Revised Syllabus For B.Sc, Part III [Mathematics] …

1 Revised Syllabus For , Part III [ mathematics ] ( &VI) To be implemented from June 2012. 1. TITLE: Subject mathematics 2. YEAR OF IMPLEMENTATION: Revised Syllabus will be implemented from June 2012 onwards. 3. DURATION: Part- III The duration of course shall be one year and two n semesters. 4. PATTERN: Pattern of examination will be semester. 5. MEDIUM OF INSTRUCTION: English 6. STRUCTURE OF COURSE: THIRD YEAR B.

2 Sc. ( mathematics ) (Semester V & VI) Semester V Paper Name of Paper Marks Compulsory Theory Papers 1. IX Real Analysis 40 ( Theory) 10 (Internal) 2. X Modern Algebra 40 ( Theory) 10 (Internal) 3. XI Partial Differential Equations 40 ( Theory) 10 (Internal) Optional Theory Papers (Select Any one) 4. XII(A) Symbolic Logic & Graph Theory 40 ( Theory) 10 (Internal) 5. XII(B) Special Theory of Relativity I 40 ( Theory) 10 (Internal) 6. XII(C) Differential Geometry I 40 ( Theory) 10 (Internal) 7.

3 XII(D) Mathematical Modeling - I 40 ( Theory) 10 (Internal) 8. XII(E) Applications of mathematics in Finance 40 ( Theory) 10 (Internal) 9. XII(F) Mechanics I 40 ( Theory) 10 (Internal) Semester VI Paper Name of Paper Marks Compulsory Theory Papers 1. XIII Metric Spaces 40 ( Theory) 10 (Internal) 2. XIV Linear Algebra 40 ( Theory) 10 (Internal) 3. XV Complex Analysis 40 ( Theory) 10 (Internal) Optional Theory Papers (Select Any one) 4. XVI(A) Algorithms & Boolean Algebra 40 ( Theory) 10 (Internal) 5.

4 XVI (B) Special Theory of Relativity II 40 ( Theory) 10 (Internal) 6. XVI (C) Differential Geometry II 40 ( Theory) 10 (Internal) 7. XVI (D) Mathematical Modeling - II 40 ( Theory) 10 (Internal) 8. XVI (E) Applications of mathematics in Insurance 40 ( Theory) 10 (Internal) 9. XVI (F) Mechanics II 40 ( Theory) 10 (Internal) Practical (Annual Pattern) COMPUTATIONAL mathematics LABORATRY IV (Operations Research Techniques) 50 Marks COMPUTATIONAL mathematics LABORATRY V ( laplace Transform) 50 Marks COMPUTATIONAL mathematics LABORATRY VI (Numerical Recipes in C++, Matlab & Microsoft Excel) 50 Marks COMPUTATIONAL mathematics LABORATRY VII (Project Work, Study Tour, Viva - Voce) 50 Marks EQIVALENCE IN ACCORDANCE WITH TITLES AND CONTENTS OF PAPERS (FOR Revised Syllabus ) Sr.

5 No. Title of Old Paper Title of New paper Compulsory Theory Papers Sem. V :- Real Analysis 1 mathematics Paper V (Analysis) Sem. VI :- Metric Spaces :- Modern Algebra 2 mathematics Paper VI (Algebra) :- Linear Algebra Sem. V :- Partial Differential Equations 3 mathematics Paper VII (Complex Analysis & Integral Transform ) Sem. VI :- Complex Analysis Optional Theory Papers Sem. V :- Symbolic Logic & Graph Theory 4 mathematics Paper VIII(A) (Discrete mathematics ) Sem. VI :- Algorithms & Boolean Algebra :- Special Theory of Relativity I 5 mathematics Paper VIII(B) (Special Theory Of Relativity) :-Special Theory of Relativity II Sem.

6 V :- Differential Geometry I 6 mathematics Paper VIII(C) (Differential Geometry) Sem. VI :- Differential Geometry II Sem. V :- Mathematical Modeling - I 7 mathematics Paper VIII(D) (Mathematical Modeling) :- Mathematical Modeling -II Sem. V :- Applications of mathematics in Finance 8 mathematics Paper VIII(E) (Application of mathematics in Finance and Insurance ) Sem. VI :- Applications of mathematics in Insurance Title of Old Paper Title of New paper Computational mathematics Laboratory (CML) 1 Computational mathematics Laboratory -- IV (Operations Research Techniques) Computational mathematics Laboratory -- IV (Operations Research Techniques) 2 Computational mathematics Laboratory -- V ( Complex Variables and Applications of Differential Equations) Computational mathematics Laboratory -- V ( laplace Transform)

7 3 Computational mathematics Laboratory -- VI ( Numerical Recipes in C++, Matlab & Microsoft Excel) Computational mathematics Laboratory -- VI (Numerical Recipes in C++, Matlab & Microsoft Excel) 4 Computational mathematics Laboratory -- VII (Project, Viva, Seminar, Tour Report) Computational mathematics Laboratory -- VII (Project, Viva, Tour Report) SHIVAJI UNIVERSITY, KOLHAPUR Part-III mathematics Detail Syllabus of semester III and IV SEMESTER V Paper IX (Real Analysis) UNIT - 1: SETS AND FUNCTIONS 7 lectures Sets and Elements , Operations on sets Functions Definition of Cartesian product, Function, Extension and restriction of functions, onto function.

8 THEOREM: If and if then THEOREM: If and if then THEOREM: If and if then THEOREM: If and if then Definition of composition of functions. Real Valued functions Definition : Real Valued function. Sum, difference, product, and quotient of real valued functions, Characteristics function. Equivalence, Countability Definition : one - to - one function, inverse function, 1-1 correspondence and equivalent sets, finite and infinite sets, countable and uncountable set.

9 Theorem : The countable union of countable sets is countable. Corollary : The set of rational number is countable. Theorem : If B is an infinite subset of the countable set A, then B is countable. Corollary: The set of all rational numbers in [0, 1] is countable. Real Numbers Theorem: The set is uncountable. Corollary: The of all real numbers is uncountable. Least Upper Bounds Definition: Upper bound, lower bound of a set, least upper bound. Least upper bound axiom, Theorem: If A is any non-empty subset of R that is bounded below, then A has greatest lower bound in R.

10 UNIT 2: SEQUENCES OF REAL NUMBERS 13 Lectures Definition of sequence and subsequence Limit of a sequence Definition. Theorem: If is a sequence of nonnegative numbers and if , then L 0. Convergent sequences Definition Theorem: If the sequence of real numbers is convergent to L, then cannot also converge to a limit distinct from is, if and , then L = M.