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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;
Attached Files
File Type: pdf Calicut University Bsc Mathematics Syllabus.pdf (361.0 KB, 1806 views)


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