III	DIFFERENTIAL EQUATIONS	Determine solutions of homogeneous equations, non-homogeneous equations of degree one in two variables, solve Bernoulli’s equations and exact differential equations Find the solutions of equations of first order but not of higher degree and to Determine particular integrals of algebraic, exponential, trigonometric functions and their products Find solutions of simultaneous linear differential equations, linear equations of second order and to find solutions using the method of variations of parameters Form a PDE by eliminating arbitrary constants and arbitrary functions, find complete, singular and general integrals, to solve Lagrange’s equations Explain standard forms and Solve Differential equations using Char pit’s method
EC-III	III	MATHEMATICAL STATISTICS - I	Acquire the knowledge of basic concepts in statistics Be able to understand various types of random variables and the distributions Calculate moments, cumulates, moment generating function and various constants of probability distributions Illustrate the theory of random variables, distribution functions and probability distributions with suitable examples Be able to evaluate solution of real-life problems under the concept of probability and probability distributions
SEC-IV	III	MAXIMA	Use maxima for symbolic math effectively Simplify complex mathematical expressions Solve advanced mathematical problems Develop problem-solving skills Communicate mathematical solutions effectively Build a foundation in computer algebra systems
CC-VII	IV	OPTIMIZATION TECHNIQUES	Describe the concepts involved in solving linear programming problems which are widely used in business operation Apply mathematical techniques used in optimizing transportation and assignment problems Solve job sequencing problems Breakdown different inventory models Evaluate PERT, CPM problems and develop applications
CC-VIII	IV	ELEMENTS OF MATHEMATICAL ANALYSIS	Explain in detail about sets and functions, equivalence and countability, and the LUB axiom Explain Sequence and Subsequence of real numbers and to find the limit of sequence to test for convergent, divergent, bounded and monotone sequences Explain the operations on convergent and divergent sequences and to explain the concepts of limit superior and limit inferior and the notion of Cauchy sequences Classify the series of real numbers and the alternating series and their convergence and divergence, the conditional convergence and absolute convergence and solve problems on convergence of the sequences Explain about the metric spaces and functions continuous on a Metric space
EC-IV	IV	MATHEMATICAL STATISTICS - II	Recognize the parameter and statistics to test the significance of sampling Finding the Goodness of Fit Derive the various measures of Chi-square, t-distributions Correlation coefficients between Observed and Estimated values Analyze the Regression lines
SEC-VI	IV	R LANGUAGE FOR STATISTICS	Explain practical implications of expectation and variance and how they predict the shapes of distribution and density (mass) functions of a random variable Demonstrate capability to write programming codes for plotting different distributions Evaluate the independence of attributes and design of experiments Describe and apply probability distribution function and different types of distributive functions through R Language Know and understand about Tests of Hypothesis through R
CC-IX	V	ABSTRACT ALGEBRA	Explain groups, subgroups and cyclic groups Explain about Normal subgroup, Quotient groups, Homeomorphisms and Automorphisms and verify the functions for homomorphism and automorphism properties Explain Permutation groups and apply Coyle’s theorem to problems Explain Rings, Ideals and Quotient Rings and examine their structure Discuss about the field of quotient of an integral domain and to Explain in detail about Euclidean Rings
CC-X	V	REAL ANALYSIS	Explain the concepts of Continuous and Discontinuous functions, open and close sets, Connectedness, Completeness and Compactness Explain the concepts of bounded and totally bounded sets, continuity of inverse functions and Uniform continuity Define the sets of measure zero, to explain about the existence and properties of Riemann integral Explain the concept of differentiability and to explain Roll’s theorem, Law of mean and Fundamental theorem of calculus Explain the pointwise and uniform convergence of sequence of functions and to derive Taylor’s theorem
CC-XI	V	MATHEMATICAL MODELLING	Explain simple situations requiring Mathematical Modeling and determine the characteristics of such models Model using differential equations in terms of linear growth and decay models Model using systems of ordinary differential equations of first order, to discuss about various models under the categories ‘Epidemics’ and ‘Medicine’ Explain in detail about difference equations Model using difference equations
CC-XII	V	PROJECT WITH VIVA VOCE
EC-V	V	TRANSFORM TECHNIQUES	Find the Laplace Transform and evaluation of integrals using Laplace Transform Find the Inverse Laplace Transforms Expansion of Periodic Functions of Period 2, Expansion of Odd and Even Functions Find the Fourier Transforms, Infinite Fourier Transforms and their properties Evaluate Fourier sine and cosine transform
CC-III	VI	LINEAR ALGEBRA	Acquire a detailed knowledge about vector spaces and subspaces Explain the concepts of Linear Dependence, Linear Independence, Bases and Dimension of basis Explain the concept of Linear Transformations, their Matrix representation and the notion of dual spaces Find the Eigen values and Eigen vectors, to apply the concepts for diagonalisation Explain about Inner product and norms and to apply Gram Schmidt Orthogonalization Process to problems on inner product spaces
CC-XIV	VI	COMPLEX ANALYSIS	Explain about analytic functions, their differentiation and continuity and to verify the Harmonic functions using analyticity conditions. Explain the concept of Conformal mappings and mappings by linear transformations and linear fractional transformations. Explain about the integrations of functions over simply and multiply connected domains and to derive the Cauchy integral formula, Liouvlle’s theorem, Fundamental theorem of Algebra and Maximum Module Principle. Find the convergence of sequences and series, to derive Taylor’s and Laurent’s series. Find the nature of singularities, to find the residue of a given function at a given singular point, to explain about zeros and poles and to evaluate real improper integrals (Excluding poles on the real axis).
CC-XV	VI	MECHANICS	Define Resultant, Component of a Force, Coplanar forces, like and unlike parallel forces, Equilibrium of a Particle, Limiting equilibrium of a particle on an inclined plane. Define Moment of a force and Couple with examples. Define Parallel Forces and Forces acting along a Triangle, Solve problems on frictional forces. Define work, energy, power, rectilinear motions under varying forces. Define Simple Harmonic Motion and find its Geometrical representation. Define Projectile, impulse, impact and laws of impact. Prove that the path of a projectile is a parabola. Find the direct and oblique impact of smooth elastic spheres. Define central orbits, explain conic as centered orbits and solve problems related to central orbits.
EC-VI	VI	PROGRAMMING CONCEPTS USING C++	Remember the program structure of C with its syntax and semantics. Understand the programming principles in C (data types, operators, branching and looping, arrays, functions, structures, pointers, and files). Apply the programming principles learnt in real-time problems. Analyze the various methods of solving a problem and choose the best method. Code, debug and test the programs with appropriate test cases.
EC-VIII	VI	DISCRETE MATHEMATICS	Analyse and perceive various graph theoretic concepts and familiarize with their applications. Describe about partially ordered sets, Boolean algebra, lattices and their types. Apply Karnaugh map for simplifying the Boolean expression. Demonstrate the skill to construct simple mathematical proofs and to validate. Achieve greater accuracy, clarity of thought and language.

SL. NO.	NAME	DESIGNATION	QUALIFICATION
1	Ms.M.Dharanisri	Assistant Professor & Head	M.Sc., B.Ed., M.Phil
2	Mrs.M.Bhuvaneswari	Assistant Professor	D.T.Ed.,M.Sc., B.Ed., M.Phil

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BACHELOR OF SCIENCE IN MATHEMATICS - ANR COLLEGE OF ARTS & SCIENCE, VADAMAVANDAL

Departments

BSC MATHEMATICS

Course Overview

Courses Offered

Vision & Mission

Our Vision

Our Mission

Programme Outcomes

Programme Specific Outcomes

B.Sc MATHEMATICS COURSE DETAILS

Vadamavandal, Thiruvannamalai District

admin@anrcas.edu.in

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