B Sc Mathematics Honours Syllabus Christ University-Books Pdf

B Sc Mathematics Honours Syllabus Christ University
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1 COURSE OBJECTIVE AND METHODOLOGY 1,1 1 COURSE OBJECTIVE 1. 1 2 METHODOLOGY 2,2 PAPER OBJECTIVES 3,2 1 B Sc MATHEMATICS Honours 3. 2 1 1 MAT 131 INTRODUCTORY ALGEBRA 3,2 1 2 MAT 231 CALCULUS 3. 2 1 3 MAT 331 DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS 3. 2 1 4 MAT 431 ANALYTICAL GEOMETRY AND VECTOR CALCULUS 3. 2 1 5 MAT 531 ALGEBRA 3, 2 1 6 MAT 532 INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING 4. 2 1 7 MAT 533 INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY 4. 2 1 8 MAT 534 PROGRAMMING IN C 4,2 1 9 MAT 535 GRAPH THEORY 4.
2 1 10 MAT 536 NUMBER THEORY 4,2 1 11 MAT 631 REAL AND COMPLEX ANALYSIS 5. 2 1 12 MAT 632 NUMERICAL METHODS 5, 2 1 13 MAT 633 ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL. MODELLING 5, 2 1 14 MAT 634 INTRODUCTION TO MATHEMATICAL PACKAGES 5. 2 1 15 MAT 635 OPERATIONS RESEARCH 6,2 1 16 MAT 636 MECHANICS 6. 2 2 CERTIFICATE COURSES 6,2 2 1 MAT 101 FOUNDATION OF MATHEMATICS 6.
2 2 2 MAT 201 QUANTITATIVE TECHNIQUES FOR MANAGERS 6. 2 2 3 MAT 301 INTRODUCTION TO MATHEMATICA 7, 2 2 4 MAT 401 QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS 7. 3 COURSE STRUCTURE 7,3 1 B Sc MATHEMATICS 7,3 2 CERTIFICATE COURSES 8. 4 SYLLABI FOR REGULAR PAPERS 9,4 1 MAT 131 INTRODUCTORY ALGEBRA 9. 4 2 MAT 231 CALCULUS 11, 4 3 MAT 331 DIFFERENTIAL EQUATIONS AND APPLICATIONS 13. 4 4 MAT 431 ANALYTICAL GEOMETRY AND VECTOR CALCULUS 15. 4 5 MAT 531 ALGEBRA 17, 4 6 MAT 532 INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING 19.
4 7 MAT 533 INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY 21. 4 8 MAT 534 PROGRAMMING IN C 23,4 9 MAT 535 GRAPH THEORY 25. 4 10 MAT 536 NUMBER THEORY 27,4 11 MAT 631 REAL AND COMPLEX ANALYSIS 29. 4 12 MAT 632 NUMERICAL METHODS 31, 4 13 MAT 633 ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL. MODELING 33, 4 14 MAT 634 INTRODUCTION TO MATHEMATICAL PACKAGES 35. 4 15 MAT 635 OPERATIONS RESEARCH 37,4 16 MAT 636 MECHANICS 39.
5 SYLLABI FOR CERTIFICATE COURSES 41,5 1 MAT 101 FOUNDATIONS OF MATHEMATICS 41. 5 2 MAT 201 QUANTITATIVE TECHNIQUES FOR MANAGERS 42. 5 3 MAT 301 INTRODUCTION TO MATHEMATICA 43, 5 4 MAT 401 QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS 44. COURSE OBJECTIVE AND METHODOLOGY,1 1 COURSE OBJECTIVE. An educational institution that does not lead to research and specialization will. remain on the way side of the higher education missing the golden opportunities. for pushing farther the frontiers of knowledge and opening up new vistas of. scientific endeavor to the young Keeping the above in mind it has been. proposed to continue with triple main system with mathematics as one of the. core subjects The B Sc course aims at to fulfill the following broad. objectives, 1 Developing a respectable intellectual level seeking to expose the various. concepts in mathematics, 2 To enhance the students reasoning analytical and problem solving skills.
3 To cultivate a mathematicians habit of thought and reasoning. 4 To enlighten the student that the mathematical ideas are relevant for. oneself no matter what his her interests are,5 To cultivate a research culture in young minds. 6 Development of students competence by evolving a learner centered. curriculum, 7 To encourage the students to uphold scientific integrity and objectivity in. professional endeavors, 8 To pursue higher studies in top notch institutions. The course curriculum is intensive and extensive and includes 16 core. papers covering all major topics in mathematics Students who opt for. Mathematics Honours programme will have to follow three major syllabi of. PCM or PME or CMS or CME combinations in the first four semesters There. will be one mathematics paper in each of the first four semesters and six papers. in each of the fifth and sixth semesters Each of the sixteen papers will carry. 100 marks In each paper the minimum marks for pass will be 40 Courses like. Foundations of Mathematics Introduction to Mathematica Quantitative. methods for managers and Quantitative aptitude for competitive. examinations are offered as certificate courses, After completing three years of honours degree course students can opt. for higher studies get into the institutions like ISRO NAL etc or IT oriented. service sections,1 2 METHODOLOGY, In order to realize the objectives a methodology based on the combination of.
the following will be adopted Case studies Debates Project work Team. teaching Reflective diary writing Seminars Field visits Information and. communications technology,PAPER OBJECTIVES,2 1 B Sc MATHEMATICS Honours. 2 1 1 MAT 131 INTRODUCTORY ALGEBRA, This paper emphasizes general techniques of problem solving and explores the. creation of mathematical patters It aims at introducing a course that initiates the. students into the world of Discrete Mathematics It includes the topic like. Mathematical Logic Set Theory Relations Functions Mathematical Induction. Recursive relations and Matrices,2 1 2 MAT 231 CALCULUS. This paper aims at enabling the students to know various concepts and. principles of differential and integral calculus Sound Knowledge of calculus is. essential for the students of mathematics for the better perceptions of the. subject and its development, 2 1 3 MAT 331 DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS. This paper enables the students to know the beauty of an important branch of. mathematics viz Differential Equations and its applications in Physics. 2 1 4 MAT 431 ANALYTICAL GEOMETRY AND VECTOR CALCULUS. Three Dimensional Geometry is one of the fundamental areas of Mathematics. The course is designed to lay a strong foundation of Geometry and Vector. 2 1 5 MAT 531 ALGEBRA, This paper aims at developing the ability to write the mathematical proofs It.
helps the students to understand and appreciate the beauty of the abstract nature. of mathematics and also to develop a solid foundation of theoretical. mathematics, 2 1 6 MAT 532 INTEGRAL TRANSFORMS AND LINEAR PROGRAMMING. This paper aims at providing a solid foundation upon the fundamental theories. and transformations of Fourier Transforms and Laplace Transforms It also. covers the introduction to linear programming techniques. 2 1 7 MAT 533 INTRODUCTION TO TOPOLOGY AND DIFFERENTIAL GEOMETRY. Differential geometry is the study of geometrical objects using Calculus This. paper aims at increasing the students understanding in differential geometry due. to its connection and significance to other areas of Mathematics It helps. students in understanding some of the fundamental concepts in differential. geometry through curves and surfaces in R3,2 1 8 MAT 534 PROGRAMMING IN C. The objective of this paper is to help students learn various aspects of C. programming and make them skilled in C programming Also helps to evaluate. critically the C programs written by others,2 1 9 MAT 535 GRAPH THEORY. This paper aims at imparting in the minds of the students the fundamental. concepts in graph theory Also helps in appreciating the application of the. subject in a variety of fields to learn to understand and to construct. mathematical proofs involving graphs,2 1 10 MAT 536 NUMBER THEORY. The objective of the paper is to help the students to learn long and interesting. history of Number Theory and its problems that have attracted many of the. greatest mathematicians Consequently the study of number theory is an. excellent introduction to the development and the achievement of Mathematics. With its discrete precise nature is an ideal topic which helps the students to. perform Numerical Experiments and Calculations also to explore its wide. spread applications in Cryptography,2 1 11 MAT 631 REAL AND COMPLEX ANALYSIS.
This paper enables the students to understand the basic techniques and theories. of real and complex analysis two traditionally separated subjects. 2 1 12 MAT 632 NUMERICAL METHODS, This paper will help the students to have an in depth knowledge of various. advanced numerical methods and some interpolation techniques. 2 1 13 MAT 633 ORDINARY DIFFERENTIAL EQUATIONS AND MATHEMATICAL. Mathematical modeling is a mathematical tool for solving real world problems. In this paper students study a problem solving process and learn how to. identify a problem construct or select appropriate models find solutions and. implement the model Emphasis lies on model construction in order to promote. student creativity and demonstrate the link between theoretical mathematics and. real world applications, 2 1 14 MAT 634 INTRODUCTION TO MATHEMATICAL PACKAGES. This paper gives a comprehensive introduction to the basic commands and. operations in MATLAB It aims at introducing the students to write the script. files and function files and effective use them in implementing the built in. features of 2 D ploting and 3 D ploting Also aims at introducing the. programming with applications,2 1 15 MAT 635 OPERATIONS RESEARCH. As Operations Research OR applications continue to grow and flourish in a. number of decision making fields a number of applications of linear. programming are covered in this paper This skill based paper aims at imparting. theoretical knowledge of optimization techniques which are widely used in the. industry to optimize available resources,2 1 16 MAT 636 MECHANICS. This paper helps the students to develop an ability to apply fundamental. knowledge of mathematics and science It aims at analyzing and interpretation. of mechanical laws and theorems It also helps the students to identify. formulate and solve problems involving mechanics and to appreciate the. application of mechanics in various fields,2 2 CERTIFICATE COURSES.
2 2 1 MAT 101 FOUNDATION OF MATHEMATICS, This course is designed as a foundation course in Mathematics for those who. have not been exposed to any Mathematics course earlier This enables the. students to improve their analytical reasoning and problem solving skills. Topics included are Set Theory Theory of Equations Matrices Determinants. Differential Calculus and Integral Calculus, 2 2 2 MAT 201 QUANTITATIVE TECHNIQUES FOR MANAGERS. This skill based paper aims at imparting theoretical knowledge of optimization. techniques These techniques are widely used in the industry to optimize. available resources This will help the student to apply the mathematical. techniques to real life situations,2 2 3 MAT 301 INTRODUCTION TO MATHEMATICA. This paper can be used by students in Mathematics as an introduction to the. fundamental ideas of MATHEMATICA PACKAGE and as a foundation for the. development of more advanced concepts in MATHEMATICA Study of this. paper promotes the development of Basic Programming skills in Mathematica. 2 2 4 MAT 401 QUANTITATIVE APTITUDE FOR COMPETITIVE EXAMINATIONS. The quantitative aptitude occupies a very important place in any business. school entrance examination This skill based paper aims at imparting the. aptitude knowledge required for competitive examination and provides a well. knitted path to success This knowledge acquisition will help the students to. over come the hurdles of competitive examinations like CAT MAT XAT. JMET GMAT SWAT etc,COURSE STRUCTURE,3 1 B Sc MATHEMATICS. Semester Paper Code Title of the Paper Marks Credit. I MAT 131 INTRODUCTORY ALGEBRA 6 100 4,II MAT 231 CALCULUS 6 100 4.
DIFFERENTIAL EQUATIONS AND ITS,III MAT 331 6 100 4. APPLICATIONS,ANALYTICAL GEOMETRY AND VECTOR,IV MAT 431 6 100 4. MAT 531 ALGEBRA 5 100 4,V INTEGRAL TRANSFORMS AND LINEAR. MAT 532 5 100 4,PROGRAMMING,INTRODUCTION TO TOPOLOGY AND. MAT 533 5 100 4,DIFFERENTIAL GEOMETRY,MAT 534 PROGRAMMIN IN C 5 100 4.
MAT 535 GRAPH THEORY 5 100 4,MAT 536 NUMBER THEORY 5 100 4. MAT 631 REAL AND COMPLEX ANALYSIS 5 100 4,MAT 632 NUMERICAL METHODS 5 100 4. ORDINARY DIFFERENTIAL EQUATIONS,MAT 633 5 100 4,AND MATHEMATICAL MODELLING. INTRODUCTION TO MATHEMATICAL,MAT 634 5 100 4,MAT 635 OPERATIONS RESEARCH 5 100 4. MAT 636 MECHANICS 5 100 4,3 2 CERTIFICATE COURSES,Semester Subject Code Paper Name Credit.
I MAT 101 FOUNDATIONS OF MATHEMATICS 4 2,QUANTITATIVE TECHNIQUES FOR. II MAT 201 4 2,III MAT 301 INTRODUCTION TO MATHEMATICA 4 2. QUANTITATIVE APTITUDE FOR,IV MAT 401 4 2,COMPETITIVE EXAMINATIONS. 4 SYLLABI FOR REGULAR PAPERS,4 1 MAT 131 INTRODUCTORY ALGEBRA. CHRIST UNIVERSITY,DEPARTMENT OF MATHEMATICS,B Sc Mathematics Honours I Semester.
MAT 131 INTRODUCTORY ALGEBRA,UNIT I MATHEMATICAL LOGIC 15 Hrs. Propositions and Truth values Connectives their truth values Tautology and contradiction Logical. equivalence Standard Theorems Problems on Negation Converse Inverse and Contrapostive of. Propositions open sentences Quantifiers Logical implications involving quantifiers Rules of inferences. UNIT II SETS RELATIONS AND FUNCTIONS 25 Hrs, Sets Axiom of extension sub sets and empty set Venn diagrams Unordered pairs and Singletons. Intersections Unions complements power sets Union and intersection of subsets Ordered pairs. Cartesian product of sets Relations Properties of special binary relations equivalence relations ordering. relations Hasse Diagram Functions Types of functions composition of functions invertible functions. inverse of compositions Standard theorems and related problems. UNIT III MATHEMATICAL INDUCTION AND RECURCIVE RELATION 15 Hrs. Mathematical induction induction principle related examples Recursive Definitions Fibonacci Sequence. Lucas sequence Eulerian numbers Ackermann s numbers Other recursive definitions Union and. intersection of n sets conjunction and disjunction of n proposition well formed formulae. UNIT IV MATRIX THEORY 20 Hrs, Recapitulation of fundamentals of matrix algebra Symmetric and skew symmetric Hermitian and skew. Hermitian matrices Idempotent Nilpotent Orthogonal Unitary matrices and their properties Rank of a. matrix Normal form Finding the inverse of a matrix by elementary transformation System of linear. equations and consistency Characteristic equations Eigen values Eigen vectors and properties Cayley. Hamilton theorem and its use in finding inverse and powers of a matrix. Total Hours 75 15,TEXT BOOKS, 1 K T Lueng Doris L C Chen Elementary Set Theory Part I Reprint 2009 Hong Kong University Press. Chapter 2 A B C D E F G H I J Chapter 3 A B, 2 D S Chandrasekharaiah Discrete Mathematical Structures 2nd Edition 2005 PRISM Book Pvt Ltd Sections.
2 1 2 1 1 2 1 2 2 2 2 2 1 2 2 3 2 2 4 2 3 2 4 2 4 1 3 1 3 2 4 1 4 2 4 2 1 4 4 4 5 4 6 5 1 5 2 5 3 5 4. 3 B S Vatssa Theory of Matrices reprint 2005 New Delhi New Age International Publishers. Sections 1 5 3 5 2 6 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 6 1 6 2 6 3 6 4 8 1 8 2 8 3 8 4 8 5 8 6. 4 Kenneth H Rosen Discrete Mathematics and its Applications 5th Edition 1999 WCB McGraw Hill 10 1. 10 2 10 3 10 4,Books for Reference, 1 Tremblay Manohar Discrete Mathematical Structures with Application to Computer Science 5th Edition 2000. Tata McGraw Hill Book Company, 2 Shanti Narayan Text book of Matrices 5th edition 1968 New Delhi S Chand and Co. Suggested Web links, 1 http www cs columbia edu zeph 3203s04 lectures html. 2 http home scarlet be math matr htm,3 http www cut the knot org induction shtml. 4 http www themathpage com,5 http www abstractmath org.
6 http mathworld wolfram com DiscreteMathematics html. FORMAT OF QUESTION PAPER,MAT 131 INTRODUCTORY ALGEBRA. Unit and No of subdivisions to be set in Marks for each Max marks for. Part subdivisions to,the unit subdivision the part. be answered,Unit III 2,Unit III 2,Unit I and II 5,Unit III and IV 5. D Unit I II III and IV 4 3 8 24,4 2 MAT 231 CALCULUS. CHRIST UNIVERSITY,DEPARTMENT OF MATHEMATICS,B Sc Mathematics Honours II Semester.
MAT 231 CALCULUS, UNIT I SUCCESSIVE AND PARTIAL DIFFERENTIATIONS 15 Hrs. Successive differentiation nth derivatives of functions Leibnitz theorem and its applications Partial. differentiation First and higher order derivatives Differentiation of homogeneous functions Euler s theorem. Total derivative and differential Differentiation of implicit functions and composite functions Jacobians. UNIT II DERIVATIVES OF ARCS 25 Hrs, Polar coordinates Angle between the radius vector and the tangent Angle of intersection of curves. polar form Polar subtangent and polar subnormal Perpendicular from pole on the tangent Pedal equations. Derivative of an arc in Cartesian parameter and polar forms Equation of a conic in polar form Convexity. concavity and curvature of plane curves Formula for radius of curvature in Cartesian parametric polar and pedal. forms Centre of curvature Evolutes and involutes Envelopes Asymptotes Singular points Cusp node and. conjugate points Tracing of standard Cartesian and polar curves. UNIT III LIMITS CONTINUITY AND MEAN VALUE THEOREMS 15 Hrs. Definition of the limit of a function form Continuity Types of discontinuities Properties of. continuous functions on a closed interval Differentiability Differentiability implies continuity Converse not. true Rolle s theorem Lagrange s and Cauchy s First Mean Value Theorems Taylor s theorem Lagrange s. form Maclaurin s theorem and expansions Evaluation of limits by L Hospital s rule. UNIT IV INTEGRAL CALCULUS 20 Hrs, Integral Calculus Recapitulation of methods of integration and Definite Integral Reduction. Formulae Application of Integral Calculus Length of arcs Surface areas and Volumes of solids of. revolutions for standard curves in Cartesian and Polar forms Improper Integrals beta and gamma functions. properties relation between beta and gamma functions.

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