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15th June 2015, 08:23 AM
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BSC Mathematics Syllabus Calicut University
I have got admission in University of Calicut for Bsc Mathematics course . Will you please provide the University of Calicut Bsc Mathematics course syllabus ?
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#2
15th June 2015, 11:47 AM
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Re: BSC Mathematics Syllabus Calicut University
The University of Calicut was originated in the year 1968 and it is located at Thenjipalam in Malappuram district of Kerala state in India. The University of Calicut offers Bsc Mathematics course . Course Structure : Foundations of Mathematics Informatics and Mathematical Softwares Calculus Calculus and Analytic Geometry Vector Calculus Abstract Algebra Basic Mathematical Analysis Numerical Methods Open Course offered by other department Project Real Analysis Complex Analysis Differential Equations Number Theory and Linear Algebra Elective Course: Graph Theory Linear Programming and Game Theory C Programming for Mathematical Computing Calicut University Bsc Mathematics Syllabus DETAILS OF MATHEMATICS (CORE COURSE) Sl. No. Code Semester Title of the Course Contact Hrs/Week No. of Credit Duration of Exam Weightage 1 MM1B01 1 Foundations of Mathematics 4 4 3 hrs 30 2 MM2B02 2 Informatics and Mathematical Softwares 4 4 3 hrs 30 3 MM3B03 3 Calculus 5 4 3 hrs 30 4 MM4B04 4 Calculus and Analytic Geometry 5 4 3 hrs 30 5 MM5B05 5 Vector Calculus 5 4 3 hrs 30 6 MM5B06 5 Abstract Algebra 5 4 3 hrs 30 7 MM5B07 5 Basic Mathematical Analysis 5 4 3 hrs 30 8 MM5B08 5 Numerical Methods 5 4 3 hrs 30 9 5 Open Course offered by other department 3 4 3 hrs 30 10 5 Project 2 -- -- -- 11 MM6B09 6 Real Analysis 5 4 3 hrs 30 12 MM6B10 6 Complex Analysis 5 4 3 hrs 30 13 MM6B11 6 Differential Equations 5 4 3 hrs 30 14 MM6B12 6 Number Theory and Linear Algebra 5 4 3 hrs 30 Sl. No. Code Semester Title of the Course Contact Hrs/Week No. of Credit Duration of Exam Weightage 15 ELECTIVE COURSE* MM6B13(E01) Graph Theory MM6B13(E02) Linear Programming and Game Theory** MM6B13(E03) C Programming for Mathematical Computing*** 3 2 3 hrs 30 16 MM6B14(PR) 6 Project 2 4 -- -- * In the 6th semester an elective course shall be chosen among the three courses (Code MM6B13(E01), MM6B13(E02), MM6B13(E03)). ** Students who have chosen Mathematical Economics as a Complementary Course in the first 4 semesters shall not choose Linear Programming and Game Theory MM6B13(E02) as the elective course. *** Students who have chosen Computer Science / Computer Applications as a Complementary Course during the first 4 semesters shall not choose C Programming for Mathematical Computing (MM6B13(E03)) as the elective course. Open Course for students of other departments during the Fifth Semester Code Title of the Course No. of contact hrs/week No. of Credit Duration of Exam Weightage MM5D01 Mathematics for Physical Sciences 3 4 3 hrs 30 MM5D02 Mathematics for Natural Sciences 3 4 3 hrs 30 MM5D03 Mathematics for Social Sciences 3 4 3 hrs 30 PATTERN OF QUESTION PAPER For each course the external examination is of 3 hours duration and has maximum weightage 30. The question paper has 4 parts. Part I is compulsory which contains 12 objective type / fill in the blanks multiple choice type questions set into 3 bunches of four questions. Each bunch has weightage 1. Part II is compulsory and contains 9 short answer type questions and each has weightage 1. Part III has 7 short essay type/paragraph questions of which 5 are to be answered and each has a weightage 2. Part IV contains three essay type questions of which 2 are to be answered and each has weightage 4. Part No. of Questions No. of questions to be answered Weightage I (Objective type) 3 bunches of 4 questions All 3x1 = 3 II (Short Answer) 9 All 9x1 = 9 III (Short Essay) 7 5 5x2 = 10 IV (Long Essay) 3 2 2x4 = 8 B.Sc. DEGREE PROGRAMME MATHEMATICS (CORE COURSE) FIRST SEMESTER MM1B01: FOUNDATIONS OF MATHEMATICS 4 hours/week 4 credits 30 weightage Aims The course aims to: to explain the fundamental ideas of sets and functions; to introduce basic logic; to introduce basic Graph Theory; Brief Description of the Course This course introduces the concepts of sets and functions from a rigorous viewpoint, mathematical logic, and methods of proof. Also brief introduction of Graph theory is included. These topics underlie most areas of modern mathematics, and to be applied frequently in the succeeding semesters. Learning Outcomes On completion of this unit successful students will be able to: prove statements about sets and functions; analyze statements using truth tables; construct simple proofs including proofs by contradiction and proofs by induction; to analyze the real life problems using graphs; Future needs All Mathematics course units, particularly those in pure mathematics and computer programming. Syllabus Text Books 1. K.H. Rosen: Discrete Mathematics and its Applications (sixth edition), Tata McGraw Hill Publishing Company, New Delhi. 2. S. Lipschutz: Set Theory and related topics (Second Edition), Schaum Outline Series, Tata McGraw-Hill Publishing Company, New Delhi. 3. Arumugham & Ramachandran. Invitation to Graph theory. Scitech Publications, Chennai – 600 017. Module 1 (12 hours) Set theory Pre-requisites: Sets, subsets, Set operations and the laws of set theory and Venn diagrams. Examples of finite and infinite sets. Finite sets and the counting principle. Empty set, properties of empty set. Standard set operations. Classes of sets. Power set of a set (Quick review). Syllabus: Difference and Symmetric difference of two sets. Set identities, Generalized union and intersections (As in section 2.2 of Text book 1). Relations: Product set, Relations (Directed graph of relations on set is omitted). Composition of relations, Types of relations, Partitions, Equivalence relations with example of congruence modulo relation, Partial ordering relations, n-ary relations. (As in Chapter 3 of text book 2 excluding 3.7). Module 2 (20 hrs) Functions Pre-requisites: Basic ideas such as domain, co-domain and range of functions. Equality of functions, Injection, Surjection and Bijection (Quick review). Syllabus: Identity function, constant functions, product (composition) of functions, theorems on one-one and onto functions, Mathematical functions, Recursively defined functions (As in Chapter 4 of text book 2). Indexed collection of sets, Operations on indexed collection of sets (As in 5.1, 5.2 and 5.3 of text book 2). Special kinds of functions, Associated functions, Algorithms and functions, Complexity of Algorithms (As in Chapter 5.7 of text book 2). Equipotent sets, Denumerable and countable sets, Cardinal numbers (Definitions and examples only as in 6.1, 6.2, 6.3 and 6.5 of text book 2). Module 3 (26 hrs) Basic Logic Pre-requisite: Nil. Syllabus: Introduction, propositions, truth table, negation, conjunction and disjunction. Implications, biconditional propositions, converse, contra positive and inverse propositions and precedence of logical operators. Propositional equivalence: Logical equivalences. Predicates and quantifiers: Introduction, Quantifiers, Binding variables and Negations. Methods of proof: Rules of inference, valid arguments, methods of proving theorems; direct proof, proof by contradiction, proof by cases, proofs by equivalence, existence proofs, uniqueness proofs and counter examples. (As in Chapter 1 of Text book 1). Module 4 (14 hours) Elements of graph theory Pre-requisites: Nil Syllabus: Introduction, The Konigsberg Bridge Problem, Four Colour Problem. Graphs & Subgraphs: Introduction, Definition and Examples, degrees, Sub Graphs, Isomorphism (upto and including definition of automorphism), Matrices, Operations on Graphs (Chapter 2, Sections 2.0 to 2.4, 2.8 and 2.9 of text book 3). Degree Sequences: Introduction, Degree sequences, Graphic sequences, Chapter 3, Sections 3.0 to 3.2 of text book 3). Definitions and examples of Walks, Trials, Paths and Connectedness (Chapter 4 upto Theorem 4.4 of text book 3). Definition and properties of Directed graphs (Chapter 10 upto and including theorem 10.1 of Text book 3). References R.P. Grimaldi: Discrete and Combinatorial Mathematics, Pearson Education. P.R. Halmos: Naive Set Theory, Springer. E. Kamke, Theory of Sets, Dover Publishers. John Clark & D.A. Holton: A First look at Graph Theory, Allied Publishers Ltd. Seminar Topics Statement of fundamental theorem of Algebra: A polynomial equation of degree n>1 has n and only n roots, relation between roots and coefficients, symmetric functions of the roots. For detailed syllabus , here is the attachment; |